MathPlotAI Logo MathPlotAI

Pythagoras's Tree

Pythagoras's Tree
Loading the math board and drawing, please wait…
2022-06-22 20:46
TrianglePolygonTrigonometryMatrix
This example demonstrates the construction and growth process of Pythagoras's Tree, a fractal geometry figure. Core mathematical concepts include the Pythagorean theorem, polygon construction, matrix transformations, and trigonometry. The construction leverages commands like Polygon and objects such as A, B, poly1, f, g, h, i, C, D, q1, q2, t1, α, E, q3, q4, t2, F, H, I, J, K, q5, q6, t3, L, M, N, O, P, q7, q8, t4, Q, R, S, T, U, q9, q10 for complex geometric transformations. It is suitable for high school and above students to understand fractal geometry, matrix transformations, and dynamic geometry drawing.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. pytha(D, C, α) → E, q3, q4, t2, F, H, I, J
  3. pytha(E, J, α) → K, q5, q6, t3, L, M, N, O
  4. pytha(I, H, α) → P, q7, q8, t4, Q, R, S, T
  5. pytha(K, O, α) → U, q9, q10, t5, V, W, Z, A_1
  6. pytha(N, M, α) → B_1, q11, q12, t6, C_1, D_1, E_1, F_1
  7. pytha(P, T, α) → G_1, q13, q14, t7, H_1, I_1, J_1, K_1
  8. pytha(S, R, α) → L_1, q15, q16, t8, M_1, N_1, O_1, P_1
  9. pytha(U, A_1, α) → G, q17, q18, t9, Q_1, R_1, S_1, T_1
  10. pytha(Z, W, α) → U_1, q19, q20, t10, V_1, W_1, Z_1, A_2
  11. pytha(B_1, F_1, α) → B_2, q21, q22, t11, C_2, D_2, E_2, F_2
  12. pytha(E_1, D_1, α) → G_2, q23, q24, t12, H_2, I_2, J_2, K_2
  13. pytha(G_1, K_1, α) → L_2, q25, q26, t13, M_2, N_2, O_2, P_2
  14. pytha(J_1, I_1, α) → Q_2, q27, q28, t14, R_2, S_2, T_2, U_2
  15. pytha(L_1, P_1, α) → V_2, q29, q30, t15, W_2, Z_2, A_3, B_3
  16. pytha(O_1, N_1, α) → C_3, q31, q32, t16, D_3, E_3, F_3, G_3
  17. pytha(V_2, B_3, 45°) → H_3, q33, q34, t17, I_3, J_3, K_3, L_3
  18. pytha(A_3, Z_2, 45°) → M_3, q35, q36, t18, N_3, O_3, P_3, Q_3
  19. pytha(C_3, G_3, 45°) → R_3, q37, q38, t19, S_3, T_3, U_3, V_3
  20. pytha(F_3, E_3, 45°) → W_3, q39, q40, t20, Z_3, A_4, B_4, C_4
  21. pytha(G, T_1, 45°) → D_4, q41, q42, t21, E_4, F_4, G_4, H_4
  22. pytha(S_1, R_1, 45°) → I_4, q43, q44, t22, J_4, K_4, L_4, M_4
  23. pytha(U_1, A_2, 45°) → N_4, q45, q46, t23, O_4, P_4, Q_4, R_4
  24. pytha(Z_1, W_1, 45°) → S_4, q47, q48, t24, T_4, U_4, V_4, W_4
  25. pytha(B_2, F_2, 45°) → Z_4, q49, q50, t25, A_5, B_5, C_5, D_5
  26. pytha(E_2, D_2, 45°) → E_5, q51, q52, t26, F_5, G_5, H_5, I_5
  27. pytha(G_2, K_2, 45°) → J_5, q53, q54, t27, K_5, L_5, M_5, N_5
  28. pytha(T_2, S_2, 45°) → T_5, q57, q58, t29, U_5, V_5, W_5, Z_5
  29. pytha(Q_2, U_2, 45°) → A_6, q59, q60, t30, B_6, C_6, D_6, E_6
  30. pytha(O_2, N_2, 45°) → F_6, q61, q62, t31, G_6, H_6, I_6, J_6
  31. pytha(L_2, P_2, 45°) → K_6, q63, q64, t32, L_6, M_6, N_6, O_6
  32. pytha(J_2, I_2, 45°) → O_5, q55, q56, t28, P_5, Q_5, R_5, S_5

AI Drawing Prompt Reference

Draw a fractal tree made of multiple right triangles, where each triangle's right angle side coincides with the hypotenuse of the previous triangle, with a rotation of 45 degrees. Start by drawing a right triangle, then continue to draw new right triangles from the right angle vertex of the previous triangle, rotating 45 degrees each time, until a complex fractal structure is formed.
The prompt above was compiled from the original drawing commands and is for reference only.