Geometric Model by A. Harry Wheeler, Square Transformable into a Square and Two Rectangles, Plane Dissection

Object Details

Wheeler, Albert Harry

Description

The hinged dissection has three hinged pieces (two of the triangles and the small square are glued together). They may be arranged as a large square or as two rectangles and a smaller square. If the side of the large square is c and the sides of the triangles are a and b (a longer than b), then the area of the small square is (a-b)². The area of each of the four triangles is 1/2ab. Hence c² = (a-b)² + 4(1/2)ab. Hence c² = a² + b², as the Pythagorean theorem would indicate. The model resembles Wheeler's 6SI (square into gnommon), but has only five pieces and is quite different from MA.304723.763, which is labeled as an example of that model.

Location

Currently not on view

Credit Line

Gift of Helen M. Wheeler

ID Number

MA.304723.767

catalog number

304723.767

accession number

304723

Object Name

geometric model

Physical Description

plastic (overall material)

wood (overall material)

metal (overall material)

gold (overall color)

red (overall color)

black (overall color)

green (overall color)

yellow (overall color)

cut, glued and hinged (overall production method/technique)

Measurements

average spatial: 1.3 cm x 15.6 cm x 15.6 cm; 1/2 in x 6 5/32 in x 6 5/32 in

place made

United States: Massachusetts, Worcester

See more items in

Medicine and Science: Mathematics

Science & Mathematics

Plane Dissections

National Museum of American History

Subject

Mathematics

Record ID

nmah_1074343

Metadata Usage (text)

CC0

GUID (Link to Original Record)

https://n2t.net/ark:/65665/ng49ca746a9-38db-704b-e053-15f76fa0b4fa