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Chinese Visual Proof of Pythagoras

Chinese Visual Proof of Pythagoras
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2015-01-24 18:57
TriangleCoordinate GeometryGeometric Construction
This interactive demonstration showcases an ancient Chinese geometric proof method, particularly a visual proof of the Pythagorean theorem. It involves key concepts such as the Pythagorean theorem and rotation. Using GeoGebra commands like Segment, Point, Polygon, Rotate, and Translate, the construction process of geometric figures is clearly demonstrated. Suitable for middle school and above students to learn geometric proofs and the Pythagorean theorem.

GeoGebra Commands & Parameters

  1. Segment((0, 0), (2.25, 0)) → r
  2. Segment((0, 1), (2.25, 1)) → s
  3. Segment((1.25, 0), (1.25, 1)) → b_1
  4. Segment((2.25, 0), (2.25, 1)) → c_1
  5. Point(Segment[B, C]) → E
  6. Polygon(E, B, Rotate[E, 1.5707963267948966, (0.5, 0.5)]) → polygon1, a, b, c
  7. Rotate(polygon1, 1.5707963267948966, (0.5, 0.5)) → polygon1'
  8. Rotate(polygon1', 1.5707963267948966, (0.5, 0.5)) → polygon1''
  9. Rotate(polygon1'', 1.5707963267948966, (0.5, 0.5)) → polygon1'''
  10. Polygon(E, Rotate[E, 1.5707963267948966, (0.5, 0.5)], Rotate[E, 3.141592653589793, (0.5, 0.5)], Rotate[E, 4.71238898038469, (0.5, 0.5)]) → polygon3, e, d, f, g
  11. Segment((1.25 + a, a), (2.25, 0)) → q
  12. Segment((0, 0), (0, 1)) → t
  13. Translate(c, (1.25, 0)) → c'
  14. Translate(polygon1, (1.25, -0.008489327809275027)) → polygon1'_1
  15. Translate(polygon1'', (0.25 + a, a)) → polygon1'''_1
  16. Translate(polygon1', (1.25 + a, 0)) → polygon1''_1
  17. Translate(polygon1''', (1.25, (-b))) → polygon2
  18. Polygon((1.25, 0), (1.25, a), (1.25 + a, a), (1.25 + a, 0)) → polygon4, h, i, j, k
  19. Polygon((1.25 + a, a), (1.25 + a, 1), (2.25, 1), (2.25, a)) → polygon5, l, m, n, p
  20. Segment((1, 0), (1, 1)) → a_1