Math 488H and Math 575H: Topics in the History of Mathematics

Information Page, Spring 2012

I will be in my office on Friday, May 18, between 1 and 2 pm.

For a great account of the developement of numbers see "The Universal History of Numbers" by Georges Ifrah.

Ishango bone, ants-that-count, animals-that-count and more animals-that-count.

Here you can see Babylonian digits. Here is a table of mutiplication by 9, and here is a table of multiplication by 4.

Here are some pages of the book "Episodes from the early history of mathematic" by A. Aaboe, and here are some pages of the book "A remarkable collection of Babylonian mathematical texts" by J. Friberg.

Here, here, and here is the tablet with square root of 2. Here is an article about Babylonian way of aproximation of square roots.

Here and here is a discussion of the tablet Plimpton 322. Here is a nice article about an interpratation of Plimpton 322.

Here is a short account of the history of ancient Egypt.

Here is a short discussion of Egyptian hieroglyphic numerals, here is a picture of a stone with some numerals, here and here are both the hieroglyphic and hieratic numerals.

Here is a nice discussion of Egyptian fractions, here is an interesting article about modern results on Egyptian fractions, and here is the 2/n table of from the Rhind (Ahmes) papyrus.

Here is a discussion of the Egyptian papyri.

Here is a short discussion of the Ahmes papyrus, and here is a discussion of the Moscow papyrus.

Here is an article about mathematics of Liu Hui, who among other things computes volumes of some pyramids and of frustum, and here is some additional information about volumes.

Here is a short history of Antient Greece.

A short biography of Thales, Pythagoras, and Hippocrates.

Here is an interesting view on Pythagoras and his brotherhood.

Here is a discussion of the Wallace-Gerwien-Bolyai Theorem. Here is a discussion of an analogous problem in three dimensions (often called Hilbert's third problem).

Here and here is a discussion of Greek number systems.

Here is a discussion of the lunes (note that what I called "segment" in class is called "sector" in this note) and here is another discussion of the lunes.

Here is a short history of perfect numbers.

Here and here you can see the quadratrix, and here is a short discussion of the problems of antiquity.

Here is a short history of the problem of angle trisection and here and here is a discussion of the problem of doubling a cube. Here is the Archytas curve.

Here is a nice version of Euclids "Elements", and here is a short note about Euclid and his "Elements".

Here and here are some basic facts about continued fractions.

Here is a nice note about continued fractions and its connections to Greek geometry.

Here is a very interesting take on continued fractions and Greek mathematics (it is a challenging read though). See in particular the Appendix.

A short biography of Plato, Theaetetus, Eudoxus, and Eudoxus again.

Here is a discussion of the model of planetary motion dues to Eudoxus.

Here and here is information about the Platonic solids.

A short biography of Euclid, Euclid, and Archimedes.

Here are the works of Archimedes, and here is a nice description of Archimedes' approximation of pi.

Here is a discussion of how Archimedes arrived at the formula for a volume of a ball (his "Method").

Here is a an interesting description of Stomachion and the recent developments about it. Here and here is more about Stomachion.

Here is a nice translation of the "Quadrature of the Parabola" by Archimedes.

Here is a discussion of the spiral of Archimedes.

Here is a short biography of Apollonius.

Here is a nice essay on conic sections.

Here is a translation of "Conics" by Apollonius.

Here is a discussion of the angle trisection method of Archimedes.

Here are some basic properties of conics.

Here you can play with Apollonius circles, and here you can find a proof.

Here is the idea for angle trisection using a conchoid (note that it is incorrectly atributed to Hippocrates; it was definitely known to Nicomedes).

Here is a discussion of conchoid and its use to construct two mean proportionals. Here you can play with conchoids. Here is a conchoidograph and here is a more classical version of the tool.

A short biography of Aristarchus, Nicomedes, Eratosthenes, Hipparchus, and Ptolemy.

Here is interesting modern take on Almagest and astronomy in general.

Here and here are short movies about how Eratosthenes measured the circumference of the Earth.

Here is a discussion of Ptolemy's theorem.

A short biography of Heron, Menelaus, and Diophantus.

Here is an applet to play with spherical geometry.

Here is a discussion of Menealus's Theorem, with several proofs and additional topics.

Here is Newton's approach to the duplication of a cube. A homework problem asks you to justify this method.

Here is discussion of problem 8 in book 2 of Diophantus's "Aritmetica". Here is a page from an edition of "Arithmetica" with Fermat's commentaries.

Here is a translation of Diophantus's "Aritmetica" with extensive introduction (you need djvu viewer to open it), here are other formats available (pdf, kindle, etc.).

Here is a very nice paper about Diophantus and his influence on the development of algebra and number theory.

A short biography of Pappus, Theon, Hypatia, and Proclus.

Biographies of first Indian mathematicians Aryabhata I, Brahmagupta, Bhaskara I

A short biography of Al-Khwarizmi, Al-Karaji, and Omar Khayyam.

Here is an essay about Al-Khwarizmi.

A short biography of Fibonacci, Luca Pacioli, Scipione del Ferro, Nicolo Fontana (Tartaglia), Girolamo Cardano, Lodovico Ferrari, and Rafael Bombelli.

page 17

A short biography of François Viète, Simon Stevin, René Descartes, Pierre de Fermat, Blaise Pascal, and John Wallis.

Here is a nice article about how Wallis discovered some of his results.

Here you can see how Newton discovered his binomial theorem. Here is a short account of the main contributions of Newton and Leibniz to calculus.

A short biography of Isaac Newton and Gottfried Wilhelm von Leibniz.

A short biography of Jacob (Jacques) Bernoulli, Johann Bernoulli, and Leonhard Euler.

Here is an archive of all the works of Euler. In particular, here is a translation of the original articles in which Euler computes the sum of squeres of reciprocals of the natural numbers.

Here is a discussion of Fermat numbers.

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