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Spiral of Pythagoras

Spiral of Pythagoras
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2015-08-02 10:12
TriangleCoordinate GeometryGeometric Construction
In collections Arithmetic Operations (preGED)
This example demonstrates the construction of the Spiral of Pythagoras, using a custom tool to create a series of right triangles. Key mathematical concepts include the Pythagorean Theorem and roots. It utilizes commands like Segment, OrthogonalLine, Circle, and Intersect in GeoGebra. Suitable for middle school and above students to learn geometric construction and the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → seg1
  2. OrthogonalLine(B, seg1) → line1
  3. Circle(B, 1) → cir1
  4. Intersect(cir1, line1, 2) → C
  5. Segment(B, C) → seg2
  6. Segment(A, C) → seg3
  7. Tool1(A, C) → a, c, b, D, d, e
  8. Tool1(A, D) → f, g, h, E, i, j
  9. Tool1(A, E) → k, p, l, F, m, n
  10. Tool1(A, F) → q, r, s, G, t, a_1
  11. Tool1(A, G) → b_1, c_1, d_1, H, e_1, f_1
  12. Tool1(A, H) → g_1, h_1, i_1, I, j_1, k_1
  13. Tool1(A, I) → l_1, p_1, m_1, J, n_1, q_1
  14. Tool1(A, J) → r_1, s_1, t_1, K, a_2, b_2
  15. Tool1(A, K) → c_2, d_2, e_2, L, f_2, g_2
  16. Tool1(A, L) → h_2, k_2, i_2, M, j_2, l_2
  17. Tool1(A, M) → m_2, p_2, n_2, N, q_2, r_2
  18. Tool1(A, N) → s_2, t_2, a_3, O, b_3, c_3
  19. SurdText(a) → a_{text}
  20. SurdText(e) → e_{text}
  21. SurdText(j) → j_{text}
  22. SurdText(n) → n_{text}
  23. SurdText(a_1) → n_{1text}
  24. SurdText(f_1) → f_{1text}
  25. SurdText(q_1) → q_{1text}
  26. SurdText(b_2) → b_{2text}
  27. SurdText(g_2) → g_{2text}
  28. SurdText(r_2) → r_{2text}
  29. SurdText(c_3) → c_{3text}
  30. TableText({Sequence["\sqrt{" + (k) + "} = " + (sqrt(k)), k, 1, 14]}, "v") → table1

AI Drawing Prompt Reference

Start with a segment. At one endpoint, draw a perpendicular line and mark a point one unit away, then connect it to the other endpoint to form the first right triangle. Repeat this process: for each new hypotenuse, construct a perpendicular at its outer endpoint, mark a unit point, and connect back to the common starting vertex, creating a spiral of right triangles. Each hypotenuse length corresponds to sqrt(2), sqrt(3), sqrt(4), etc., and these radical values are displayed as text near the corresponding sides. Additionally, include a table listing the equalities from sqrt(1) to sqrt(14).
The prompt above was compiled from the original drawing commands and is for reference only.