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

Information Page, Spring 2010

The review will be from 5.30 PM till 6.30 PM in LN 1120 (I was not able to get the room from 6 to 7 PM).

The book I refered to in my lecture on 1/25/2010 is "The Universal History of Numbers" by Georges Ifrah.

Here is a nice discussion of Egyptian fractions.

Here and here is a discussion of Plimpton 322 Babylonian clay tablet.

Here is some information about the Egyptian papyri.

A short biography of Thales, Pythagoras, and Hippocrates.

Here is an interesting view on Pythagoras and his brotherhood.

Here is a short history of perfect numbers.

Here are numerous proofs of the Pythagorean Theorem.

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 squarable lunes.

Here you can see the quadratrix, and here is a short history of the problem of angle trisection.

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

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

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

Here is a short overwiev of basic properties of continued fractions. Here is a note about continued fractions.

Here, here and here is information about the Platonic solids.

A short biography of Euclid, Euclid, Archimedes, and Apollonius

Here are the works of Archimedes.

Here is a nice essay on conic sections.

Here is a translation of "Conics" by Apollonius.

Here is a nice description of Archimedes' approximation of pi, and here is a an interesting description of Stomachion and the recent developments about it.

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

Here is a discussion of conchoid and its use in angle trisection and cube duplication.

A short biography of Eratosthenes, Hipparchus, Heron, and Ptolemy.

A short biography of Menelaus, Diophantus, Pappus, Hypatia, and Proclus.

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

Here, here, and here you can learm about the Theorem of Menelaus.

Here is Newton's approach to the duplication of a cube.

Here and here you can read about Pappus' theorems, and here is a discussion of Desargues' Theorem.

Here and here is a discussion of Brahmagupta's formula.

Here is Al-Karaji's derivation of a formula for the sum of cubes of consecutive integers.

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

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

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

A short biography of Isaac Newton, Gottfried Wilhelm von Leibniz, Jacob (Jacques) Bernoulli, and Johann Bernoulli.

Here is a short account of the main contributions of Newton and Leibniz to calculus.

Here is a nice article about how Wallis discovered some of his results and here is how Newton discovered his binomial theorem.

Here is a short biography of Leonhard Euler and 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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