3D Twist-Hinged Dissection of Triangular Prisms

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This Demonstration shows a twist-hinged dissection of triangular prisms consistent with the Pythagorean relation . There are three equilateral triangles, one large one at the beginning and two smaller ones at the end. An equilateral triangle with side has area . The three equilateral triangles have side lengths 3, 4 and 5. (Check "show points" to verify this.) The dissection shows that the sum of the areas of the two smaller equilateral triangles equals the area of the larger triangle. Eliminating the factor from the equation gives .

Contributed by: Izidor Hafner (October 18)
Open content licensed under CC BY-NC-SA



[1] G. N. Frederickson, Hinged Dissections: Swinging & Twisting, New York: Cambridge University Press, 2002 p. 240. www.cs.purdue.edu/homes/gnf/book2.html.


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