Proofs of the Pythagorean Theorem

Brad Ballinger, 3 Oct 2017

This book contains a few visual proofs of the Pythagorean Theorem. I'll continue adding to it. As you play with each applet, try to (1) describe what's going, and (2) explain what conclusions we can draw from it. If you have a hard time with one of these pages, please let me know so that I can improve it. If you want to know more about shear transformations, try [url]https://www.geogebra.org/m/yZQNWxs6[/url].

Table of Contents

  1. Proofs by Moving Pieces
    1. Pythagorean Theorem by Scooting
    2. Dissection Demo
    3. Cracked Domino Proof of the Pythagorean Theorem
  2. Proofs by Transforming Pieces
    1. Pythagorean Theorem via Shear Transformation
    2. Second Proof of Pythagorean Theorem by Shear Transformation
    3. Euclid's Proof
    4. Pythagorean Theorem by Scaling
  3. Computational Proofs
    1. Pythagorean Theorem via Similar Triangles
    2. President Garfield's Proof
    3. Power Of A Point

1.

Proofs by Moving Pieces

  • 1. Pythagorean Theorem by Scooting
  • 2. Dissection Demo
  • 3. Cracked Domino Proof of the Pythagorean Theorem

1.1.

Pythagorean Theorem by Scooting

When you first see the green square: what is its area?
At the end of the transformation: what is the green area?
Area there any other areas you can compute along the way?
– Brad Ballinger

1.2.

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1.3.

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2.

Proofs by Transforming Pieces

  • 1. Pythagorean Theorem via Shear Transformation
  • 2. Second Proof of Pythagorean Theorem by Shear Transformation
  • 3. Euclid's Proof
  • 4. Pythagorean Theorem by Scaling

2.1.

Pythagorean Theorem via Shear Transformation

Proof by shear transformation:
– Brad Ballinger

2.2.

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2.3.

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2.4.

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3.

Computational Proofs

  • 1. Pythagorean Theorem via Similar Triangles
  • 2. President Garfield's Proof
  • 3. Power Of A Point

3.1.

Pythagorean Theorem via Similar Triangles

Proof by similar triangle area:
– Brad Ballinger

3.2.

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3.3.

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