'Great Calculations' Bibliography

A Re-organization of the Bibliography and Notes
(2 sections of a book by Colin Pask)
into 50 groups of references for 50 calculations

(with 'external' web links to info on the books, articles, and their authors)

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This 'Great Calculations' Bibliography page

! Preliminary ! Under construction !
More author and book (or article)
web links may be added.

Go to the Table of Contents section below
(i.e. Skip the Introduction)

INTRODUCTION :

I have an interest in developing software that uses various mathematical techniques. (I write Tcl-Tk scripts involving GUI interfaces and 'canvases' on which images may be drawn.)

Therefore, I am interested in finding information that has been assembled, over the ages, on mathematical topics.

Around 2016, I saw the book Great Calculations by Colin Pask, in my local Barnes & Noble store. In paging through it, I saw that here was a book that was not afraid to throw in some mathematical expressions and equations --- just the kind of things I am looking for.

Furthermore, this book did not treat just 'pure' mathematics. It was aimed at showing 'applications' of mathematics --- in the physical, geological, chemical, biological, and social sciences --- from the 'macro' (astronomy) to the 'micro' (quantum mechanics).

Pask chose 50 'great calculations' to feature --- and in some sections of the book, he mentioned some further calculations that he considered, but did not include because of space and time considerations.

I bought the book and started reading it. I found that in Chapter 4, titled 'Our World', there was a section on tide prediction that I was interested in. But when I started looking at the bibliography (in the back of the book) to find the books and articles referenced in the text, the tide references were scattered throughout references to about 4 other 'great calculations' discussed in Chapter 4.

If I was going to start a Tcl-Tk programming project on tide prediction calculations, I was going to have to extract the tide references (about 8) from about 40 references for Chapter 4 --- and do the same thing for at least 49 other 'great calculations'.

I decided I may as well re-organize Pask's references into about 50 groups, corresponding to the 50 (or more) 'great calculations' mentioned in the book.

There are 13 Chapters in Pask's 'Great Calculations' book --- and discussions of the 50 'great calculations' are distributed in those 13 chapters --- about 4 (or more) calculations per chapter.

The chapter titles are

  1. Introduction
  2. Ancient Mathematics
  3. Steps into Modern Mathematics
  4. Our World     [Earth]
  5. The Solar System: The First Mathematical Models
  6. The Solar System: Into the Modern Era
  7. The Universe     [stars and galaxies]
  8. About Us     [living things]
  9. Light
  10. Building Blocks
    [atoms and their components]
  11. Nuclear and Particle Physics
  12. Methods and Motion
    [esp. vibrations and oscillations]
  13. Evaluation

    The 50 calculations in these 13 chapters are listed in the Table of Contents section below --- with a brief description of each calculation --- and a question that relates to the calculation.

Instead of one big bibliography in the back of the book (or a bibliography at the end of each chapter --- or at the end of each chapter section), there were 13 bibliography sections at the end of the book --- corresponding to the 13 chapters of the book.

Furthermore, there are many 'notes' (usually quotes) in the book, and the references for those 'notes' are in a 'Notes' section, just before the 'Bibliography' section at the end of the book. Like the 'Bibliography' section, the 'Notes' section is divided into 13 notes references sections, corresponding to the 13 chapters.

---

For any 'great calculation' in which I am interested, I would have to extract and collect the pertinent 'Bibliography' references from among references to about 4 (or more) other calculations in a Chapter section of the 'Bibliography'.

And, for the 'Notes' (quotes) references for that calculation, I would have to extract and collect the pertinent 'Notes' references from references to about 4 (or more) other calculations in a Chapter section of the 'Notes'.

To me, it seems that it would have been a lot better if Pask had simply had a single 'Bibliography' section at the back of the book --- with 50 sections corresponding to the 50 calculations.

    Or, perhaps better yet, he could have had 50 sections of the book with a bibliography at the end of each section. Each of the 50 sections could then 'stand on their own'.

I decided I would re-organize his bibliography for him --- or, actually, for me --- and for anyone else who is interested.


ORGANIZATION OF THIS WEB PAGE :

A 'Table of Contents' section below lists the 50 'great calculations' --- plus some that 'missed the cut'.

Each of the entries in the Table is a link to a bibliography section further down this page.

Each of the 50 calculation sections down this page contain the references from the 'Bibliography' section --- and perhaps the 'Notes' section --- at the end of Pask's book.

Within each of the bibliography sections, the references are presented with the

  • author name(s)
  • book (or article) title --- or web page URL
  • year-of-publication
  • the publisher (city name and company name)

Some of Pask's references include page numbers. In order to help me/you find where the references are used/discussed in Pask's book, I include the 'Pask-page-numbers' with each reference --- indicated by 'PGCp.' --- which stands for Pask-Great-Calculations-page(s).

    I use 'GC' in the indicator because Pask has other books --- such as 'Magnificent Principia'. In fact, he refers to 'Magnificent Principia' in chapters 14, 15, 16 ,19, 20, and 48 of 'Great Calculations'.

Each author name and book/article title will usually be links to more information on the author(s) and book/article. Often, the author-name link will be to Wikipedia, and a book-title link will be to amazon.com (for reader reviews, in particular).

Alternatively, the author link may be to the author's web site, and an article-title link may be to a web page giving some information on the article (preferably a fast-loading page without a lot of popups and advertisements).


SEARCHING THIS PAGE :

If you are looking for some particular information, and the 'Table of Contents' below is not so helpful, you can use the text search function of your web browser.

For example, if you are looking for information on a specific topic such as 'tides' or 'orbits' or 'quantum mechanics' or 'atoms', enter a keyword such as 'tide', 'orbit', 'quantum', or 'atom' in the text search entry field of your web browser.


THE WONDERMENT OF IT ALL :

Pure and applied mathematics offer many occasions for wonderment at the logical and geometric beauties of that subject matter --- and wonderment at some of the nobler accomplishments that are possible from the minds of humans.

The development of mathematical and scientific knowledge over the centuries --- in the social sciences as well as the 'natural' sciences --- is an amazing human achievement.

Many of these books and articles are essentially 'galleries of thoughts' that pay tribute to the genius and persistence and dogged determination of curious men and women through the ages. Enjoy!

Table of Contents:

(links to sections of this page, below)

(The documents or web-links in
each bibliography section
are in order by the last name
of the lead author.)

  • Chapter 1 - 'Introduction'
  • Calc-1
    On population growth.
    How did a parson (and a microbiologist) warn us about the problems of overpopulation?

  • Additional Chapter 1 ('Introduction') Topics
    On Experiments, On Equations, On Theory-and-Experiment complementing each other



  • Chapter 2 - 'Ancient Mathematics'
  • Calc-2
    Mesopotamian Pythagorean Triples.
    How mathematically advanced were the ancient Babylonians?

  • Calc-3
    Archimedes bounds pi.
    What could have been another 'eureka' moment for Archimedes?

  • Additional Chapter 2 ('Ancient Mathematics') Topics
    Number Tablets, Map Tablets, Chinese Mathematics, Rhind Papyrus



  • Chapter 3 - 'Steps into Modern Mathematics'   [beyond geometry]
  • Calc-4
    Fibonacci's presentation in 'Liber Abaci'.
    What did Fibonacci do other than showing how rabbit populations get out of control?

  • Calc-5
    Production of tables of logarithms.
    How do you double the lifespan (and productivity) of an astronomer?

  • Calc-6
    Euler solves the Basel problem.
    Can you add up an infinite number of things?

  • Calc-7
    The prime number theorem.
    How did Gauss find a formula for number of prime numbers less than N?

  • Additional Chapter 3 ('Steps into Modern Mathematics') Topics
    Pascal's Triangle, Gaussian Elimination, Classification of Groups, Benford's Law



  • Chapter 4 - 'Our World'   [Mother Earth]
  • Calc-8
    Eratosthenes measures the circumference of the earth.
    How big is the earth?

  • Calc-9
    Kelvin and the age of the earth.
    How old is the earth?

  • Calc-10
    Seismic rays reveal the earth's interior.
    What is inside the earth?

  • Calc-11
    Galileo describes projectile motion.
    How did Galileo mathematically shoot a cannon?

  • Calc-12
    Tide predictions.
    What kind of calculations were used to plan D-day landings?

  • Additional Chapter 4 ('Our World' - Earth) Topics
    Environmental Modeling (such as weather prediction)



  • Chapter 5 - 'The Solar System: The First Mathematical Models' (Ptolemy, Kepler)
  • Calc-13
    Ptolemy's 'Almagest'.
    What book dominated planetary orbit predictions for a thousand years?

  • Calc-14
    Kepler's astronomical calculations.
    What were Kepler's 3 laws of orbital motion?



  • Chapter 6 - 'The Solar System: Into the Modern Era' (Newton, Halley, etc.)
  • Calc-15
    Newton's Moon Test.
    How are a falling apple and the orbiting moon alike?

  • Calc-16
    Newton's determination of planetary masses.
    How can we compare weights of the planets?

  • Calc-17
    Predicting the return of Halley's comet.
    How did Halley predict the return of his comet?

  • Calc-18
    The discovery of Neptune.
    How do you find a new planet without using a telescope?

  • Calc-19
    Finding the 'astronomical unit' (earth-sun distance).
    How far away is the sun?

  • Calc-20
    Rotating orbits (conditions under which they occur).
    What did Newton and Einstein have to say about rotating orbits?

  • Additional Chapter 6 ('The Solar System: Into the Modern Era') Topics
    Moon Orbit, Ceres Orbit



  • Chapter 7 - 'The Universe'   [stars and galaxies]
  • Calc-21
    Why the night sky is dark.
    Since there are 'billions and billions' of stars, why isn't the night sky brighter?

  • Calc-22
    Age of the universe.
    How old is our universe?

  • Calc-23
    Hoyle describes making of carbon (from hydrogen, helium).
    How did nuclear physics lead to carbon-based life?

  • Calc-24
    Galaxy rotation and dark matter.
    How do we know there is 'dark matter' if we can't see it?

  • Calc-25
    Escaping gravity ('escape velocity').
    How did a parson's dark stars turn into black holes?

  • Additional Chapter 7 ('The Universe') Topics
    Cosmic Background Radiation



  • Chapter 8 - 'About Us'   [people and other mammals and living things]
  • Calc-26
    Harvey properly describes blood circulation.
    How did a little calculation of pumping by the heart overturn over 1,000 years of medical practice?

  • Calc-27
    Halley provides first annuity calculations.
    Who links a famous comet and the cost of an annuity?

  • Calc-28
    The Hardy-Weinberg law in genetics (attribute propagation).
    How did a pure mathematician who claimed to have never done any "useful" mathematics give his name to one of the first major results in genetics?

  • Calc-29
    Mathematics behind the CT scan.
    Why is the CT scan unfairly named?

  • Calc-30
    Scaling from mice to elephants.
    What links a mouse to an elephant?



  • Chapter 9 - 'Light'
  • Calc-31
    Determination of light's finite speed.
    How can Jupiter's moons tell us the speed of light?

  • Calc-32
    Explanation of cause of primary and secondary rainbows.
    How did Newton upset the poet John Keats?

  • Calc-33
    Diffraction and a limit to visual acuity.
    What limits the details you can see?

  • Calc-34
    Light is electromagnetism.
    How did Maxwell see the light?

  • Calc-35
    Photons (light particles) exist.
    What is light?

  • Calc-36
    Light bends.
    How was light bending predicted and tested?



  • Chapter 10 - 'Building Blocks'   [atoms and their components]
  • Calc-37
    Atoms really do exist.
    How were essentially all physicists finally convinced that atoms exist?

  • Calc-38
    Spectral line patterns.
    What Swiss schoolteacher found math patterns in light spectra?

  • Calc-39
    New (quantum) mechanics explains atoms,
    How did a French prince explain the Swiss schoolteacher's math patterns?

  • Calc-40
    Determining the mass of the neutron.
    How can you measure the mass of a neutron?



  • Chapter 11 - 'Nuclear and Particle Physics'
  • Calc-41
    Magnetic moment of the electron.
    What is the most accurate calculation of all?

  • Calc-42
    Why we must have a neutrino.
    How did a threat to the conservation of energy lead to discovery of the tiny neutrino particle?

  • Calc-43
    Time dilation.
    Can you stay younger by going faster?

  • Calc-44
    Quarks tell us particle masses.
    Why should you believe in quarks?

  • Calc-45
    Why the sun shines.
    What kind of reaction causes the sun to shine?

  • Calc-46
    Planning for a bomb.
    How do you plan to make the biggest bomb ever?



  • Chapter 12 - 'Methods and Motion'
  • Calc-47
    Vibrating strings.
    Who discovered a mathematical poem for violin strings?

  • Calc-48
    Tabulating Bessel functions.
    How were those amazing mathematical tables made?

  • Calc-49
    FPU (Fermi-Pasta-Ulam) and oscillation surprises.
    What happens when a computer simulates a string of non-linear oscillators?

  • Calc-50
    'Chaos' (instability, sensitivity, divergence).
    Where can we find instability and bi-furcation, tri-furcation, and so on?



  • Chapter 13 - 'Evaluation'   [a review of the previous chapters]
  • This chapter gives an 'evaluation' (overview) of the above calculations --- why they were included --- and selects a Top-Ten.

  • This chapter includes some additional references on topics such as

    • WM - Women Mathematicians
      (mostly ones mentioned in the above calcs)

    • LM - Lise Meitner
      (Nuclear Physicist. See Chapter 11, AB - Atomic Bomb)

    • TM - Table Making

    • CM - Computing Machines

    • H - Halley

    • K - Kelvin



End of Table of Contents.

Start of Bibliography Sections for each Calculation.


< Go to Top of this page. >

Calc-1 -
PG - Population Growth
( Leeuwenhoek ca. 1679 ; Malthus ca. 1798)
Chapter 1 - 'Introduction' - Additional Bibliography
  • On Experiments (and their value):

  • Crease, R. P.,
    'The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science',
    2004, New York: Random House, PGCp. 16

  • Johnson, G.,
    'The Ten Most Beautiful Experiments',
    2009, London: Vintage, PGCp. 16

  • Shamos, M. H.,
    'Great Experiments in Physics',
    1959, New York: Holt, Rinehart, and Winston, PGCp. 16

  • On Equations (great ones):

  • Crease, R. P.,
    'The Great Equations',
    2008, New York: Norton, PGCp. 16

  • On Theory and Experiment
    (how they complement each other):

  • Baggot, J. ,
    'Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth',
    2013, New York: Pegasus, PGCp. 16


END of Chapter 1
START of Chapter 2
'Ancient Mathematics'

< Go to Table of Contents, above. >

< Go to Top of this page. >

Calc-2 -
PT - Pythagorean Triples
  • Britton, J. P., C. Proust and S. Shnider,
    'Plimpton 322: A Review and a Different Perspective',
    2011, Archive for the History of the Exact Sciences, 519-66, PGCp. 28, 31, 32

  • Robson, Eleanor,
    "Mathematics Education in an Old Babylonian Scribal School",
    in 'The Oxford Handbook of the History of Mathematics',
    edited by Eleanor Robson and Jacqueline Stedall,
    2009, Oxford: Oxford U. Press, PGCp. 27

  • Robson, Eleanor,
    "Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322",
    2001, Historia Mathematica 28, 167-206, PGCp. 28

  • Robson, Eleanor,
    "Tables and Tabular Formatting in Sumer, Babylonia, and Assyria, 2500BCE-50CE"
    in 'The History of Mathematical Tables',
    edited by M. Campbell-Kelly, M. Croaken, R. Flood, and E. Robson,
    2003, Oxford: Oxford U. Press, PGCp. 28

  • Robson, Eleanor,
    "Words and Pictures: New Light on Plimpton 322",
    2002, American Mathematical Monthly 108, 105-20, PGCp. 28


Calc-3 -
AP - Archimedes approximates Pi
  • Berggren, L. J. Borwein, and P. Borwein,
    'Pi: A Source Book',
    1997, New York: Springer-Verlag, PGCp. 39

  • Dijksterhuis, E. J.,
    'Archimedes',
    1987, Princeton NJ: Princeton U. Press, PGCp. 38, 43, 56

  • Heath, Sir Thomas,
    'A History of Greek Mathematics', Vol. 2,
    1965, Oxford: The Clarendon Press, PGCp. 38

  • Stein, S.,
    'Archimedes: What Did He Do besides Cry Eureka?',
    1999, Mathematical Assoc. of America, Washington DC, PGCp. 38, 56


Chapter 2 - 'Ancient Mathematics' - Additional Bibliography
  • Numeric Tablets (NT):

  • Chabert, Jean-Luc, ed.,
    'A History of Algorithms',
    1999, Berlin: Springer-Verlag, PGCp. 33

  • George, Andrew,
    'The Epic of Gilgamesh',
    1999, London: Penguin Books, PGCp. 26

  • Gill, A.,
    'The Rise and Fall of Babylon',
    2011, London: Quercus, PGCp. ?

  • Neugebauer, O.,
    'The Exact Science in Antiquity',
    1959, New York: Dover, PGCp. 27, 28, 32, 33

  • Robinson, A.,
    'Writing and Script: A Very Short Introduction',
    2009, Oxford: Oxford U. Press, PGCp. 26

  • Map Tablets (MT):

  • British Museum,
    'Map of the World',
    at britishmuseum.org (accessed 2015 Jan 15), PGCp.26

  • Brotton, Jerry,
    'A History of the World in Twelve Maps',
    2013, London: Penguin, PGCp. 26

  • Chinese Mathematics (CM):

  • Joseph, G. G.,
    'The Crest of the Peacock: Non-European Roots of Mathematics',
    1992, London: Penguin, PGCp. 41

  • Martzloff, J.-C.,
    'A History of Chinese Mathematics',
    1997, Berlin: Springer-Verlag, PGCp. 41, 64, 65

  • Yan, Li, and Du Shiran,
    'Chinese Mathematics: A Concise History',
    translated by N. Crossley and A. W.-C. Lun,
    1987, Oxford: Clarendon Press, PGCp. 41, 64, 65

  • Rhind Papyrus (RP):

  • Calinger, R.,
    'A Contextual History of Mathematics',
    1999, Upper Saddle River, NJ: Prentice Hall, PGCp. 33

  • Gillings, R. J.,
    'Mathematics in the Time of the Pharaohs',
    1972, New York: Dover, PGCp. 33, 34

  • Robins, G., and C. Shute,
    'The Rhind Mathematical Papyrus',
    1987, London: British Museum Publications, PGCp. ?


END of Chapter 2
START of Chapter 3
'Steps into Modern Mathematics'

< Go to Table of Contents, above. >

< Go to Top of this page. >

Calc-4 -
LA - Liber Abaci (Fibonacci)
  • Devlin, K.,
    'The Man of Numbers: Fibonacci's Arithmetic Revolution',
    2011, London: Bloomsbury, PGCp. 44, 48

  • Gies, J., and F. Gies,
    'Leonardo of Pisa and the New Mathematics of the Middle Ages',
    1969, New York: Thomas Y. Crowell, PGCp. 44

  • Sigler, L. E.,
    'Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation',
    2002, New York: Springer-Verlag, PGCp. 45, 46


Calc-5 -
LT - Logarithm Tables (Napier, Briggs)
  • Bruce, I.,
    "The Agony and the Ecstasy -- The Development of Logarithms by Henry Briggs",
    2002, Mathematical Gazette 86, 216-27, PGCp. 52, 53

  • Bruce, I.,
    "Napier's Logarithms",
    2000, American Journal of Physics, 148-54, PGCp. 52

  • Calinger, R.,
    'A Contextual History of Mathematics',
    1999, Upper Saddle River NJ: Prentice Hall, PGCp. 51, 52, 53

  • Carslaw, H. S.,
    "The Discovery of Logarithms by Napier",
    1915, Mathematical Gazette 8, 76-84, 115-19, PGCp. 52

  • Goldstine, H. H.,
    'A History of Numerical Analysis',
    1977, New York: Springer-Verlag, PGCp. 52, 53

  • Horsburgh, E. M.,
    'Modern Instruments and Methods of Calculation: A Handbook of the Napier Tercentenary Exhibition',
    1915, London: G. Bell and Sons, PGCp. 54

  • Jagger, G.,
    "The Making of Logarithm Tables"
    in 'History of Mathematical Tables',
    edited by M. Campbell-Kelly, M. Croaken, R. Flood, and E. Robson,
    2003, Oxford: Oxford U. Press, PGCp. 52, 53

  • Williams, M. R.,
    'A History of Computing Technology',
    1985, Englewood Cliffs NJ: Prentice Hall, PGCp. 54
    (See Chapter 2.)


Calc-6 -
BP - Basel Problem (Euler)
  • Dunham, W.,
    'Euler: The Master of Us All',
    1999, Washington DC: Mathematical Assoc. of America, PGCp. 58

  • Euler, L.,
    'Introduction to Analysis of the Infinite',
    tranlated by J. D. Blanton,
    1988, New York: Springer-Verlag, PGCp. 58

  • Kline, M.,
    "Euler and Infinite Series",
    1983, Mathematics Magazine 56, 307-14, PGCp. 58


Calc-7 -
PN - Prime Number theorem (Gauss)
  • Conway, J. H., and R. K. Guy,
    'The Book of Numbers',
    1996, New York: Copernicus Springer-Verlag, PGCp. 61

  • Goldstein, L. J.,
    "A History of the Prime Number Theorem",
    1973, American Mathematical Monthly 80, 599-615, PGCp. 63

  • Lehmer, D. N.,
    "On the History of the Problem of Separating a Number into Its Prime Factors",
    1918, Scientific Monthly 7, 227-34, PGCp. 62

  • Tshinkel, Y.,
    "About the Cover: On the Distribution of Primes --- Gauss' Tables",
    2005, Bulletin of the American Math. Society 43, 89-91, PGCp. 63

  • Wells, D.,
    'Prime Numbers: The Most Mysterious Figures in Math',
    2005, Hoboken NJ: John Wiley, PGCp. 61, 63, 64


Chapter 3 - 'Steps into Modern Mathematics' -
Additional Bibliography
  • Pascal's Triangle (PT) :

  • Edwards, A.,
    'Pascal's Arithmetical Triangle',
    1987, London: Charles Griffin, PGCp. 64

  • Martzloff, J.-C.,
    'A History of Chinese Mathematics',
    1997, Berlin: Springer-Verlag, PGCp. 41, 64, 65

  • Yan, Li, and Du Shiran,
    'Chinese Mathematics: A Concise History',
    translated by N. Crossley and A. W.-C. Lun,
    1987, Oxford: Clarendon Press, PGCp. 41, 64, 65

  • Gaussian Elimination (GE) :

  • Martzloff, J.-C.,
    'A History of Chinese Mathematics',
    1997, Berlin: Springer-Verlag, PGCp. 41, 64, 65

  • Yan, Li, and Du Shiran,
    'Chinese Mathematics: A Concise History',
    translated by N. Crossley and A. W.-C. Lun,
    1987, Oxford: Clarendon Press, PGCp. 41, 64, 65

  • Classification of Groups (CG) :

  • Sautoy, Marcus du,
    'Symmetry: A Journey into the Patterns of Nature',
    2008, New York: Harper Collins, PGCp. 65

  • Benford's Law (BN) :

  • Berger, A., and T. P. Hill,
    "Benford's Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem",
    2011, Mathematical Intelligencer 33, 85-91, PGCp. 65

  • Hill, T. P.,
    "The First Digit Phenomenon",
    1998, American Scientist 86, 358-63, PGCp. 65

  • UnReferenced (?) :

  • Chabert, Jean-Luc, editor,
    'A History of Algorithms',
    1999, Berlin: Springer-Verlag, PGCp. ?

  • Stillwell, J.,
    'Mathematics and Its History',
    1989, New York: Springer-Verlag, PGCp. ?


END of Chapter 3
START of Chapter 4
'Our World' (Earth)

< Go to Table of Contents, above. >

< Go to Top of this page. >

Calc-8 -
ME - Measure Earth (Eratosthenes)
  • Dutka, J.,
    "Eratosthanes' Measurement of the Earth Reconsidered",
    1993, Archive for the History of Exact Sciences 46, 55-66, PGCp. 70

  • Nicastro, N.,
    'Circumference: Eratosthanes and the Ancient Quest to Measure the Globe',
    2008, New York: St. Martin's, PGCp. 68, 70


Calc-9 -
AE - Age of Earth (Kelvin, others)
  • Badash, L.,
    "The Age-of-the-Earth Debate",
    1989 August, Scientific American, 78-83, PGCp. 71

  • England, P. C., P. Molnar and F. M. Richter,
    "Kelvin, Perry and the Age of the Earth",
    2007, American Scientist 95, 342-349, PGCp. 76, 77

  • Perry, J.,
    "On the Age of the Earth",
    1895, Nature 51, 224-27, 341-42, 582-85, PGCp. 76

  • Ruddock, I.,
    "Lord Kelvin, Science and Religion",
    2004 February, Physics World, 56, PGCp. 74

  • Smith, C., and M. Norton Wise,
    'Energy and Empire: A Biographical Study of Lord Kelvin',
    1989, Cambridge UK: Cambridge U. Press, PGCp. 73, 76, 77

  • Thomson, Sir William (Lord Kelvin),
    "On the Age of the Earth",
    1895, Nature 51, 438-40, PGCp. 76

  • Thomson, Sir William (Lord Kelvin),
    "On the Secular Cooling of the Earth",
    1862, Transactions of the Royal Society of Edinburgh 23, 157-69, PGCp. 73

  • Weintraub, D. A.,
    'How Old is the Universe?',
    2011, Princeton NJ: Princeton U. Press, PGCp. 72


Calc-10 -
IE - Inside Earth
  • Auer, M., and M. Prior,
    "A New Era of Nuclear Test Verification",
    2014 September, Physics Today, 39-43, PGCp. 85

  • Bolt, B. A.,
    'Earthquakes', 5th edition,
    2004, New York: W. H. Freeman, PGCp. 78

  • Brush, S. G.,
    "Discovery of the Earth's Core",
    1980, American Journal of Physics 48, 705-24, PGCp. 79

  • Buffet, B.,
    "Earth's Enigmatic Inner Core",
    2013 November, Physics Today 66, 37-41, PGCp. 85

  • Bullen, K. E., and B. A. Bolt,
    'An Introduction fo the Theory of Siesmology', 4th edition,
    1985, Cambridge: Cambridge U. Press, PGCp. 78

  • Herak, Marijan,
    "Mohorovicic Discontinuity",
    Andrija Mohorovicic's Memorial Rooms, at gfz.hr, accessed 2014 Mar 12, PGCp. 83

  • Jarchow, C. M., and G. A. Thompson,
    "The Nature of the Mohorovicic Discontinuity",
    1989, Annual Review of Earth and Planetary Science 17, 475-506, PGCp. 83, 84

  • Kolbl-Ebert, M.,
    "Inge Lehmann's Paper: 'P' (1936)",
    2001, Classic Papers in the History of Geology 24, 262-67, PGCp. 82

  • Lehmann, Inge,
    "Seismology in the Days of Old",
    1987, Eos Transactions American Geophysical Union 68, 33-35, PGCp. 81, 82

  • Oldham, R. D.,
    "The Constitution of the Interior of the Earth as Revealed by Earthquakes",
    1906, Quarterly Journal of the Geological Society 62, 456-75, PGCp. 80

  • Oldham, R. D.,
    On the Propagation of Earthquake Motion to Great Distances",
    1900, Philosophical Transactions of the Royal Society of London, Series A, 194, 135-74, PGCp. 80

  • Oldroyd, D. R.,
    'Thinking about the Earth: A History of Ideas in Geology',
    1996, Cambridge MA: Harvard U. Press, PGCp. 78

  • Olson, P.,
    "The Geodynamo's Unique Longevity",
    2013 November, Physics Today 66, 30-35, PGCp. 85

  • Physics Update,
    "Iron's Structure at Earth's Core",
    2010 December, Physics Today, 26, PGCp. 85

  • Rousseau, C.,
    "How Inge Lehmann Discovered the Inner Core of the Earth",
    2013, College Mathematics Journal 44, 399-408, PGCp. 83

  • Umino, S., K. Nealson, and B. Wood,
    "Drilling to Earth's Mantle",
    2013 August, Physics Today 66, 36-41, PGCp. 84


Calc-11 -
GM - Galileo Motion (falling bodies)
  • Galillei, Galileo,
    'Two New Sciences',
    translated by Stillman Drake,
    1974, Madison: University of Wisconsin Press, PGCp. 86
    (Many versions of this book are available.)


Calc-12 -
Tides - Tide Predictions
Chapter 4 - 'Our World' (Earth) -
Additional Bibliography
  • Environmental Modeling (EM) :

  • Wainwright, J. and M. Mulligan,
    'Environmental Modelling: Finding Simplicity in Complexity',
    2013, Chichester UK: Wiley-Blackwell, PGCp. 97


END of Chapter 4
START of Chapter 5
'The Solar System: The First Mathematical Models'

< Go to Table of Contents, above. >

< Go to Top of this page. >

Calc-13 -
P - Ptolemy (Solar System Model)
  • Chabert, Jean-Luc, editor,
    'A History of Algorithms',
    1999, Berlin: Springer-Verlag, PGCp. 103, 104

  • Hanson, N. R.,
    "The Mathematical Power of Epicycle Astronomy",
    1960, Isis 51, 150-58, PGCp. 107

  • Linton, C. M.,
    'From Eudoxus to Einstein: A History of Mathematical Astronomy',
    2004, Cambridge UK: Cambridge U. Press, PGCp. 104, 107, 108

  • Pederson, O.,
    "Scientific Accounts of the Universe from Antiquity to Kepler",
    1994, European Review 2, 125-40, PGCp. 100

  • Ptolemy,
    'Almagest',
    translated and annotated by G. J. Toomer,
    1984, London: Duckworth, PGCp. 100

  • Thurston, H.,
    'Early Astronomy',
    1996, New York: Springer, PGCp. 100

  • Toomer, G. J.,
    "Ptolemy",
    in 'Dictionary of Scientific Biography',
    edited by C. C. Gillespie,
    1975, New York: Charles Scribner's Sons, PGCp. 100, 102

  • Van Brummelen, G.,
    'The Mathematics of the Heavens and the Earth: The Early History of Trigonometry',
    2009, Princeton NJ: Princeton U. Press, PGCp. 103, 104, 105


Calc-14 -
K - Kepler (Solar System Model)
  • Beer, A., and P. Beer, editors,
    'Kepler, Four Hundred Years',
    1975, Proceedings of Conferences Held in Honour of Johannes Kepler, Oxford: Pargamon, PGCp. 110

  • Gingerich, O.,
    "The Great Martian Catastrophe and How Kepler Fixed It",
    2011 September, Physics Today 64, 50-54, PGCp. 112

  • Gingerich, O.,
    "Johannes Kepler",
    in 'The General History of Astronomy, Vol. 2,
    Planetary Astronomy from the Renaissance to the Rise of Astrophysics Part A: Tycho Brahe to Newton',
    edited by R. Taton and C. Wilson,
    1989, Cambridge UK: Cambridge U. Press, PGCp. 112

  • Gingerich, O.,
    "Kepler",
    in 'Dictionary of Scientific Biography',
    edited by C. C. Gillespie,
    1975, New York: Charles Scribner's Sons, PGCp. 110

  • Koyre, A.,
    'The Astronomical Revolution',
    2009, London: Routledge, PGCp. 112

  • Linton, C. M.,
    'From Eudoxus to Einstein: A History of Mathematical Astronomy',
    2004, Cambridge UK: Cambridge U. Press, PGCp. 112

  • Pask, C.,
    'Magnificent Principia: Exploring Isaac Newton's Masterpiece',
    2013, Amherst NY: Prometheus Books, PGCp. 115 (See Chapter 12.)

  • Thurston, H.,
    'Early Astronomy',
    1996, New York: Springer, PGCp. 112


END of Chapter 5
START of Chapter 6
'The Solar System: Into the Modern Era'

< Go to Table of Contents, above. >

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Calc-15 -
MT - Moon Test (Newton)
  • Pask,C.,
    'Magnificent Principia: Exploring Isaac Newton's Masterpiece',
    2013, Amherst NY: Prometheus Books, PGCp. 115, 117


Calc-16 -
NM - Newton Masses (planets)
  • Cohen, I. B.,
    "Newton's Determination of the Masses and Densities of the Sun, Jupiter, Saturn, and the Earth",
    1998, Archive for the History of Exact Sciences 53, 83-95, PGCp. 123

  • Pask,C.,
    'Magnificent Principia: Exploring Isaac Newton's Masterpiece',
    2013, Amherst NY: Prometheus Books, PGCp. 123, 125


Calc-17 -
HC - Halley's Comet
  • Green, D. W. E.,
    'The Mystery of Comets',
    1986, Cambridge UK: Cambridge U. Press, PGCp. 124

  • Grier, D. A.,
    'When Computers Were Human',
    2005, Princeton NJ: Princeton U. Press, PGCp. 127, 128

  • Ronan, C. A.,
    "Edmond Halley"
    in 'Dictionary of Scientific Biography',
    edited by C. C. Gillespie,
    1975, New York: Charles Scribner's Sons, PGCp. 126

  • Ronan, C. A.,
    'Edmond Halley: Genius in Eclipse',
    1970, London: MacDonald, PGCp. 126

  • Waff, C. B.,
    "Predicting the Mid-Eighteenth-Century Return of Halley's Comet",
    in 'The General History of Astronomy, Vol. 2,
    Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part B: The Eighteenth and Nineteenth Centuries',
    edited by R. Taton and C. Wilson,
    1989, Cambridge UK: Cambridge U. Press, PGCp. 127


Calc-18 -
PN - Planet Neptune (Leverrier)
  • Grosser, M.,
    'The Discovery of Neptune',
    1979, New York: Dover, PGCp. 130, 133(2), 136

  • Hanson, N. R.,
    "Leverrier: The Zenith and Nadir of Newtonian Mechanics",
    1962, Isis 53, 359-78, PGCp. 130

  • Kent, D.,
    "The Curious Aftermath of Neptune's Discovery",
    2011 December, Physics Today 64, 46-51, PGCp. 136

  • Linton, C. M.,
    'From Eudoxus to Einstein: A History of Mathematical Astronomy',
    2004, Cambridge UK: Cambridge U. Press, PGCp. 130(2), 137

  • Morando, B.,
    "The Golden Age of Celestial Mechanics",
    in 'The General History of Astronomy, Vol. 2,
    Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part B: The Eighteenth and Nineteenth Centuries',
    edited by R. Taton and C. Wilson,
    1989, Cambridge UK: Cambridge U. Press, PGCp. 130

  • Smith, R. W.,
    "The Cambridge Network in Action: The Discovery of Neptune",
    1989, Isis 80, 395-422, PGCp. 130, 133

  • Sandage, T.,
    'The Neptune File',
    2000, London: Allen Lane Penguin, PGCp. ?


Calc-19 -
AU - Astronomical Unit (Halley, Venus transit)
  • Halley, E.,
    "A New Method of Determining the Parallax of the Sun",
    1716, Philosophical Transactions 29, 454-56, PGCp. 138, 140
    (Translation from the Latin is available at
    eclipse.gsfc.nasa.gov backed up at web.archive.org,
    accessed 2017 Mar 27.)

  • Lomb, N.,
    'Transit of Venus 1631 to the Present',
    2011, Sydney: NewSouth, PGCp. 141

  • Pask,C.,
    'Magnificent Principia: Exploring Isaac Newton's Masterpiece',
    2013, Amherst NY: Prometheus Books, PGCp. 146

  • Phillips, T.,
    'The 2012 Transit of Venus',
    at science.nasa.gov/science-news/,
    accessed 2017 Mar 27, PGCp. 140(2)

  • Van Helden, A.,
    "Measuring Solar Parallax: The Venus Transits of 1761 and 1769 and their Nineteenth Century Sequels",
    in 'The General History of Astronomy, Vol. 2,
    Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part B: The Eighteenth and Nineteenth Centuries',
    edited by R. Taton and C. Wilson,
    1989, Cambridge UK: Cambridge U. Press, PGCp. 136

  • Van Helden, A.,
    'Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley',
    1985, Chicago: University of Chicago Press, PGCp. 136, 137

  • Woolf, H.,
    'The Transits of Venus: A Study of Eighteenth Century Science',
    1959, Princeton NJ: Princeton U. Press, PGCp. 143(2)


Calc-20 -
RO - Rotating Orbits (Newton, others)
  • Einstein, A.,
    "The Foundations of the General Theory of Relativity",
    in 'The Principle of Relativity',
    1952, New York: Dover, PGCp. 146
    (A translation by W. Perrett and G. B. Jeffery of Einstein's original "Die Grundlage der allgemainen Relativitatstheorie",
    1916, Annalen der Physik 49, 769.)

  • Fernie, J. D.,
    "In Pursuit of Vulcan",
    1994, American Scientist 82, 412-15, PGCp. 145

  • Hanson, N. R.,
    "Leverrier: The Zenith and Nadir of Newtonian Mechanics",
    1962, Isis 53, 359-78, PGCp. 145

  • Morando, B.,
    "The Golden Age of Celestial Mechanics",
    in 'The General History of Astronomy, Vol. 2,
    Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part B: The Eighteenth and Nineteenth Centuries',
    edited by R. Taton and C. Wilson,
    1989, Cambridge UK: Cambridge U. Press, PGCp. 145

  • Newton, I.,
    Principia,
    PGCp. 143

  • Pais, A.,
    'Subtle is the Lord: The Science and Life of Albert Einstein',
    1982, Oxford UK: Oxford U. Press, PGCp. 147

  • Park, D.,
    'Classical Dynamics and Its Quantum Analogues',
    1979, Berlin: Springer-Verlag, PGCp.145

  • Pask,C.,
    'Magnificent Principia: Exploring Isaac Newton's Masterpiece',
    2013, Amherst NY: Prometheus Books, PGCp. 142, 143


Chapter 6 ('The Solar System: Into the Modern Era') -
Additional Bibliography
  • Moon Orbit (MO) :

  • Morando, B.,
    "The Golden Age of Celestial Mechanics",
    in 'The General History of Astronomy, Vol. 2,
    Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part B: The Eighteenth and Nineteenth Centuries',
    edited by R. Taton and C. Wilson, 1989, Cambridge UK: Cambridge U. Press, PGCp. 147
    (American astronomer George W. Hill, 1838-1913, made advances in predicting the moon's orbit.)

  • Ceres Orbit (CO) :

  • Marsden, B. G.,
    "Eighteenth and Nineteenth Century Developments in the Theory and Practice of Orbit Determination",
    in 'The General History of Astronomy, Vol. 2,
    Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part B, The Eighteenth and Nineteenth Centuries',
    edited by R. Taton and C. Wilson,
    1989, Cambridge UK: Cambridge U. Press, PGCp. 147
    (Gauss used limited data to find the orbit of the asteroid Ceres.)


END of Chapter 6
START of Chapter 7
'The Universe'

< Go to Table of Contents, above. >

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Calc-21 -
DS - Dark Sky
  • Harrison, E. R.,
    'Cosmology: The Science of the Universe', 2nd edition,
    2000, Cambridge UK: Cambridge U. Press, PGCp. 150

  • Harrison, E. R.,
    'Darkness at Night: A Riddle of the Universe',
    1987, Cambridge MA: Harvard U. Press, PGCp. 150

  • Harrison, E. R.,
    "The Dark Night-Sky Riddle: A Paradox that Resisted Solution",
    1984, Science 226, 941-45, PGCp. 150

  • Harrison, E. R.,
    "The Dark Sky Paradox",
    1977, American Journal of Physics 45, 119-24, PGCp. 150

  • Harrison, E. R.,
    "Kelvin on an Old Celebrated Hypothesis",
    1986, Nature 322, 417-18, PGCp. 150


Calc-22 -
EU - Expanding Universe (Hubble)
  • Coles, P.,
    'Cosmology: A Very Short Introduction',
    2001, Oxford: Oxford U. Press, PGCp. 155, 179

  • Earman, J.,
    "Lambda: The Constant that Refuses to Die",
    2001, Archive for History of the Exact Sciences 55, 189-220, PGCp. 160

  • Freedman, W. L., and B. F. Madore,
    "The Hubble Constant",
    2010, Annual Review of Astronomy and Astrophysics 48, 673-710, PGCp. 157

  • Harrison, E. R.,
    'Cosmology: The Science of the Universe', 2nd edition,
    2000, Cambridge UK: Cambridge U. Press, PGCp. 157

  • Hubble, E.,
    "A Relation between the Distance and Radial Velocity among Extra- Galactic Nebulae"
    1929, Proceedings of the National Academy of Sciences 15, 168-73, PGCp. 155

  • Lambourne, R. J. A.,
    'Relativity, Gravitation, and Cosmology',
    2010, Cambridge UK: Cambridge U. Press, PGCp. 158

  • Livio, M.,
    "Mystery of the Missing Text Solved",
    2011, Nature 479, 171-73, PGCp. 156

  • Roos, M.,
    'Introduction to Cosmology', 3rd edition,
    2003, Chichester UK: Wiley, PGCp. 158, 171

  • Way, M. and H. Nussbaumer,
    "Lematire's Hubble Relationship",
    2011 August, Physics Today, Letters, 8, PGCp. 156

  • Weinberg, S.,
    'The First Three Minutes', 2nd edition,
    1988, New York: Basic Books, PGCp. 155


Calc-23 -
HC - Hoyle Carbon
  • Burbidge, E. M., G. R. Burbidge, W. A. Fowler, and F. Hoyle,
    "Synthesis of the Elements in Stars",
    1957, Reviews of Modern Physics 29, 547-650, PGCp. 163

  • Davies, Paul,
    'The Goldilocks Enigma: Why is the Universe Just Right for Life?',
    2008, Boston: Houghton-Mifflin, PGCp. 166

  • Gardner, Martin,
    "WAP, SAP, PAP, and FAP",
    in 'The Night is Large: Collected Essays 1938-1995',
    1996, New York: St. Martin's, PGCp. 166

  • Harrison, E. R.,
    'Cosmology: The Science of the Universe', 2nd edition,
    2000, Cambridge UK: Cambridge U. Press, PGCp. 166

  • Hoyle, Fred,
    'Astronomy and Cosmology: A Modern Course',
    1975, San Francisco: W. H. Freeman, PGCp. 164

  • Hoyle, Fred,
    'Home is Where the Wind Blows: Chapters from a Cosmologist's Life',
    1994, Mill Valley CA: University Science Books, PGCp. 165

  • Hoyle, Fred,
    "On Nuclear Reactions Occurring in Very Hot Stars. The Synthesis of Elements from Carbon to Nickel", Supplement 1,
    1954, Astrophysics Journal 1, 121-46, PGCp. 163

  • Kragh, H.,
    "An Anthropic Myth: Fred Hoyle's Carbon-12 Resonance Level",
    2010, Archive for the History of Exact Sciences 64, 721-51, PGCp. 166


Calc-24 -
DM - Dark Matter (Vera Rubin)
  • Burbidge, E. M., and G. R. Burbidge,
    "The Masses of Galaxies",
    Chapter 3 in 'Galaxies and the Universe',
    edited by A. Sandage, M. Sandage, and J. Kristian,
    1975, Chicago: University of Chicago Press, p. 171

  • Caldwell, R., and M. Kamionkowski,
    "Dark Matter and Dark Energy",
    2009, Nature 458, 587-89, PGCp. 171

  • Einasto, J., A. Kaasik,and E. Saar,
    "Dynamic Evidence on the Massive Coronas of Galaxies",
    1974, Nature 250, 309-10, PGCp. 171

  • Irion, Robert,
    "The Bright Face behind the Dark Side of Galaxies",
    2002, Science 295, 960-61, PGCp. 167

  • Ostriker, J. P., P. J. E. Peebles, and A. Yahil,
    "The Size and Mass of Galaxies, and the Mass of the Universe",
    1974, The Astrophysical Journal 193, L1-L4, PGCp. 169

  • Rubin, Vera C., and W. Kent Ford,
    "Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions",
    1970, Astrophysical Journal 159, 379-92, PGCp. 168

  • Rubin, Vera C.,
    "Dark Matter in Spiral Galaxies",
    1983, Scientific American, 96-108, PGCp. 168

  • Rubin, Vera C.,
    "The Rotation of Spiral Galaxies",
    1983, Science 220, 1339-44, PGCp. 168

  • Rubin, Vera C.,
    "Seeing Dark Matter in the Andromeda Galaxy",
    2006 December, Physics Today, 8-9, PGCp. 168, 172

  • Oert, PGCp. 167, 171

  • Zwicky, PGCp. 167(2), 171


Calc-25 -
EG - Escaping Gravity (Newton)
  • Barger, V. D., and M. G. Olsson,
    'Classical Mechanics: A Modern Perspective', 2nd edition,
    1995, New York: McGraw Hill, PGCp. 175(2)

  • Hansen, J. R.,
    'Enchanted Rendezvous: John C. Houbolt and the Genesis of the Lunary-Orbit Rendezvous Concept',
    1995, Washington DC: NASA Monographs in Aerospace History Series 4, PGCp. 175

  • Konopliv, A. S., et. al.,
    "Improved Gravity Field of the Moon from Lunar Prospector",
    1998, Science 281, 1476-80, PGCp. 175

  • Lee, T. E.,
    'Bizarre Lunar Orbits',
    NASA Science, 2006, at science.nasa.gov/science-news/,
    accessed 2017 Mar 27, PGCp. ?

  • Roos, M.,
    'Introduction to Cosmology', 3rd edition,
    2003, Chichester UK: Wiley, PGCp. 178

  • Roy, A. E., 'Orbital Motion', 4th edition,
    2005, Bristol UK: Institue of Physics Publishing, PGCp. 175

  • Van Allen, J. A.,
    "Gravitational Assist in Celestial Mechanics -- A Tutorial",
    2003, American Journal of Physics 71, 448- 51, PGCp. 175

  • Dyson, PGCp. 178

  • Finkelstein, PGCp. 178

  • Houbolt, PGCp. 174

  • Oppenheimer, PGCp. 178

  • Schwarzchild, PGCp. 178

  • Snyder, PGCp. 178

  • Wheeler, PGCp. 179


Chapter 7 ('The Universe') -
Additional Bibliography
  • Cosmic Background Radiation (CBR) :

  • Weinberg, p. 179


END of Chapter 7
START of Chapter 8
'About Us'

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Calc-26 -
BF - Blood Flow (Harvey)
  • Gregory, Andrew,
    'Harvey's Heart: The Discovery of Blood Circulation',
    2001, Duxford UK: Icon Books, PGCp. 185

  • Harvey, W.,
    'An Anatomical Disquisition on the Motion of the Heart and Blood in Animals, A Translation of the 1628 Original',
    1990, Exercitatio Anatomica de Motu Cordis et Sanguinis in Animalibus,
    Chicago, Great Books of the Western World,
    Encyclopedia Britannica, PGCp. 183


Calc-27 -
HA - Halley Annuities
  • Ciecka, J. E.,
    "Edmond Halley's Life Table and Its Uses",
    2008, Journal of Legal Economics 15, 65-74, PGCp. 189, 190

  • Cohen, I. Bernard,
    'The Triumph of Numbers',
    2005, New York: W. W. Norton, PGCp. 191

  • Hald, A.,
    "The Early History of Life Insurance Mathematics",
    Chapter 9 in
    'A History of Probability and Statistics and Their Application before 1750',
    1990, New York: John Wiley, PGCp. 189, 190, 191

  • Halley, E.,
    "An Estimate of the Degrees of the Mortality of Mankind, Drawn from Curious Tables of the Births and Funerals at the City of Breslaw; with an Attempt to Ascertain the Price of Annuities upon Lives",
    1693, Philosophical Transactions 17, 596-610, PGCp. 187

  • Kopf, E. W.,
    "The Early History of the Annuity",
    a 42-page PDF file at casact.org,
    accessed 2017 Mar 27, PGCp. 189

  • Lewin, C., and M. De Valois,
    "History of Actuarial Tables",
    in 'The History of Mathematical Tables',
    edited by M. Campbell-Kelly, M. Croaken, R. Flood, and E. Robson,
    2003, Oxford UK: Oxford U. Press, PGCp. 186, 189, 191

  • Newman, J. R.,
    'The World of Mathematics',
    1961, London: George Allen and Unwin, PGCp. 187
    (Vol. 3 contains excerpts from the work of Graunt and Halley on annuities.)


Calc-28 -
GV - Genetic Variability (Hardy-Weinberg)
  • Hardy, G. H.,
    "A Mathematician's Apology',
    1992 (a reprint?), Cambridge UK: Cambridge Canto Edition, PGCp. 196

  • Hardy, G. H.,
    "Mendelian Proportions in a Mixed Population",
    1908, Science 28, 49-50, PGCp. 195

  • Okasha, S.,
    "Population Genetics",
    Stanford Encyclopedia of Philosophy, at plato.stanford.edu,
    accessed 2017 Mar 27, PGCp. 191


Calc-29 -
CT - Computerized Tomography
  • Cormack, A. M.,
    "Early Two-Dimensional Reconstruction and Recent Topics Stemming From It",
    1980, Science 209, 1482-86, PGCp. 201

  • Cormack, A. M.,
    "Representation of a Function by Its Line Integrals, with Some Radiological Applications",
    1963, Journal of Applied Physics 34, 2722-27, PGCp. 201

  • Cormack, A. M.,
    "Representation of a Function by Its Line Integrals, with Some Radiological Applications II",
    1964, Journal of Applied Physics 35, 2908-13, PGCp. 201

  • Epstein, C. L.,
    'Introduction to the Mathematics of Medical Imaging',
    2003, Upper Saddle river NJ: Pearson Education, PGCp. 200

  • Gordon, R., G. T. Herman, and S. A. Johnson,
    "Image Reconstruction from Projections",
    1975 October, Scientific American 233, 56-68, PGCp. 197, 199

  • Kac, A. C.,
    'Principles of Computerized Tomographic Imaging',
    1988, New York: IEEE, PGCp. 199, 200

  • Shepp, L. A., and J. B. Kruskal,
    "Computerized Tomography: The New Medical X-ray Technology",
    1978, American Mathematical Monthly 85, 420-39, PGCp. 200

  • Webb, S.,
    'From the Watching of Shadows: The Origins of Radiological Tomography',
    1990, Bristol UK: Adam Hilger, PGCp. 197, 202


Calc-30 -
SA - Scaling Animals
  • Banavar, J. R., et al.,
    "A General Basis for Quarter-Power Scaling in Animals",
    2010, Proceedings of the National Academy of Sciences 107, 15816-20- PGCp. 212

  • Brown, G. H., and G. B. West, editors,
    'Scaling in Biology',
    2000, Oxford: Oxford U. Press, PGCp. 209, 212
    (This book contains many papers given at a symposium on scaling.)

  • Burton, R. F.,
    'Biology by Numbers: An Encouragement to Quantitative Thinking',
    1998, Cambridge UK: Cambridge U. Press, PGCp. 205

  • Glazier, D. S.,
    "The 3/4-Power Law is Not Universal: Evolution of Isometric, Ontogenetic Metabolic Scaling in Pelagic Animals",
    2006, Bioscience 56, 325-32, PGCp. 212

  • Glazier, D. S.,
    "A Unifying Explanation for Diverse Metabolic Scaling in Animals and Plants",
    2010, Biological Reviews 85, 111-38, PGCp. 212

  • Kleiber, Max,
    'The Fire of Life',
    1961, PGCp. 209, 210

  • Kleiber, Max,
    "Body Size and Metabolism",
    1932, PGCp. 208

  • Prange, H. D., J. F. Anderson, and H. Rahn,
    "Scaling of Skeletal Mass to Body Mass in Birds and Mammals",
    1979, American Naturalist 113, 103-22, PGCp. 206

  • Rubner, Max,
    papers up to 1924, PGCp. 209

  • Savage, V. M., et al.,
    "The Predominance of Quarter-Power Scaling in Biology",
    2004, Functional Ecology 18, 257-82, PGCp. 212

  • Schmidt-Nielsen K.,
    'How Animals Work',
    1972, Cambridge UK: Cambridge U. Press, PGCp. 205

  • Schmidt-Nielsen K.,
    'Scaling: Why is Animal Size So Important?',
    1984, Cambridge UK: Cambridge U. Press, PGCp. 205, 206

  • Spence, A. J.,
    "Scaling in Biology",
    2009 Jan 27, Current Biology 19, R57-R61, PGCp. 212

  • Vogel, S.,
    'Life's Devices',
    1988, Princeton NJ: Princeton U. Press, PGCp. 205

  • West, J. B., and J. H. Brown,
    "Life's Universal Scaling Laws",
    2004 September, Physics Today, 36-42, PGCp. 211

  • Whitfield, J.,
    'In the Beat of a Heart: Life, Energy, and the Unity of Nature',
    2006, Washington DC: Joseph Henry, PGCp. 208, 209


Chapter 8 ('About Us'- animals) -
Additional Bibliography
  • Nervous System (NS) - signal transmission:

  • Hodgkins, Huxley, PGCp. 212

  • Pattern Formation (PF) :

  • Turing, PGCp. 212

  • DNA calculations:

  • No references cited by Pask.


END of Chapter 8
START of Chapter 9
'Light'

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Calc-31 -
LS - Light Speed (Roemer)
  • Boyer, C. B.,
    'The Rainbow: From Myth to Mathematics',
    1989, Princeton NJ: Princeton U. Press, PGCp. 217

  • Brush, S. G.,
    "Early Estimates of the Velocity of Light",
    1941 March, Isis 33, 24-40, PGCp. ?

  • Cohen, I. B.,
    "Roemer and the First Determination of the Velocity of Light (1676)",
    1940 April, Isis 31, 327-79, PGCp. 215
    (This paper contains a facsimile of Roemer's original 1676 paper.)

  • Daukantas, P.,
    "Ole Roemer and the Speed of Light",
    2009 July, Optics and Photonic News, 43-47, PGCp. 215

  • Roemer, O.,
    "A Demonstration Showing the Motion of Light",
    in 'Physical Thought from the Presocratics to the Quantum Physicists: An Anthology',
    edited by S. Sambursky,
    1975, New York: Pica, PGCp. 215


Calc-32 -
RE - Rainbow Explanation (Descartes, Newton)
  • Boyer, C. B.,
    'The Rainbow: From Myth to Mathematics',
    1989, Princeton NJ: Princeton U. Press, PGCp. 217

  • Casselman, B.,
    'The Mathematics of Rainbows',
    American Mathematical Society Monthly Essays, at
    www.ams.org/samplings/feature-colum/fcarc-rainbows,
    accessed 2017 Mar 27, PGCp. 220

  • Heath-Stubbs, J., and P. Salman, editors,
    'Poems of Science',
    1984, Hammondsworth UK: Penguin, PGCp. 223

  • Newton, Isaac,
    'Opticks',
    1952, New York: Dover, PGCp. 218, 219, 221
    (A reprint of the original 4th edition published in London in 1730.)

  • Nicholson, Marjorie Hope,
    'Newton Demands the Muse',
    1966, Princeton NJ: Princeton U. Press, PGCp. 223

  • Nussenzveig, H. M.,
    "The Theory of the Rainbow",
    in 'Atmospheric Phenonmena: Readings from Scientific American',
    1980, SanFrancisco: W. H. Freeman, PGCp. 220, 222

  • Williamson, S. J., and H. Z. Cummins,
    'Light and Color in Nature and Art',
    1983, New York: John Wiley, PGCp. 223?


Calc-33 -
DV - Diffraction and Vision (acuity)
  • Airy, G. B.,
    "On the Diffraction of an Object-Glass with Circular Aperture",
    1835, Transactions of the Cambridge Philosophical Society 5, 283-91, PGCp. 229

  • Cantor, G. N.,
    'Optics After Newton',
    1983, Manchester UK: Manchester U. Press, PGCp. 226

  • Denny, M., and A. McFadzean,
    'Engineering Animals: How Life Works',
    2011, Cambridge MA: Belknap, PGCp. 232
    (See chapter 10 for photoreceptors and image sampling.)

  • Heavens, O. S., and R. W. Ditchburn,
    'Insight into Optics',
    1991, Chichester UK: John Wiley, PGCp. 226, 227, 230, 234

  • Huygens, C.,
    'Treatise on Light',
    1690, PGCp. 224, 225
    (Available in many sources such as vol. 34 of
    'Great Books of the Western World', Chapter 1,
    1952, Chicago: Encyclopedia Britannica.)

  • Lipson, S. G., and H. Lipson,
    'Optical Physics',
    1969, Cambridge UK: Cambridge U. Press, PGCp. 227, 234, 235

  • Newton, Isaac,
    'Opticks',
    1952, New York: Dover, PGCp. 224
    (A reprint of the original 4th edition published in London in 1730.)

  • Robinson, A.,
    'The Last Man Who Knew Everything',
    2006, New York: Pi Press, PGCp. 226, 227
    (This refers to Thomas Young, 1773-1829, who performed a double-slit optical interference experiment.)

  • Wandell, B. A.,
    'Foundations of Vision',
    1995, Sunderland MA: Sinauer, PGCp. 231


Calc-34 -
EM - ElectroMagnetism ... and light (Maxwell)
  • Feynman, R. P.,
    'The Feynman Lectures on Physics, Vol. 2, Mainly Electromagnetism and Matter',
    1971, Reading MA: Addison-Wesley, PGCp. 236

  • Harman, P. M.,
    'The Natural Philosophy of James Clerk Maxwell',
    1998, Cambridge UK: Cambridge U. Press, PGCp. 232

  • Mahon, B.,
    'The Man Who Changed Everything: The Life of James Clerk Maxwell',
    2004, Chichester UK: Wiley, PGCp. 232

  • Maxwell, J.C.,
    'A Treatise on Electricity and Magnetism', 3rd edition,
    1904, Oxford UK: Clarendon, PGCp. 232, 236

  • Segre, E.,
    'From Falling Bodies to Radio Waves',
    1984, New York: W. H. Freeman, PGCp. 232, 234, 235
    (See chapter 4, "Electricity: From Thunder to Motors and Waves".)


Calc-35 -
PE - Photons Exist (Einstein)
  • Compton, A. H.,
    Physical Review paper,
    1923, PGCp. 243

  • Einstein, A.,
    "On a Heuristic Point of View about the Creation and Conversion of Light",
    1905, Annalen der Physik 17, 132-48, PGCp. 238
    (This paper is reprinted in various books and in Einstein's collected papers.)

  • Feynman, R. P.,
    'QED: The Strange Theory of Light and Matter',
    1985, Princeton NJ: Princeton U. Press, PGCp. 249

  • Gamow, G.,
    'Thirty Years That Shook Physics',
    1966, New York: Dover, PGCp. 238, 241

  • Newton, Isaac,
    'Opticks',
    1952, New York: Dover, PGCp. 243
    (A reprint of the original 4th edition published in London in 1730.)

  • Pais, A.,
    'Subtle is the Lord: The Science and Life of Albert Einstein',
    1982, Oxford UK: Oxford U. Press, PGCp. 238, 241, 246

  • Rigden, J. S.,
    'Einstein 1905: The Standard of Greatness',
    2005, Cambridge MA: Harvard U. Press, PGCp. 238, 241

  • Roychaudhuri, C., and R. Roy, editors,
    "The Nature of Light. What is a Photon?",
    2003 October, 'Trends' supplement of 'Optics and Photonics News', S1-S35, PGCp. 249

  • Williams, B., editor,
    'Compton Scattering',
    1977, London: McGraw-Hill, PGCp. 241
    (The paper "History" by R. H. Stuewer and M. J. Cooper, gives a good introduction to Compton scattering.)


Calc-36 -
LB - Light Bends (Soldner, Einstein)
  • Brush, S. G.,
    "Prediction and Theory Evaluation: The Case of Light Bending",
    1989 December 01, Science 246, 1124-29, PGCp. 247

  • Eddington, A.,
    'Space, Time and Gravitation: An Outline of the General Theory of Relativity',
    1959, New York: Harper, PGCp. 246
    (A reprint of the original 1920 edition.)

  • Feynman, R. P.,
    'QED: The Strange Theory of Light and Matter',
    1985, Princeton NJ: Princeton U. Press, PGCp. 249

  • Kennefick, D.,
    "Testing Relativity from the 1919 Eclipse --- A Question of Bias",
    2009 March, Physics Today, 37-42, PGCp. 246

  • Lambourne, R. J. A.,
    'Relativity, Gravitation, and Cosmology',
    2010, Cambridge UK: Cambridge U. Press, PGCp. 245(2), 247

  • Pais, A.,
    'Subtle is the Lord: The Science and Life of Albert Einstein',
    1982, Oxford UK: Oxford U. Press, PGCp. 247

  • Roychaudhuri, C., and R. Roy, editors,
    "The Nature of Light. What is a Photon?",
    2003 October, 'Trends' supplement of 'Optics and Photonics News', S1-S35, PGCp. 249

  • Soldner, Johann Georg van,
    "On the Deflection of a Light Ray from Its Rectilinear Motion, by the Attraction of a Celestial Body at Which It Nearly Passes By",
    1804, Berliner Astronomisches Jahrbuch, 161-72, PGCp. 245
    (Translations are readily available. For example, see S. L. Jaki in Foundations of Physics 8, 1978, 927-50.)

  • Weinberg, S.,
    'Gravitation and Cosmology: Principles and Applications of the Theory of Relativity',
    1972, New York: John Wiley, PGCp. 245(2), 247

  • Will, C. M.,
    'Was Einstein Right? Putting General Relativity to the Test',
    1993, New York: Basic Books, PGCp. 244, 246

  • Will, C. M.,
    "Henry Cavendish, Johann von Soldner, and the Deflection of Light",
    1988 May, American Journal of Physics 56, 413-15, PGCp. 244, 245


END of Chapter 9
START of Chapter 10
'Building Blocks'

< Go to Table of Contents, above. >

< Go to Top of this page. >

Calc-37 -
AE - Atoms Exist (Einstein - Brownian Motion)
  • Bernstein, J.,
    "Einstein and the Existence of Atoms",
    2006 October, American Journal of Physics 74, 863-72, PGCp. 254

  • Brush, S. G.,
    'Kinetic Theory, Vol 1, The Nature of Gases and of Heat',
    1965, Oxford UK: Pergamon Press, PGCp. 253

  • Einstein, A.,
    'The Collected Papers of Albert Einstein',
    translated by Anna Beck,
    1989, Princeton NJ: Princeton U. Press, PGCp. 253
    (Vol. 2 contains the relevant Brownian motion papers.)

  • Einstein, A.,
    thesis, 1905 paper, 1906 paper, PGCp. 254 (Summarized in Pais?)

  • Feynman, R. P.,
    'The Feynman Lectures on Physics',
    1971, Reading MA: Addison-Wesley, PGCp. 251, 254

  • Gamow, George,
    'Thirty Years That Shook Physics',
    1966, New York: Dover, PGCp. 253

  • Holton, G., and S. G. Brush,
    'Introduction to Concepts and Theories in Physical Science', 2nd edition,
    1973, Reading MA: Addison-Wesley, PGCp. 253

  • Lucretius,
    'De Rerum Natura',
    written around 50 BCE,
    translated as 'The Poem on Nature', by C. H. Sisson,
    1975, Manchester UK: Carcanet, PGCp. 251

  • Newburgh, R., J. Peidle, and W. Ruekner,
    "Einstein, Perrin,, and the Reality of Atoms: 1905 Revisited",
    2006 June, American Journal of Physics 74, 478-81, PGCp. 254, 257

  • Pais, A.,
    "Introducing Atoms and Their Nuclei",
    in 'Twentieth Century Physics', Vol. 1,
    edited by L. M. Brown, A. Pais, and Sir Brian Pippard,
    1995, Bristol UK: Institute of Physics Publishing, PGCp. 253, 254

  • Perrin, M. Jean,
    'Brownian Movement and Molecular Reality',
    1910, London: Taylor and Francis, PGCp. 257
    (This is a translation by F. Soddy of Perrin's article in 'Annales de Chimie et de Physique', 8th series, 1909 September.)

  • Rechenberg, H.,
    "Quanta and Quantum Mechanics",
    in 'Twentieth Century Physics', Vol. 1,
    edited by L. M. Brown, A. Pais, and Sir Brian Pippard,
    1995, Bristol UK: Institute of Physics Publishing, PGCp. 253

  • Rigden, J. S.,
    'Einstein 1905: The Standard of Greatness',
    2005, Cambridge MA: Harvard U. Press, PGCp. 254
    (See the 'Seeing Atoms' chapter.)


Calc-38 -
SL - Spectral Lines (Balmer)
  • Balmer, J. J.,
    "Notiz uber die Spectrallinien des Wasserstoffs",
    1885, Annalen der Physik und Chemie 25, 80
    translated as "The Hydrogen Spectral Series",
    in 'A Source Book in Physics', edited by W. F. Magie,
    1963, Cambridge MA: Harvard U. Press, PGCp. 260

  • Kirchoff, G., and R. Bunsen,
    "Chemische Analyse durch Spektralbeobachtungen",
    'Ostwalds Klassiker der exacten Wissenschaften', no. 72, 1860
    translated as "Chemical Analysis by Observation of the Spectrum"
    in 'Physical Thought from the Presocratics to the Quantum Physicists: An Anthology", edited by S. Sambursky,
    1975, New York: Pica, PGCp. 258


Calc-39 -
AM - Atom Mechanics (Bohr, et al)
  • De Broglie, Louis,
    "The Wave Nature of the Electron",
    1929 Nobel Prize acceptance speech,
    reprinted in 'Physical Thought from the Presocratics to the Quantum Physicists: An Anthology", edited by S. Sambursky,
    1975, New York: Pica, PGCp. 265

  • Clark, C. W., and J. Reader,
    "The Optical Discovery of Deuterium",
    2012 May, 'Optics and Photonics News 23, 36-41, PGCp. 268

  • Bohr, 1913 paper, PGCp. 263
    ("easy to follow"; reproduced in Ter Haar's book, below.)

  • Fayer, M. D.,
    'Absolutely Small: How Quantum Theory Explains Our Everyday World',
    2010, New York: AMACOM, PGCp. 267

  • Ter Haar, D.,
    'The Old Quantum Theory',
    1967, Oxford UK: Pergamon, PGCp. 262, 263
    (an excellent introduction to the dawn of quantum mechanics; includes the seminal original papers by Planck, Einstein, Rutherford, Bohr, and others)

  • Wallace, P. R.,
    'Paradox Lost: Images of the Quantum',
    1996, New York: Springer, PGCp. 268
    (One of Pask's 'favorite' books on quantum physics and the wave function.)


Calc-40 -
NM - Neutron Mass (Chadwick)
  • Chadwick, J.,
    1935 Nobel Prize in Physics Award Address,
    reprinted in 'The World of Physics, Vol. 2',
    edited by F. H. Weaver,
    1987, New York: Simon and Schuster, PGCp. 269

  • Chadwick, J.,
    "Possible Existence of a Neutron",
    1932, Letter to the Editor in 'Nature' 129, 312, PGCp. 269, 271

  • Pask, C.,
    'Math for the Frightened',
    2011, Amherst NY: Prometheus Books, PGCp. 270
    (See chapter 13.)


END of Chapter 10
START of Chapter 11
'Nuclear and Particle Physics'

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Calc-41 -
EMM - Electron Magnetic Moment
  • Dirac, P. A. M.,
    1933 Nobel Prize in Physics Award Address,
    in 'The World of Physics, Vol. 2', edited by J. H. Weaver,
    1987, New York: Simon and Schuster, PGCp. 275

  • Dirac, P. A. M.,
    'The Principles of Quantum Mechanics', 4th edition,
    1958, Oxford UK: Clarendon, PGCp. 275

  • Farmelo, G.,
    'The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom',
    2009, New York: Basic Books, PGCp. 274

  • Feynman, R. P.,
    'QED: The Strange Theory of Light and Matter',
    1985, Princeton NJ: Princeton U. Press, PGCp. 276, 278

  • Feynman, R. P.,
    "Space-Time Approach to Quantum Electrodynamics",
    1949, Physical Review 76, 769-89, PGCp. 277

  • Gabrielse, G.,
    "The Standard Model's Greatest Triumph",
    2013 Dec, Physics Today, 64-65, PGCp. 279

  • Weisskoph, V. F.,
    "Growing Up with Field Theory: The Development of Quantum Electrodynamics",
    in 'The Birth of Particle Physics',
    edited by L. M. Brown and L. Hoddleson,
    2010, Cambridge UK: Cambridge U. Press, PGCp. 276


Calc-42 -
NE - Neutrino Exists
  • Brown, L.,
    "The Idea of the Neutrino",
    1978 September, Physics Today, 23-28, PGCp. 281, 282

  • Dunlap, R. A.,
    'The Physics of Nuclei and Particles',
    2004, Toronto: Thomson Brooks/Cole, PGCp. 281(2)

  • Lee and Wang, PGCp. 287

  • McManus, PGCp. 287 ("entertaining")

  • Pais, A.,
    "Introducing Atoms and Their Nuclei",
    in 'Twentieth Century Physics', Vol. 1,
    edited by L. M. Brown, A. Pais, and Sir Brian Pippard,
    1995, Bristol UK: Institute of Physics Publishing, PGCp. 281, 282, 285

  • Sutton, C.,
    'Spaceship Neutrino',
    1992, Cambridge UK: Cambridge U. Press, PGCp. 281

  • Wu, PGCp. 287


Calc-43 -
TD - Time Dilation (Einstein)
  • Ashby, N.,
    "Relativity and the Global Positioning System",
    2002 May, Physics Today, 41-47, PGCp. 291

  • Greenberg, A. J., et al.,
    "Charged-Pion Lifetime and a Limit on a Fundamental Length",
    1969, Physical Review Letters 23, 1267-70, PGCp. 290

  • Lambourne, R. J. A.,
    'Relativity, Gravitation and Cosmology',
    2010, Cambridge UK: Cambridge U. Press, PGCp. 288(2)

  • Mermin, D.,
    'It's About Time: Understanding Einstein's Relativity',
    2005, Princeton NJ: Princeton U. Press, PGCp. 290

  • Reinhardt, S., et al.,
    "Test of Relativistic Time Dilation with Fast Optical Atomic Clocks at Different Velocities",
    2007, Nature Physics 3, 861-64, PGCp. 290

  • Rossi, B.,
    "The Decay of Mesotrons, 1939-1943: Experimental Particle Physics in the Age of Innocence",
    in 'The Birth of Particle Physics',
    edited by L. M. Brown and L. Hoddleson,
    2010, Cambridge UK: Cambridge U. Press, PGCp. 290

  • Rossi, B., N. Hilberry, and J. Barton Hoag,
    "The Variation of the Hard Component of Cosmic Rays with Height and the Disintegration of Mesotrons",
    1940, Physical Review 57, 461-68, PGCp. 290

  • Sartoff, G., et al.,
    "Improved Test of Time Dilation in Special Relativity",
    2003, Physical Review Letters 91, 190403-1 to 190403-4, PGCp. 290

  • Wikipedia article Time Dilation,
    accessed 2017 Mar 27, PGCp. 290


Calc-44 -
QM - Quarks and Masses (Gell-Mann et al)
  • Dunlap, R. A.,
    'The Physics of Nuclei and Particles',
    2004, Toronto: Thomson Brooks/Cole, PGCp. 292

  • Durr, S., et al.,
    "Ab-Initio Determination of Light Hadron Masses",
    2008 Nov 21, Science 322, no. 5905, 1224-27, PGCp. 294

  • Fayer, M. D.,
    'Absolutely Small: How Quantum Theory Explains Our Everyday World',
    2010, New York: AMACOM, PGCp. 291

  • Olsen, S. L.,
    "Exotic Particles with Four or More Quarks",
    2014 September, Physics Today, 56-57, PGCp. 294

  • Wilczek, F.,
    'The Lightness of Being: Mass, Ether, and the Unification of Forces',
    2008, New York: Basic Books, PGCp. 294


Calc-45 -
SF - Sun Fusion
  • Atkinson, R., and F. Houtermans,
    "Aufbaumoelichkeit in Sternen",
    1929, Zeitschrift fur Physik 54, 656-65, PGCp. 300

  • Bahcall, J. N.,
    "Solving the Mystery of the Missing Neutrinos",
    at nobelprize.org/ nobel_prizes/ themes/ physics/ bahcall/,
    accessed 2017 Mar 27, PGCp. 304

  • Bethe, H. A.,
    "Energy Production in Stars",
    1939, Physical Review 55, 434-56, PGCp. 301

  • Cockcroft, J., and E. Walton,
    "Disintegration of Lithium by Swift Protons",
    1932, Nature 129, PGCp. 297

  • Cockcroft, J., and E. Walton,
    "Experiments with High Velocity Positive Ions II - The Disintegration of Elements by High Velocity Protons",
    1932, Proceedings of the Royal Society A 227, 229-36, PGCp. 297

  • Dunlap, R. A.,
    'The Physics of Nuclei and Particles',
    2004, Toronto: Thomson Brooks/Cole, PGCp. 295, 303(2)

  • Eddington, A. S.,
    'The Internal Constitution of Stars',
    1959, New York: Dover, PGCp. 299
    (A reprint of the 1926 original. The relevant part is also reprinted in the book by Kilmister, noted below.)

  • Halzen, F., and S. R. Klein,
    "Astronomy and Astrophysics with Neutrinos",
    2008 May, Physics Today, 29-35, PGCp. 304

  • Kelvin, Lord,
    "On the Age of the Sun's Heat",
    1862, Macmillan's Magazine 5, 388-93, PGCp. 299

  • Kilmister, C. W.,
    'Men of Physics: Sir Arthur Eddington',
    1966, Oxford UK: Pergamon Press, PGCp. 299

  • King, A.,
    'Stars: A Very Short Introduction',
    2012, Oxford UK: Oxford U. Press, PGCp. 298, 302

  • Lang, K. R., and O. Gingerich, editors,
    'A Sourcebook in Astronomy and Astrophysics, 1900-1975',
    1975, Cambridge MA: Harvard U. Press, PGCp. 303

  • McCracken, G., and P. Stott,
    "Fusion: The Energy of the Universe",
    2005, Amsterdam: Elsevier, PGCp. 303(2)

  • National Research Council, Committee on Nuclear Physics,
    'Nuclear Physics: The Core of Matter, the Fuel of Stars',
    1999, Washington DC: National Academy Press, PGCp. 295


Calc-46 -
AB - Atomic Bomb
  • Cockcroft, J., and E. Walton,
    "Disintegration of Lithium by Swift Protons",
    1932, Nature 129, PGCp. 297

  • Cockcroft, J., and E. Walton,
    "Experiments with High Velocity Positive Ions II - The Disintegration of Elements by High Velocity Protons",
    1932, Proceedings of the Royal Society A 227, 229-36, PGCp. 297

  • Dunlap, R. A.,
    'The Physics of Nuclei and Particles',
    2004, Toronto: Thomson Brooks/Cole, PGCp. 295, 306

  • Frank, Sir Charles,
    'Operation Epsilon: The Farm Hall Transcripts',
    1993, Berkley CA: U. of California Press, PGCp. 313

  • Graetzer, H. G., and D. L. Anderson,
    'The Discovery of Nuclear Fission: A Documentary History',
    1971, New York: Van Nostrand, PGCp. 304, 306
    ("A wonderful collection of original papers and commentary on them." - Pask)

  • Logan, J.,
    "The Critical Mass",
    1996 May-June, American Scientist 84, 263-77, PGCp. 312, 313

  • Meitner and Frisch, PGCp. 304

  • National Research Council, Committee on Nuclear Physics,
    'Nuclear Physics: The Core of Matter, the Fuel of Stars',
    1999, Washington DC: National Academy Press, PGCp. 295

  • Rhodes, R.,
    'The Making of the Atomic Bomb',
    1986, New York: Simon and Schuster, PGCp. 306

  • Rose, P. L.,
    'Heisenberg and the Nazi Atomic Bomb Project: A Study in German Culture',
    1998, Berkeley CA: U. of California Press, PGCp. 312, 313

  • Serber, Robert,
    'The Los Alamos Primer',
    1992, Berkeley CA: U. of California Press, PGCp. 307


END of Chapter 11
START of Chapter 12
'Methods and Motion'

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Calc-47 -
VS - Vibrating Strings
(D. Bernoulli, Fourier, et al)
  • D. Bernoulli, d'Alembert, Euler, PGCp. 317

  • D. Bernoulli, LaGrange, Euler, PGCp. 318

  • Cannon, J. T., and S. Dostrovsky,
    'The Evolution of Dynamics: Vibration Theory from 1687 to 1742',
    1981, New York: Springer-Verlag, PGCp. 316

  • Coulson, C. A., and A. Jeffrey,
    'Waves', 2nd edition,
    1977, London: Longman, PGCp. 316, 318

  • Dirac, PGCp. 323

  • Feynman, R. P.,
    'The Feynman Lectures on Physics',
    1971, Reading MA: Addison-Wesley, PGCp. 322
    (See chapters 25, 49, and 50 in volume 1.)

  • Fourier,
    'Analytical Theory of Heat',
    PGCp. 321

  • Kline, M.,
    'Mathematical Thought from Ancient to Modern Times',
    1972, New York: Oxford U. Press, PGCp. 316, 318

  • Magie, W. F., editor,
    'A Source Book in Physics',
    1963, Cambridge MA: Harvard U. Press, PGCp. 316

  • Mersenne, Taylor, PGCp. 316

  • Prestini, E.,
    'The Evolution of Applied Harmonic Analysis',
    2004, Boston: Birkhauser, PGCp. 322

  • Struik, D. J., editor,
    'A Source Book in Mathematics 1200-1800',
    1969, Cambridge MA: Harvard U. Press, PGCp. 316

  • Thomson, Sir William (Lord Kelvin), and P. G. Tait,
    'Principles of Mechanics and Dynamics',
    (formerly titled 'Treatise on Natural Philosophy'),
    1962, New York: Dover, PGCp. 321
    (A republication of the last revised editon of 1912. See section 75 in vol. 1.)

  • Wandell, B. A.,
    'Foundations of Vision',
    1995, Sunderland MA: Sinauer, PGCp. 322

  • Westheimer, G.,
    "The Fourier Theory of Vision",
    2001, Perception 30, 531-41, PGCp. 322


Calc-48 -
BF - Bessel Functions
  • Campbell-Kelly, M., M. Croaken, R. Flood, and E. Robson, editors,
    'The History of Mathematical Tables',
    2003, Oxford UK: Oxford U. Press, PGCp. 329, 330

  • Bernoulli, PGCp. 326

  • Bessel, PGCp. 323, 328

  • Dutka, J.,
    "On the Early History of Bessel Functions",
    1995, Archive for History of the Exact Sciences 49, 105-34, PGCp. 326

  • Euler, Fourier, Poisson, PGCp. 327

  • Fricke, W.,
    "Bessel, Friedrich Wilhelm",
    in 'Dictionary of Scientific Biography',
    edited by C. C. Gillespie,
    1975, New York: Charles Scribner's Sons, PGCp. 323

  • Horsburgh, E. M.,
    'Modern Instruments and Methods of Calculation: A Handbook of the Napier Tercentenary Exhibition',
    1915, London: G. Bell and Sons, PGCp. 329

  • LaGrange, PGCp. 328

  • McFarland, D. M.,
    "Quarter Squares Revisited",
    at escholarship.org/uc/,
    accessed 2017 Mar 27, PGCp. 329

  • McLachlan, N. W.,
    'Bessel Functions for Engineers', 1st edition,
    1934, Oxford UK: Clarendon Press, PGCp. 328(2)

  • Norberg, A. L.,
    "Table Making in Astronomy",
    in 'The History of Mathematical Tables',
    edited by M. Campbell-Kelly, M. Croaken, R. Flood, and E. Robson,
    2003, Oxford UK: Oxford U. Press, PGCp. 323

  • Pask, C.,
    'Magnificent Principia: Exploring Isaac Newton's Masterpiece',
    2013, Amherst MA: Prometheus Books, PGCp. 328
    (See chapter 12.)

  • Roegel, D.,
    "A Reconstruction of Blater's Table of Quarter Squares",
    a 212-page PDF file at locmat.loria.fr/blater1887/,
    accessed 2017 Mar 27, PGCp. 329

  • Watson, G. N.,
    'A Treatise on the Theory of Bessel Functions', 2nd edition,
    1944, Cambridge UK: Cambridge U. Press, PGCp. 325, 326, 328
    (800-plus pages)


Calc-49 -
NO - Nonlinear Oscillations
  • Akhmediev, N. N.,
    "Deja Vu in Optics",
    2001 Sep 20, Nature 413, 267-68, PGCp. 340

  • Berman, G. P.,
    "The Fermi-Pasta-Ulam Problem: Fifty Years of Progress",
    2005 March, CHAOS 15, 05104-1-18, PGCp. 340

  • Dauxios, T.,
    "Fermi, Pasta, Ulam, and a Mysterious Lady",
    2008 Jan, Physics Today, 55-57, PGCp. 342, 343

  • Fermi, e., J. Pasta, and S. Ulam,
    "Studies of Nonlinear Problems",
    1955 May, Los Alamos Document LA-1940, PGCp. 334, 338, 339

  • Gallovatti, G.,
    'The Fermi-Pasta-Ulam Problem: A Status Report',
    2008, Berlin: Springer, PGCp. 340

  • Kevrekidis, P. G.,
    "Non-linear Waves in Lattices: Past, Present, Future",
    2011, IMA Journal of Applied Mathematics 76, 389-423, PGCp. 340

  • Kibble, T. W. B.,
    'Classical Mechanics',
    1966, London: McGraw-Hill, PGCp. 336, 341
    (See chapter 12.)

  • Kortweg and DeVries, PGCp. 341

  • Pettini, M., L. Casetti, M. carutti-Sola, R. Franzosi, and E. D. G. Cohen,
    "Weak and Strong Chaos in Fermi-Pasta-Ulam Models and Beyond",
    2005 March, CHAOS 15, 05106-1-13, PGCp. 340

  • Porter, M. A., N. J. Zabusky, Bambi Hu, and D. K. Campbell,
    "Fermi, Pasta, Ulam and the Birth of Experimental Mathematics",
    2009 May-June, American Scientist 97, 214-21, PGCp. 340, 341

  • Segre, E., editor,
    'Collected Papers of Enrico Fermi', Vol. 2,
    1965, Chicago: U. of Chicago Press, PGCp. 334(?)

  • Zabusky, PGCp. 340


Calc-50 -
LE - Logistic Equation
('chaos' - instability, sensitivity, divergence)
  • Barger, V. D., and M. G. Olsson,
    'Classical Mechanics: A Modern Perspective', 2nd edition,
    1995, New York: McGraw-Hill, PGCp. 340
    (See chapter 11.)

  • Cvitanovic, P.,
    'Universality in Chaos', 2nd edition,
    1989, Bristol UK: Adam Hilger, PGCp. 349

  • Feigenbaum, PGCp. 349

  • Gleick, J.,
    'Chaos: Making a New Science',
    1988, London: Heinemann, PGCp. 349

  • Hall, N., editor,
    'The New Scientist Guide to Chaos',
    1991, London: Penguin, PGCp. 349
    (Contains a broad range of introductory articles.)

  • May, R. M.,
    "Simple Mathematical Models with Very Complicated Dynamics",
    1976 June 10, Nature 261, 459-67, PGCp. 345

  • Moon, F. C.,
    'Chaotic Vibrations: An Introduction for Applied Scientists and Engineers',
    2004, Hoboken NJ: John Wiley, PGCp. 349

  • Motter, A. E., and D. K. Campbell,
    "Chaos at Fifty",
    2013 May, Physics Today, 27-33, PGCp. 349, 350

  • Stewart, I.,
    'Does God Play Dice? The New Mathematics of Chaos',
    1990, London: Penguin Books, PGCp. 349


Chapter 12 ('Methods and Motion') -
Additional Bibliography
  • Tables and Computing (TC) :

  • Abramowitz, M., and I. A. Stegun,
    'Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables',
    1964, Washington DC: National Bureau of Standards, PGCp. 331

  • Airy, PGCp. 330

  • Aldis, PGCp. 330

  • Blater, PGCp. 329

  • Campbell-Kelly, M., M. Croaken, R. Flood, and E. Robson, editors,
    'The History of Mathematical Tables',
    2003, Oxford UK: Oxford U. Press, PGCp. 329, 330

  • Croaken, M.,
    "Table Making by Committee",
    in 'The History of Mathematical Tables',
    edited by M. Campbell-Kelly, M. Croaken, R. Flood, and E. Robson,
    2003, Oxford UK: Oxford U. Press, PGCp. 331

  • Croaken, M., and M. Campbell-Kelly,
    "Beautiful Numbers: The Rise and Decline of the British Association Mathematical Tables Committee, 1871-1965",
    2000 Oct-Dec, IEEE Annals of the History of Computing, 44-61, PGCp. 331

  • Grier, D. A.,
    'When Computers Were Human',
    2005, Princeton NJ: Princeton U. Press, PGCp. 330

  • McFarland, D. M.,
    "Quarter Squares Revisited",
    at escholarship.org/uc/,
    accessed 2017 Mar 27, PGCp. 329

  • McLachlan, N. W.,
    'Bessel Functions for Engineers', 1st edition,
    1934, Oxford UK: Clarendon Press, PGCp. 328(2)

  • Meissel, PGCp. 330

  • Rayleigh, PGCp. 330

  • Roegel, D.,
    "A Reconstruction of Blater's Table of Quarter Squares",
    a 212-page PDF file at locomat.loria.fr/blater1887/,
    accessed 2017 Mar 27, PGCp. 329

  • Watson, G. N.,
    'A Treatise on the Theory of Bessel Functions', 2nd edition,
    1944, Cambridge UK: Cambridge U. Press, PGCp. 330 (and 325, 326, 328)
    (800-plus pages)

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Page was created 2017 Mar 09.
(Started with the 'Tide Prediction' references.)

Page was changed 2017 Mar 27.
(Added almost all Pask's references. The intent is to add many web links for these references, later, someday.)


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