| Project Mathematics! | |
|---|---|
| Also known as | Project MATHEMATICS! |
| Genre | Educational |
| Created by | Tom M. Apostol |
| Written by | Benedict Freedman |
| Directed by | Tom M. Apostol |
| Narrated by | Al Hibbs Susan Gray Davis |
| Country of origin | United States |
| Original language | English |
| No. of seasons | 1 |
| No. of episodes | 9 |
| Production | |
| Producer | Tom M. Apostol |
| Production locations | Pasadena, California, US |
| Editor | Robert Lattanzio |
| Running time | 19–30 minutes |
| Production company | California Institute of Technology |
| Original release | |
| Network | PBS,NASA TV |
| Release | 1988 (1988) – 2000 (2000) |
| Related | |
| The Mechanical Universe | |
Project Mathematics! (stylized asProject MATHEMATICS!), is a series of educational video modules and accompanying workbooks for teachers, developed at theCalifornia Institute of Technology to help teach basic principles of mathematics to high school students.[1] In 2017, the entire series of videos was made available onYouTube.
TheProject Mathematics! series of videos is a teaching aid for teachers to help students understand the basics ofgeometry andtrigonometry. The series was developed byTom M. Apostol andJames F. Blinn, both from theCalifornia Institute of Technology. Apostol led the production of the series, while Blinn provided thecomputer animation used to depict the ideas beings discussed. Blinn mentioned that part of his inspiration was theBell Lab Science Series of films from the 1950s.[2]
The material was designed for teachers to use in their curriculums and was aimed at grades 8 through 13. Workbooks are also available to accompany the videos and to assist teachers in presenting the material to their students. The videos are distributed as either 9 VHS videotapes or 3 DVDs, and include a history of mathematics and examples of how math is used in real world applications.[3]
A total of nine educational video modules were created between 1988 and 2000. Another two modules,Teachers Workshop andProject MATHEMATICS! Contest, were created in 1991 for teachers and are only available on videotape. The content of the nine educational modules follows below.
In 1988,The Theorem of Pythagoras was the first video produced by the series and reviews thePythagorean theorem.[4] For allright triangles, the square of thehypotenuse is equal to the sum of the squares of the other two sides (a2 + b2 = c2). Thetheorem is named afterPythagoras of ancient Greece.Pythagorean triples occur when all three sides of a right triangle areintegers such as a = 3, b = 4 and c = 5. Aclay tablet shows that theBabylonians knew of Pythagorean triples 1200 years before Pythagoras, but nobody knows if they knew the more-general Pythagorean theorem. TheChinese proof uses four similar triangles to prove the theorem.
Today, we know of the Pythagorean theorem because ofEuclid's Elements, a set of 13 books on mathematics—from around 300BCE—and the knowledge it contained has been used for more than 2000 years.Euclid's proof is described in book 1, proposition 47 and uses the idea of equal areas along withshearing androtating triangles. In thedissection proof, the square of the hypotenuse is cut into pieces to fit into the other two squares. Proposition 31 in book 6 of Euclid's Elements describes thesimilarity proof, which states that the squares of each side can be replaced by shapes that aresimilar to each other and the proof still works.
The second module created wasThe Story of Pi, in 1989, and describes the mathematical constantpi and its history.[5] The first letter in the Greek word for "perimeter" (περίμετρος) isπ, known in English as "pi". Pi is theratio of acircle'scircumference to itsdiameter and is roughly equal to 3.14159. The circumference of a circle is and its area is. Thevolume andsurface area of acylinder,conesphere andtorus are calculated using pi. Pi is also used in calculating planetary orbit times,gaussian curves and alternating current. Incalculus, there areinfinite series that involve pi and pi is used intrigonometry. Ancient cultures used different approximations for pi. The Babylonian's used and theEgyptians used.
Pi is afundamental constant of nature.Archimedes discovered that the area of the circle equals the square of itsradius times pi. Archimedes was the first to accurately calculate pi by usingpolygons with 96 sides both inside and outside a circle then measuring the line segments and finding that pi was between and. A Chinese calculation used polygons with 3,000 sides and calculated pi accurately to fivedecimal places. The Chinese also found that was an accurate estimate of pi to within 6 decimal places and was the most accurate estimate for 1,000 years untilarabic numerals were used forarithmetic.
By the end of the 19th century,formulas were discovered to calculate pi without the need for geometric diagrams. These formulas used infinite series andtrigonometric functions to calculate pi to hundreds of decimal places. Computers were used in the 20th century to calculate pi and its value was known to one billion decimals places by 1989. One reason to accurately calculate pi is to test the performance of computers. Another reason is to determine if pi is a specificfraction, which is a ratio of twointegers called arational number that has a repeating pattern ofdigits when expressed in decimal form. In the 18th century,Johann Lambert found that pi cannot be a ratio and is therefore anirrational number. Pi shows up in many areas having no obvious connection to circles. For example; the fraction of points on alattice viewable from an origin point is equal to.
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.[6]
Visually depicts howsines and cosines are related to waves and aunit circle. Also reviews their relationship to the ratios of side lengths ofright triangles.
Explains thelaw of sines andcosines how they relate to sides and angles of a triangle. The module also gives some real life examples of their use.[7]
Describes theaddition formulas of sines and cosines and discusses the history ofPtolemy'sAlmagest. It also goes into details ofPtolemy's Theorem. Animation shows how sines and cosines relate toharmonic motion.
Howpolynomials can approximate sines and cosines. Includes information aboutcubic splines in design engineering.[8]
How did the ancients dig theTunnel of Samos from two opposite sides of a mountain in 500BCE? And how were they able to meet under the mountain? Maybe they used geometry and trigonometry.[9][10]
Reviews some of the major developments in mathematical history.
TheProject Mathematics! series was created and directed by Tom M. Apostol and James F. Blinn, both from the California Institute of Technology. The project was originally titledMathematica but was changed to avoid confusion with themathematics software package.[11] A total of four full-time employees and four part-time employees produce the episodes with help from several volunteers.[3] Each episode took between four and five months to produce.[12] Blinn headed the creation of the computer animation used in each episode, which was done on a network of computers donated by Hewlett-Packard.[12][13]
The majority of the funding came from two grants from theNational Science Foundation totaling $3.1 million.[12][14][15][16][17] Free distribution of some of the modules was provided by a grant from Intel.[13][18]
 | This section needs to beupdated. Please help update this article to reflect recent events or newly available information.(July 2017) |
Project Mathematics! video tapes, DVDs and workbooks are primarily distributed to teachers through the California Institute of Technology bookstore and were popular to a standard that the bookstore hired an extra person just for processing orders of the series.[12] An estimated 140,000 of the tapes and DVDs were sent to educational institutions around the world, and have been viewed by approximately 10 million people until 2003.[when?][19]
The series is also distributed through theMathematical Association of America andNASA's Central Operation of Resources for Educators (CORE).[20] In addition, over half of the states in the US have received master copies of the videotapes so they can produce and distribute copies to their various educational institutions.[12][21] The videotapes may be freely copied for educational purposes with a few restrictions, but the DVD version is not freely reproducible.[20]
The video segments for the first 3 modules can be viewed for free at theProject Mathematics! website as streaming video. Selected video segments of the remaining 6 modules are also available for free viewing.
In 2017, Caltech made the entirety of the series, as well as threeSIGGRAPH demo videos, available onYouTube.[22]
The videos have been translated into Hebrew, Portuguese, French, and Spanish with the DVD version being both English and Spanish.[23] PAL versions of the videos are available as well and efforts are underway to translate the materials into Korean.[13]
All of the following were published by the California Institute of Technology:
Project Mathematics! has received numerous awards including the Gold Apple award in 1989 from the National Educational Film and Video Festival.[24]
| This section needs to beupdated. Please help update this article to reflect recent events or newly available information.(July 2017) |
A web-based version of the materials was funded by a third grant from the National Science Foundation and was in phase 1, as of 2010[update].[26]
Borwein, Jonathan M. (2002) [2002]. Jonathan M. Borwein (ed.).Multimedia tools for communicating Mathematics, Volume 1. Vol. 1 (illustrated ed.). Springer. p. 1.ISBN 978-3-540-42450-5.OCLC 50598138. RetrievedAugust 20, 2010.