1.

Introduction  
2.

From Euclid to the Seventeenth Century  
3.

From Scratch Marks to Number Systems  
4.

From Numerology to Number Theory  
5.

The Pythagorean Theorem  
6.

A Shocking Discovery  
7.

Pi Through the Ages  
8.

From Astronomy to Trigonometry  
9.

From Archimedes to Fermat and Descartes  
10.

The Race for the Calculus 
Two introductory segments give an overview of the program. The first outlines some of the important developments in the period from 3000 B.C. to 300 B.C., which culminated with the publication of Euclid's Elements. The second gives an outline of some of the landmark achievements from 300 B.C. up to the events that led to the development of calculus. The remaining segments describe in more detail some of the important highlights on the road to calculus. They discuss number systems developed in different cultures; numerology or number mysticism as practiced by the Pythagoreans; the origin of number theory as an outgrowth of numerology; the Pythagorean Theorem for right triangles and how it led to the discovery of irrational numbers; the golden age of Hellenistic mathematics as it flourished in the ancient city of Alexandria; the multicultural search for an understanding of the number pi and the landmark contributions to this effort by Archimedes; how astronomy gave birth to trigonometry; and other developments such as algebra and analytic geometry that eventually led to the calculus.
The program also includes some mathematical derivations in animated form: proofs of the Pythagorean Theorem, an new geometric proof of the irrationality of the square root ot two, two methods for calculating the area of a circular disk, and the Archimedes method for estimating pi.