Project MATHEMATICS!

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Project MATHEMATICS! Video Introduction

See mathematics brought to life with imaginative computer animation, live action, music and special effects in this brief introduction to the award-winning series of videotapes developed by Professor

Tom M. Apostol at the California Institute of Technology.

Project description

Project MATHEMATICS! produces videotape-and-workbook modules that explore basic topics in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. The tapes use live action, music, special effects, and imaginative computer animation. They are distributed on a nonprofit basis.

The goal of the project is to attract young people to mathematics through high-quality instructional modules that show mathematics to be understandable, exciting, and eminently worthwhile. Each module consists of a videotape together with a workbook, and explores a basic topic in mathematics that can be easily integrated into any existing high school or community college curriculum. The modules are crafted to encourage interaction between students and teachers.

More than 10 million students have seen one or more of the videotapes. They have been enthusiastically received by teachers and students nationwide and have captured first-place honors at many major film and video festivals.

All tapes have closed captions for the hearing impaired. They are also available in PAL format for use abroad.

Project modules were produced by Tom M. Apostol and James F. Blinn at the California Institute of Technology in Pasadena, CA.

The modules

The following modules are currently available

• The Theorem of Pythagoras Several engaging animated proofs of the Pythagorean theorem are presented, with applications to real-life problems and to Pythagorean triples. The theorem is extended to 3-space, but does not hold for spherical triangles.
• The Story of Pi Although pi is the ratio of circumference to diameter of a circle, it appears in many formulas that have nothing to do with circles. Animated sequences dissect a circular disk of radius r and transform it to a rectangle of base pi*r and altitude r. Animation shows how Archimedes estimated pi using perimeters of approximating polygons.
• Similarity Scaling multiplies lengths by the same factor and produces a similar figure. It preserves angles and ratios of lengths of corresponding line segments. Animation shows what happens to perimeters, areas, and volumes under scaling, with various applications from real life.
• Polynomials Animations show how the Cartesian equation changes if the graph of a polynomial is translated or subjected to a vertical change of scale. Zeros, local extrema, and points of inflection are discussed. Real-life examples include parabolic trajectories and the use of cubic splines in designing sailboats and computer-generated teapots.
• Sines and Cosines, Part 1 (Periodic functions) Sines and cosines occur as rectangular coordinates of a point moving on a unit circle, as graphs related to vibrating motion, and as ratios of sides of right triangles. They are related by reflection or translation of their graphs. Animations demonstrate the Gibbs phenomenon of Fourier series.
• Sines and Cosines, Part 2 (Trigonometry) This program focuses on trigonometry, with special emphasis on the law of cosines and the law of sines, together with applications to The Great Survey of India by triangulation. The history of surveying instruments is outlined, from Hero's dioptra to modern orbiting satellites.
• Sines and Cosines, Part 3 (Addition formulas) Animation relates the sine and cosine of an angle with chord lengths of a circle, as explained in Ptolemy's Almagest. This leads to elegant derivations of addition formulas, with applications to simple harmonic motion.
• The Tunnel of Samos This video describes a remarkable engineering work of ancient times: excavating a one-kilometer tunnel straight through the heart of a mountain, using separate crews that dug from the two ends and met in the middle. How did they determine the direction for excavation? The program gives Hero's explanation (ca. 60 A.D.), using similar triangles, as well as alternate methods proposed in modern times.
• Teachers Workshop This 28-minute tape, accompanied by a 90-page transcript, contains excerpts from a two-day workshop held in 1991 for teachers who have sucessfully used project materials in their classrooms.
• Project MATHEMATICS! Contest In 1994 Project MATHEMATICS! conducted a contest open to all teachers who had used project materials in their classrooms. Entries were judged on the basis of innovative and effective use of the materials. This videotape, accompanied by a 30-page booklet, shows the classroom implementation of the entries of the first-place winners.
• Early History of Mathematics This 30-minute videotape traces some of the landmarks in the early history of mathematics--from Babylonian clay tablets produced some 5000 years ago, when calendar makers calculated the onset of the seasons--to the development of calculus in the seventeenth century.