Dihedral Kaleidoscopes

Synopsis

A dihedral kaleidoscope is formed by two plane mirrors intersecting at an angle pi/n. When an object is placed before the mirrors of such a kaleidoscope, 2n objects are seen: the original and 2n-1 reflections. This illustrates the fact that a dihedral kaleidoscope generates, by two reflections, a group order of 2n. Accordingly, the group is called the nth dihedral group. The film discusses the special cases for n=1,2,3,4, makes some observations in the general case and proceeds to the limiting case in which two mirrors are parallel. Dihedral kaleidoscopes are then used to show some regular figures and their stellations. Finally, three mirrors are placed to form a dihedral kaleidoscope which can be used to produce an infinite variety of symmetric patterns.

Language

English

Country

United States

Medium

Video; Videocassette. VHS. col. 13 min.

Year of production

1973

Availability

Out of Distribution

Uses

Elementary courses in finite group theory.*

Subjects

Mathematics

Keywords

kaleidoscopes; symmetry

Credits

Contributor

H S M Coxeter

Production Company

Name

College Geometry Project

Sponsor

Name

International Film Bureau

Name

USA

Distributor

Name

Patterson (Edward) Associates

Phone

01303 264195

Fax

01303 264195

Address

Treetops
Cannongate Road
HYTHE
Kent
CT21 5PT