Project MATHEMATICS!
Encyclopedia
Project Mathematics! is a series of educational video modules and accompanying workbooks for teachers, developed to help teach the principles of mathematics to high school students.
and trigonometry
and include a history of Mathematics and examples of how math is used in real world applications. The modules were produced by Dr. Tom M. Apostol
at the California Institute of Technology
. The series uses computer animation
, created by Dr. James F. Blinn, to visually depict the principles being discussed. Approximately 140,000 of the tapes and DVDs were sent to educational institutions and have been viewed by about 10,000,000 people worldwide over the last 20 years.
. Visually shows the dissection proof to show how the theorem works in real life.
was determined and its history. Multiple animations show various ways to determine pi.
s and cosines are related to waves and a unit circle
. Also reviews their relationship to the ratios of side lengths of right triangle
s.
and cosines
how they relate to sides and angles of a triangle. The module also gives some real life examples of their use.
's Almagest
. Animation shows how sines and cosines relate to harmonic motion
.
s can approximate sines and cosines. Includes information about cubic splines in design engineering.
The modules are available on a set of 9 videotapes or 3 DVDs. The videotapes may be freely copied for educational purposes with a few caveats. The DVD version is not freely reproducible.
The video segments for the first 3 modules can be viewed for free at the Project Mathematics! website as streaming video. Selected video segments of the remaining 6 modules are also available for free viewing.
totaling $3.1 million. The animation sequences were done on a network of computers donated by Hewlett-Packard. Free distribution of some of the modules was provided by a grant from Intel.
Overview
The video modules cover geometryGeometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
and include a history of Mathematics and examples of how math is used in real world applications. The modules were produced by Dr. Tom M. Apostol
Tom M. Apostol
Tom Mike Apostol is a Greek-American analytic number theorist and professor at the California Institute of Technology.He was born in Helper, Utah in 1923. His parents, Emmanouil Apostolopoulos and Efrosini Papathanasopoulos, originated from Greece. Mr...
at the California Institute of Technology
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
. The series uses computer animation
Computer animation
Computer animation is the process used for generating animated images by using computer graphics. The more general term computer generated imagery encompasses both static scenes and dynamic images, while computer animation only refers to moving images....
, created by Dr. James F. Blinn, to visually depict the principles being discussed. Approximately 140,000 of the tapes and DVDs were sent to educational institutions and have been viewed by about 10,000,000 people worldwide over the last 20 years.
Similarity
Discusses how scaling objects does not change their shape and how angles stay the same. Also shows how ratios change for perimeters, areas and volumes.The Theorem of Pythagoras
Explains the Pythagorean theoremPythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
. Visually shows the dissection proof to show how the theorem works in real life.
The Story of Pi
This module shows how piPi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
was determined and its history. Multiple animations show various ways to determine pi.
Sines and Cosines, Part I (Waves)
Visually depicts how sineSine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....
s and cosines are related to waves and a unit circle
Unit circle
In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, "the" unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system in the Euclidean plane...
. Also reviews their relationship to the ratios of side lengths of right triangle
Right triangle
A right triangle or right-angled triangle is a triangle in which one angle is a right angle . The relation between the sides and angles of a right triangle is the basis for trigonometry.-Terminology:The side opposite the right angle is called the hypotenuse...
s.
Sines and Cosines, Part II (Trigonometry)
Explains the law of sinesLaw of sines
In trigonometry, the law of sines is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles...
and cosines
Law of cosines
In trigonometry, the law of cosines relates the lengths of the sides of a plane triangle to the cosine of one of its angles. Using notation as in Fig...
how they relate to sides and angles of a triangle. The module also gives some real life examples of their use.
Sines and Cosines, Part III (Addition formulas)
Describes the addition formulas of sines and cosines and discusses the history of PtolemyPtolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
's Almagest
Almagest
The Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths. Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt,...
. Animation shows how sines and cosines relate to harmonic motion
Harmonic motion
Harmonic motion can mean:*The motion of a Harmonic oscillator , which can be:**Simple harmonic motion**Complex harmonic motion*Keplers laws of planetary motion...
.
Polynomials
How polynomialPolynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
s can approximate sines and cosines. Includes information about cubic splines in design engineering.
The Tunnel of Samos
How did the ancients dig the tunnel of Samos from two opposite sides of a mountain in 500 BC? And how were they able to meet under the mountain? Maybe they used geometry and trigonometry.Awards
Project Mathematics! has received numerous awards including the Gold Apple award in 1989 from the National Educational Film and Video Festival.Availability in different languages and formats
The videos have been translated in to Hebrew, Portuguese, French, and Spanish with the DVD version being both English and Spanish. PAL versions of the videos are available as well and efforts are underway to translate the materials in to Korean.The modules are available on a set of 9 videotapes or 3 DVDs. The videotapes may be freely copied for educational purposes with a few caveats. The DVD version is not freely reproducible.
The video segments for the first 3 modules can be viewed for free at the Project Mathematics! website as streaming video. Selected video segments of the remaining 6 modules are also available for free viewing.
Funding
The majority of the funding came from two grants from the National Science FoundationNational Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
totaling $3.1 million. The animation sequences were done on a network of computers donated by Hewlett-Packard. Free distribution of some of the modules was provided by a grant from Intel.