A Twist-Hinged Dissection of Triangles

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This Demonstration shows a twist-hinged dissection of triangles showing that . The three main triangles pictured are equilateral. An equilateral triangle with side length
has area
, and the lengths of the sides of the three main triangles (check "show points" to see this) have side lengths 3, 4, and 5. The dissection shows that the sum of the areas of the two smaller triangles is equal to the area of the larger triangle. When you eliminate the factor
from the equation, you obtain
.
Contributed by: Izidor Hafner (September 2013)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Reference
[1] G. N. Frederickson, Hinged Dissections: Swinging & Twisting, New York: Cambridge University Press, 2002 p. 240.
Permanent Citation
"A Twist-Hinged Dissection of Triangles"
http://demonstrations.wolfram.com/ATwistHingedDissectionOfTriangles/
Wolfram Demonstrations Project
Published: September 30 2013