This is an outline of the topics covered in the 1973 "The Music of the Spheres" episode of the Ascent of Man series. The series is written by Jacob Bronowski and filmed by the BBC and Time-Life Films. The numbers in parentheses represent the approximate time into the film when that subject is presented.

The beginning of math and counting.
Samos (a Greek island).
``Numbers are the language of nature.''
Music and harmonics.
Right angles/vertical and horizontal.
3-4-5 right triangles.
Proof of Pythagorean Theorem with manipulatives.
The Pythagorean Theorem is the "most important single theorem in all of mathematics." (14:00)
Euclid and the Elements.
Ptolemy and his model of the solar system.
Islam.
Astrolabe. (22:00)
Roman and Arabic numbers.
Arabic numerals to Europe in 750 AD, but didn't take hold for another 500 years.
The Alhambra in Spain.
Tilings and symmetry. (30:00)
Natural symmetries and crystals.
Christianity surges in 1000 AD.
Beginning of the Renaissance: translation of ancient Greek texts into Latin.
Alhazen and perspective.
Perspective and painting. (44:00)
Durer.
Circular motion.
Kepler.
Newton and Leibniz. (49:00)
Time. (51:00)

Return to Bob Gardner's Foundations and Structure of Mathematics 1 webpage.