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Pythagorean Theorem by Tessellation

Pythagorean Theorem by Tessellation
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2015-02-08 00:12
TriangleFunctionGeometric Construction
This example visually demonstrates the Pythagorean Theorem through tessellations, illustrating that the sum of the squares of the two legs of a right triangle equals the square of the hypotenuse. Core mathematical concepts include the Pythagorean Theorem, squares, and area calculations. It is constructed using GeoGebra commands/objects like Line, OrthogonalLine, Point, Segment, and Intersect. Suitable for middle school students and above to learn and understand the geometric meaning of the Pythagorean Theorem, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. OrthogonalLine(A, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Point(b) → D
  7. OrthogonalLine(D, b) → e
  8. Point(b) → E
  9. OrthogonalLine(E, b) → f
  10. Point(b) → F
  11. OrthogonalLine(F, b) → g
  12. Point(b) → G
  13. OrthogonalLine(G, b) → h
  14. Point(b) → H
  15. OrthogonalLine(H, b) → i
  16. Point(i) → I
  17. OrthogonalLine(I, i) → j
  18. Point(g) → J
  19. OrthogonalLine(J, g) → k
  20. Point(g) → K
  21. OrthogonalLine(K, g) → l
  22. Point(g) → L
  23. OrthogonalLine(L, g) → m
  24. Point(g) → M
  25. OrthogonalLine(M, g) → n
  26. Point(c) → N
  27. Point(b) → O
  28. Segment(N, O) → p
  29. Point(j) → P
  30. Segment(P, N) → q
  31. Point(a) → Q
  32. Point(d) → R
  33. Segment(Q, R) → r
  34. Point(b) → S
  35. Point(c) → T
  36. Segment(S, T) → s
  37. Point(c) → U
  38. Point(k) → V
  39. Segment(U, V) → t
  40. Point(a) → W
  41. Point(e) → Z
  42. Segment(W, Z) → a_1
  43. Point(a) → A_1
  44. Point(d) → B_1
  45. Segment(A_1, B_1) → b_1
  46. Point(a) → C_1
  47. Point(e) → D_1
  48. Segment(C_1, D_1) → c_1
  49. Point(d) → E_1
  50. Point(f) → F_1
  51. Segment(E_1, F_1) → d_1
  52. Point(j) → G_1
  53. Point(b) → H_1
  54. Segment(G_1, H_1) → e_1
  55. Point(b) → I_1
  56. Point(c) → J_1
  57. Segment(I_1, J_1) → f_1
  58. Point(c) → K_1
  59. Point(k) → L_1
  60. Segment(K_1, L_1) → g_1
  61. Point(j) → M_1
  62. Point(k) → N_1
  63. Segment(M_1, N_1) → h_1
  64. Point(d) → O_1
  65. Point(f) → P_1
  66. Segment(O_1, P_1) → i_1
  67. Point(e) → Q_1
  68. Point(g) → R_1
  69. Segment(Q_1, R_1) → j_1
  70. Point(f) → S_1
  71. Point(h) → T_1
  72. Segment(S_1, T_1) → k_1
  73. Point(g) → U_1
  74. Point(i) → V_1
  75. Segment(U_1, V_1) → l_1
  76. Point(h) → W_1
  77. Point(i) → Z_1
  78. Segment(W_1, Z_1) → m_1
  79. Point(b) → A_2
  80. Point(j) → B_2
  81. Segment(A_2, B_2) → n_1
  82. Point(c) → C_2
  83. Point(b) → D_2
  84. Segment(C_2, D_2) → p_1
  85. Point(b) → E_2
  86. Point(j) → F_2
  87. Segment(E_2, F_2) → q_1
  88. Point(c) → G_2
  89. Point(b) → H_2
  90. Segment(G_2, H_2) → r_1
  91. Point(b) → I_2
  92. Point(j) → J_2
  93. Segment(I_2, J_2) → s_1
  94. Point(c) → K_2
  95. Point(b) → L_2
  96. Segment(K_2, L_2) → t_1
  97. Point(b) → M_2
  98. Point(j) → N_2
  99. Segment(M_2, N_2) → a_2
  100. Point(c) → O_2
  101. Point(b) → P_2
  102. Segment(O_2, P_2) → b_2
  103. Point(k) → Q_2
  104. Point(c) → R_2
  105. Segment(Q_2, R_2) → c_2
  106. Point(e) → S_2
  107. Point(g) → T_2
  108. Segment(S_2, T_2) → d_2
  109. Point(f) → U_2
  110. Point(h) → V_2
  111. Segment(U_2, V_2) → e_2
  112. Point(g) → W_2
  113. Point(i) → Z_2
  114. Segment(W_2, Z_2) → f_2
  115. Point(c) → A_3
  116. Point(k) → B_3
  117. Segment(A_3, B_3) → g_2
  118. Point(h) → C_3
  119. Point(i) → D_3
  120. Segment(C_3, D_3) → h_2
  121. Point(k) → E_3
  122. Point(c) → F_3
  123. Segment(E_3, F_3) → i_2
  124. Point(g) → G_3
  125. Point(i) → H_3
  126. Segment(G_3, H_3) → j_2
  127. Point(h) → I_3
  128. Point(i) → J_3
  129. Segment(I_3, J_3) → k_2
  130. Point(k) → K_3
  131. Point(j) → L_3
  132. Segment(K_3, L_3) → l_2
  133. Point(k) → M_3
  134. Point(j) → N_3
  135. Segment(M_3, N_3) → m_2
  136. Point(f) → O_3
  137. Point(h) → P_3
  138. Segment(O_3, P_3) → n_2
  139. Point(k) → Q_3
  140. Point(c) → R_3
  141. Segment(Q_3, R_3) → p_2
  142. Point(e) → S_3
  143. Point(g) → T_3
  144. Segment(S_3, T_3) → q_2
  145. Point(j) → U_3
  146. Point(k) → V_3
  147. Segment(U_3, V_3) → r_2
  148. Point(f) → W_3
  149. Point(e) → Z_3
  150. Segment(W_3, Z_3) → s_2
  151. Point(d) → A_4
  152. Segment(A_4, Z_3) → t_2
  153. Point(a) → B_4
  154. Point(d) → C_4
  155. Segment(B_4, C_4) → a_3
  156. Point(a) → D_4
  157. Point(e) → E_4
  158. Segment(D_4, E_4) → b_3
  159. Point(l) → F_4
  160. Point(j) → G_4
  161. Segment(F_4, G_4) → c_3
  162. Point(a) → H_4
  163. Point(d) → I_4
  164. Segment(H_4, I_4) → d_3
  165. Point(a) → J_4
  166. Point(e) → K_4
  167. Segment(J_4, K_4) → e_3
  168. Point(k) → L_4
  169. Point(m) → M_4
  170. Segment(L_4, M_4) → f_3
  171. Point(d) → N_4
  172. Point(f) → O_4
  173. Segment(N_4, O_4) → g_3
  174. Point(l) → P_4
  175. Segment(P_4, N_1) → h_3
  176. Point(m) → Q_4
  177. Point(k) → R_4
  178. Segment(Q_4, R_4) → i_3
  179. Point(m) → S_4
  180. Point(k) → T_4
  181. Segment(S_4, T_4) → j_3
  182. Point(l) → U_4
  183. Segment(U_4, V_3) → k_3
  184. Point(m) → V_4
  185. Point(l) → W_4
  186. Segment(V_4, W_4) → l_3
  187. Point(e) → Z_4
  188. Point(g) → A_5
  189. Segment(Z_4, A_5) → m_3
  190. Point(k) → B_5
  191. Point(m) → C_5
  192. Segment(B_5, C_5) → n_3
  193. Point(f) → D_5
  194. Point(h) → E_5
  195. Segment(D_5, E_5) → p_3
  196. Point(l) → F_5
  197. Point(k) → G_5
  198. Segment(F_5, G_5) → q_3
  199. Point(g) → H_5
  200. Point(i) → I_5
  201. Segment(H_5, I_5) → r_3
  202. Point(l) → J_5
  203. Segment(J_5, K_3) → s_3
  204. Point(l) → K_5
  205. Point(k) → L_5
  206. Segment(K_5, L_5) → t_3
  207. Point(d_1) → M_5
  208. Point(d_1) → N_5
  209. Point(d_1) → O_5
  210. Point(k) → P_5
  211. Point(m) → Q_5
  212. Segment(P_5, Q_5) → a_4
  213. Point(f) → R_5
  214. Point(h) → S_5
  215. Segment(R_5, S_5) → b_4
  216. Point(g) → T_5
  217. Point(i) → U_5
  218. Segment(T_5, U_5) → c_4
  219. Point(m) → V_5
  220. Point(l) → W_5
  221. Segment(V_5, W_5) → d_4
  222. Point(l) → Z_5
  223. Segment(M_3, Z_5) → e_4
  224. Point(m) → A_6
  225. Segment(A_6, K_5) → f_4
  226. Point(h) → B_6
  227. Point(i) → C_6
  228. Segment(B_6, C_6) → g_4
  229. Point(h) → D_6
  230. Point(i) → E_6
  231. Segment(D_6, E_6) → h_4
  232. Point(m) → F_6
  233. Point(l) → G_6
  234. Segment(F_6, G_6) → i_4
  235. Point(m) → H_6
  236. Point(l) → I_6
  237. Segment(H_6, I_6) → j_4
  238. Point(e) → J_6
  239. Point(g) → K_6
  240. Segment(J_6, K_6) → k_4
  241. Point(d) → L_6
  242. Point(f) → M_6
  243. Segment(L_6, M_6) → l_4
  244. Point(a) → N_6
  245. Point(d) → O_6
  246. Segment(N_6, O_6) → m_4
  247. Point(a) → P_6
  248. Point(e) → Q_6
  249. Segment(P_6, Q_6) → n_4
  250. Point(d) → R_6
  251. Point(f) → S_6
  252. Segment(R_6, S_6) → p_4
  253. Point(l) → T_6
  254. Point(n) → U_6
  255. Segment(T_6, U_6) → q_4
  256. Point(n) → V_6
  257. Point(m) → W_6
  258. Segment(V_6, W_6) → r_4
  259. Point(n) → Z_6
  260. Point(m) → A_7
  261. Segment(Z_6, A_7) → s_4
  262. Point(m) → B_7
  263. Point(n) → C_7
  264. Segment(B_7, C_7) → t_4
  265. Point(l) → D_7
  266. Segment(D_7, A_7) → a_5
  267. Point(a) → E_7
  268. Point(d) → F_7
  269. Segment(E_7, F_7) → b_5
  270. Point(a) → G_7
  271. Point(e) → H_7
  272. Segment(G_7, H_7) → c_5
  273. Point(e) → I_7
  274. Point(g) → J_7
  275. Segment(I_7, J_7) → d_5
  276. Point(f) → K_7
  277. Point(h) → L_7
  278. Segment(K_7, L_7) → e_5
  279. Point(g) → M_7
  280. Point(i) → N_7
  281. Segment(M_7, N_7) → f_5
  282. Point(h) → O_7
  283. Point(i) → P_7
  284. Segment(O_7, P_7) → g_5
  285. Point(n) → Q_7
  286. Segment(Q_7, V_5) → h_5
  287. Point(n) → R_7
  288. Segment(R_7, F_6) → i_5
  289. Point(n) → S_7
  290. Segment(S_7, H_6) → j_5
  291. Point(n) → T_7
  292. Segment(T_7, V_4) → k_5
  293. Point(m) → U_7
  294. Point(n) → V_7
  295. Segment(U_7, V_7) → l_5
  296. Point(m) → W_7
  297. Point(n) → Z_7
  298. Segment(W_7, Z_7) → m_5
  299. Point(m) → A_8
  300. Point(n) → B_8
  301. Segment(A_8, B_8) → n_5
  302. Point(m) → C_8
  303. Point(n) → D_8
  304. Segment(C_8, D_8) → p_5
  305. Point(j) → E_8
  306. Segment(E_8, G_5) → q_5
  307. Segment(G_7, F_8) → r_5
  308. Segment(G_7, B) → s_5
  309. Segment(B, H) → t_5
  310. Point(n) → G_8
  311. Segment(H, G_8) → a_6
  312. Segment(F_8, G_8) → b_6
  313. Segment(R_6, C) → c_6
  314. Segment(J_6, D) → d_6
  315. Segment(S_6, E) → e_6
  316. Segment(K_6, F) → f_6
  317. Segment(D_6, G) → g_6
  318. Point(c) → H_8
  319. Segment(H_8, A) → h_6
  320. Point(j) → I_8
  321. Segment(I_8, I) → i_6
  322. Intersect(i, k) → J_8
  323. Intersect(a, k) → K_8
  324. Segment(J_8, K_8) → j_6
  325. Intersect(a, l) → L_8
  326. Intersect(i, l) → M_8
  327. Segment(L_8, M_8) → k_6
  328. Intersect(h, n) → N_8
  329. Segment(N_8, D_6) → l_6
  330. Segment(M, K_6) → m_6
  331. Intersect(f, n) → O_8
  332. Segment(O_8, S_6) → n_6
  333. Intersect(i, m) → P_8
  334. Intersect(a, m) → Q_8
  335. Segment(P_8, Q_8) → p_6
  336. Intersect(d, n) → R_8
  337. Segment(R_8, R_6) → q_6
  338. Intersect(e, n) → S_8
  339. Segment(S_8, J_6) → r_6

AI Drawing Prompt Reference

Draw a right triangle and tessellate it infinitely by drawing orthogonal lines around its hypotenuse, forming a geometric pattern. Start by drawing the two legs of the right triangle, then draw orthogonal lines from each vertex, and continue to draw new points and lines on these orthogonal lines to form a grid-like pattern.
The prompt above was compiled from the original drawing commands and is for reference only.