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Parameterized Visual Proof of the Pythagorean Theorem
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A visual proof of the Pythagorean Theorem using a variety of right triangles. Parameterized OpenSCAD file included.
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Model information
- Source
- Printables
- Category
- Math
- License
- Creative Commons — Public Domain
Tiles for exploring the Pythagorean theorem and binomial expansion. Based on the algebraic proofs from Wikipedia.
- Put the A,B, and C squares against one copy of the ABC triangle to see that the sizes are the same.
- Show that the A^2 + B^2 = C^2 by showing that either the C*C square or the A*A and B*B squares fit in the (A+B)*(A+B) frame with four copies of the right triangle.
- Also shows the expansion of (a+b) * (a+b) = a^2 + 2ab + b^2.
- Different triangle ratios are included, allowing students to see that the relationship holds for any right triangle.
- 15-75-90
- 30-60-90
- 45-45-90,
- 3-4-5 (side ratio)
- By holding A+B constant, the different sets build intuition about the relative impact of a and b as the triangle ratio changes.
There are two sets sized by the dimension of A+B.
- 75mm - can be printed on a single MK3/MK4 build plate
- 150mm - needs to be split into to two prints
The OpenSCAD file is included. It is fully parameterized, allowing anyone to adjust the total size, thickness, tolerance, font, and other parameters of the design and generate their own models.