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在竖直数轴上探索整数

在竖直数轴上探索整数
几何画板及绘图内容加载中，请稍等……
2020-12-07 01:34
数列解析几何滑块动画函数图像
该范例在竖直数轴上动态展示整数的分布与运算，通过可视化方式帮助学生理解正负数、数轴方向及整数序列。核心数学概念包括整数、数轴、序列与数列，以及数轴上的点与线段关系。作图要点：使用GeoGebra的Line、Point、Segment、Sequence等命令构建数轴和整数点，通过Dilate、Mirror、Rotate等变换操作生成对称或旋转图形，利用Textfield和Random实现交互输入与随机生成，结合PolyLine和Text标注数值。适合小学高年级至初中阶段学习整数概念、数轴应用及序列规律的课堂演示或自主探索。

GeoGebra 命令及参数

  1. Line(A_2, A_1) → c
  2. Point(c) → P_0
  3. Dilate(B_1, 1 / brPodjela, A_1) → B_p
  4. Point(Circle[A, a]) → B
  5. Segment(A, B) → b
  6. Sequence(Segment[Translate[A_2, Vector[(i * Vector[A_1, B_p])]], Translate[A_1, Vector[(i * Vector[A_1, B_p])]]], i, 1, brPodjela - 1) → lista1
  7. Line(B_2, B_1) → d
  8. Point(c) → C_1
  9. Point(c) → C_2
  10. Point(d) → D_1
  11. Point(d) → D_2
  12. Dilate(D_1, 1 / brPodjela, C_1) → D_p
  13. Sequence(Segment[Translate[C_2, Vector[(i * Vector[C_1, D_p])]], Translate[C_1, Vector[(i * Vector[C_1, D_p])]]], i, 1, brPodjela - 1) → lista2
  14. Line(B_p, D_p) → e
  15. Point(e) → C
  16. Line(C, yAxis) → f
  17. Point(f) → D
  18. Circle(D, C) → g
  19. Mirror(C, D) → C'
  20. CircleSector(D, C, C') → h
  21. CircleSector(D, C', C) → k
  22. Segment(A_1, B_1) → i
  23. Point(i) → E
  24. Line(E, xAxis) → j
  25. Intersect(f, c) → F
  26. Intersect(f, j) → G
  27. Line(H, yAxis) → l
  28. Intersect(l, c) → I
  29. Intersect(l, j) → J
  30. Polygon(F, I, J, G) → mnogokut1, f_1, i_1, j_1, g_1
  31. Line(K, yAxis) → m
  32. Segment(C_2, D_2) → n
  33. Point(n) → L
  34. Line(L, xAxis) → p
  35. Intersect(p, f) → M
  36. Intersect(m, p) → N
  37. Intersect(m, c) → O
  38. Polygon(O, F, M, N) → mnogokut2, o, f_2, m_1, n_1
  39. Segment(A_1, C_2) → q
  40. Segment(B_1, D_2) → r
  41. Segment(E, G) → s
  42. Segment(L, M) → t
  43. Segment(A_2, P_0) → a_1
  44. Segment(R_1, P_1) → b_1
  45. Segment(R_2, P_2) → c_1
  46. Segment(R_3, P_3) → d_1
  47. Segment(R_4, P_4) → e_1
  48. Segment(R_5, P_5) → h_1
  49. Segment(R_6, P_6) → k_1
  50. Segment(R_7, P_7) → l_1
  51. Segment(B_2, P_8) → p_1
  52. Point(c) → Q_0
  53. Segment(Q_8, D_1) → q_1
  54. Segment(Q_7, T_7) → r_1
  55. Segment(Q_6, T_6) → s_1
  56. Segment(Q_5, T_5) → t_1
  57. Segment(Q_4, T_4) → a_2
  58. Segment(Q_3, T_3) → b_2
  59. Segment(Q_2, T_2) → c_2
  60. Segment(Q_1, T_1) → d_2
  61. Segment(Q_0, C_1) → e_2
  62. Segment(F, C') → g_2
  63. Point(i) → P
  64. Point(i) → Q
  65. Point(n) → R
  66. Point(n) → S
  67. Intersect(c, l) → T
  68. Intersect(c, m) → U
  69. Segment(U, T) → h_2
  70. Midpoint(h_2) → V
  71. Segment(V, T) → i_2
  72. Midpoint(i_2) → W
  73. Segment(V, U) → j_2
  74. Midpoint(j_2) → Z
  75. Line(R, xAxis) → k_2
  76. Line(Z, yAxis) → l_2
  77. Intersect(m, k_2) → E_1
  78. Intersect(l_2, k_2) → F_1
  79. Polygon(U, Z, F_1, E_1) → mnogokut3, u_1, z, f_3, e_3
  80. Segment(R, F_1) → m_2
  81. Line(Q, xAxis) → n_2
  82. Line(V, yAxis) → p_2
  83. Intersect(n_2, p_2) → G_1
  84. Intersect(n_2, l_2) → H_1
  85. Polygon(V, G_1, H_1, Z) → mnogokut4, v, g_3, h_3, z_1
  86. Segment(Q, H_1) → q_2
  87. Line(S, xAxis) → r_2
  88. Line(W, yAxis) → s_2
  89. Intersect(r_2, s_2) → I_1
  90. Intersect(r_2, p_2) → J_1
  91. Polygon(V, W, I_1, J_1) → mnogokut5, v_1, w, i_3, j_3
  92. Segment(S, I_1) → t_2
  93. Line(P, xAxis) → a_3
  94. Intersect(s_2, a_3) → K_1
  95. Intersect(a_3, l) → L_1
  96. Polygon(W, T, L_1, K_1) → mnogokut6, w_1, t_3, l_3, k_3
  97. Segment(P, K_1) → b_3
  98. Sequence(Random[-20, 20] + (0 * u), i, 1, 10) → Zad1SviBrojevi
  99. Unique(Zad1SviBrojevi) → Zad1Unique
  100. Shuffle(Zad1Unique) → Zad1Rnd, {-20, -9, 19, -8, 9, 18, 20, -1, 14}
  101. Sequence(Element[Zad1Rnd, i], i, 1, 4) → Zad1Odabrani
  102. Point(xAxis) → M_1
  103. Point(xAxis) → N_1
  104. Point(xAxis) → O_1
  105. Point(xAxis) → S_1
  106. Line(M_1, yAxis) → c_3
  107. Line(N_1, yAxis) → d_3
  108. Line(O_1, yAxis) → m_3
  109. Line(S_1, yAxis) → n_3
  110. Point(yAxis) → U_1
  111. Line(U_1, xAxis) → p_3
  112. Intersect(p_3, c_3) → V_1
  113. Intersect(p_3, d_3) → W_1
  114. Intersect(p_3, m_3) → Z_1
  115. Intersect(p_3, n_3) → E_2
  116. Circle(V_1, 1) → q_3
  117. Circle(W_1, 1) → r_3
  118. Circle(Z_1, 1) → s_3
  119. Circle(E_2, 1) → c_4
  120. OrthogonalLine(V_1, p_3) → a_4
  121. Intersect(q_3, a_4) → F_2, G_2
  122. Intersect(q_3, p_3) → H_2, I_2
  123. Polygon(F_2, I_2, 4) → mnogokut7, b_4, d_4, e_4, f_4, J_2, K_2
  124. Point(r_3) → L_2
  125. Rotate(L_2, 60°, W_1) → M_2
  126. Angle(L_2, W_1, M_2) → α
  127. Rotate(L_2, 300°, W_1) → N_2
  128. Angle(N_2, W_1, L_2) → β
  129. Polygon(N_2, M_2, 3) → mnogokut8, g_4, h_4, i_4, O_2
  130. Point(s_3) → S_2
  131. Rotate(S_2, 30°, Z_1) → U_2
  132. Angle(S_2, Z_1, U_2) → γ
  133. Rotate(S_2, 330°, Z_1) → V_2
  134. Angle(V_2, Z_1, S_2) → δ
  135. Polygon(V_2, U_2, 6) → mnogokut9, j_4, B_3, k_4, l_4, m_4, n_4, p_4, W_2, Z_2, A_3
  136. Point(c_4) → C_3
  137. Rotate(C_3, 60°, E_2) → D_3
  138. Rotate(C_3, 300°, E_2) → E_3
  139. Angle(E_3, E_2, C_3) → ε
  140. Polygon(E_3, D_3, 3) → mnogokut10, q_4, r_4, s_4, F_3
  141. Element(Zad1Odabrani, 1) → Zad1br1
  142. Element(Zad1Odabrani, 2) → Zad1br2
  143. Element(Zad1Odabrani, 3) → Zad1br3
  144. Element(Zad1Odabrani, 4) → Zad1br4
  145. If(Zad1br1 > Zad1br2, 1, 0) → Gscore_1
  146. If(Zad1br1 > Zad1br4, 1, 0) → Gscore_3
  147. If(Zad1br1 > Zad1br3, 1, 0) → Gscore_2
  148. If(Zad1br2 > Zad1br1, 1, 0) → Hscore_1
  149. If(Zad1br2 > Zad1br3, 1, 0) → Hscore_2
  150. If(Zad1br2 > Zad1br4, 1, 0) → Hscore_3
  151. If(Zad1br3 > Zad1br1, 1, 0) → Iscore_1
  152. If(Zad1br3 > Zad1br2, 1, 0) → Iscore_2
  153. If(Zad1br3 > Zad1br4, 1, 0) → Iscore_3
  154. If(Zad1br4 > Zad1br1, 1, 0) → Jscore_1
  155. If(Zad1br4 > Zad1br2, 1, 0) → Jscore_2
  156. If(Zad1br4 > Zad1br3, 1, 0) → Jscore_3
  157. If((abs(x(G_3) - x(V_1)) ≤ 0.1 ∨ abs(x(G_3) - x(W_1)) ≤ 0.1 ∨ abs(x(G_3) - x(Z_1)) ≤ 0.1 ∨ abs(x(G_3) - x(E_2)) ≤ 0.1) ∧ abs(y(G_3) - y(U_1)) ≤ 0.1, 1, 0) → GMoved
  158. If((abs(x(H_3) - x(V_1)) ≤ 0.1 ∨ abs(x(H_3) - x(W_1)) ≤ 0.1 ∨ abs(x(H_3) - x(Z_1)) ≤ 0.1 ∨ abs(x(H_3) - x(E_2)) ≤ 0.1) ∧ abs(y(H_3) - y(U_1)) ≤ 0.1, 1, 0) → HMoved
  159. If((abs(x(I_3) - x(V_1)) ≤ 0.1 ∨ abs(x(I_3) - x(W_1)) ≤ 0.1 ∨ abs(x(I_3) - x(Z_1)) ≤ 0.1 ∨ abs(x(I_3) - x(E_2)) ≤ 0.1) ∧ abs(y(I_3) - y(U_1)) ≤ 0.1, 1, 0) → IMoved
  160. If((abs(x(J_3) - x(V_1)) ≤ 0.1 ∨ abs(x(J_3) - x(W_1)) ≤ 0.1 ∨ abs(x(J_3) - x(Z_1)) ≤ 0.1 ∨ abs(x(J_3) - x(E_2)) ≤ 0.1) ∧ abs(y(J_3) - y(U_1)) ≤ 0.1, 1, 0) → JMoved
  161. If(abs(x(G_3) - GscoreTOT) ≤ 0.1 ∧ abs(y(G_3) - y(U_1)) ≤ 0.1, 1, 0) → GTrue
  162. If(abs(x(H_3) - HscoreTOT) ≤ 0.1 ∧ abs(y(H_3) - y(U_1)) ≤ 0.1, 1, 0) → HTrue
  163. If(abs(x(I_3) - IscoreTOT) ≤ 0.1 ∧ abs(y(I_3) - y(U_1)) ≤ 0.1, 1, 0) → ITrue
  164. If(abs(x(J_3) - JscoreTOT) ≤ 0.1 ∧ abs(y(J_3) - y(U_1)) ≤ 0.1, 1, 0) → JTrue
  165. If(GTrue ≟ 1 ∧ HTrue ≟ 1 ∧ ITrue ≟ 1 ∧ JTrue ≟ 1, "Excellent! The correct order!", "This is not the correct solution. Use the thermometer on the left for help.") → Zad1Provjera
  166. Element(Zad1Odabrani, 1) → Zad2br1
  167. Element(Zad1Odabrani, 2) → Zad2br2
  168. If(Zad2br1 > Zad2br2, 1, 0) → GreaterTrue
  169. If(Zad2br1 < Zad2br2, 1, 0) → LessTrue
  170. If(GreaterTrue ≟ 1 ∧ ClickedGreater ≟ 1 ∨ LessTrue ≟ 1 ∧ ClickedLess ≟ 1, "Excellent! You have compared numbers correctly.", "You didn't compare numbers correctly. Next time use the thermometer on the left for help.") → Zad2Provjera
  171. Textfield(Zad3Upisano) → txtPolje1
  172. Textfield(Zad4Upisano) → txtPolje2
  173. Textfield(Zad5Upisano) → txtPolje3
  174. Textfield(Zad6Upisano) → txtPolje4
  175. Random(0, 40) → promjKoordK
  176. Line(K_3, xAxis) → t_4
  177. Intersect(t_4, l) → L_3
  178. Intersect(t_4, m) → M_3
  179. Polygon(O, I, L_3, M_3) → mnogokut11, o_3, i_5, l_5, m_5
  180. Segment(L_3, K_3) → a_5
  181. Circle(D, C) → c_5
  182. Textfield(Zad7Upisano) → txtPolje5
  183. Dilate(O_3, 1 / brPodjela, N_3) → S_3
  184. Sequence(Segment[Translate[U_3, Vector[(i * Vector[N_3, S_3])]], Translate[N_3, Vector[(i * Vector[N_3, S_3])]]], i, 0, brPodjela) → lista3
  185. Sequence(Random[-20, 20] + (0 * u), i, 1, 8) → Zad8Brojevi
  186. Element(Zad8Brojevi, 1) → C1
  187. Element(Zad8Brojevi, 2) → C2
  188. Element(Zad8Brojevi, 3) → C3
  189. Element(Zad8Brojevi, 4) → C4
  190. Element(Zad8Brojevi, 5) → C5
  191. Element(Zad8Brojevi, 6) → C6
  192. Element(Zad8Brojevi, 7) → C7
  193. Element(Zad8Brojevi, 8) → C8
  194. PolyLine({V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4}) → b_5
  195. Line(O_3, xAxis) → d_5
  196. Line(N_3, xAxis) → e_5
  197. Point(xAxis) → F_4
  198. Line(F_4, yAxis) → f_5
  199. Intersect(f_5, d_5) → G_4
  200. Intersect(f_5, e_5) → H_4
  201. Polygon(N_3, H_4, G_4, O_3) → mnogokut12, n_5, h_5, g_5, o_4
  202. Line(L_4, xAxis) → q_5
  203. Intersect(q_5, h_5) → Z_4
  204. Segment(L_4, Z_4) → j_5
  205. Point(h_5) → U_4
  206. Line(U_4, xAxis) → k_5
  207. Intersect(k_5, o_4) → V_4
  208. Segment(V_4, U_4) → p_5
  209. Line(I_4, xAxis) → r_5
  210. Line(J_4, xAxis) → s_5
  211. Line(K_4, xAxis) → t_5
  212. Line(M_4, xAxis) → a_6
  213. Line(N_4, xAxis) → b_6
  214. Line(O_4, xAxis) → c_6
  215. Intersect(r_5, h_5) → W_4
  216. Intersect(s_5, h_5) → A_5
  217. Intersect(t_5, h_5) → B_5
  218. Intersect(a_6, h_5) → C_5
  219. Intersect(b_6, h_5) → D_5
  220. Intersect(c_6, h_5) → E_5
  221. Segment(I_4, W_4) → d_6
  222. Segment(J_4, A_5) → e_6
  223. Segment(K_4, B_5) → f_6
  224. Segment(M_4, C_5) → g_6
  225. Segment(N_4, D_5) → h_6
  226. Segment(O_4, E_5) → i_6
  227. Random(1, 5) → Zad8RndNum
  228. Element(Zad8Odgovori, Zad8RndNum) → Zad8Answer
  229. Text(Element[Zad8Pitanja, Zad8RndNum]) → Zad8Question
  230. Textfield(Zad8Upisano) → txtPolje6

AI 绘图提示语参考

画一个垂直数轴，从-10到10，包括正负整数点。首先画一条垂直线作为数轴，然后在数轴上标出0点。接着，使用0点为基准，向上下方向等距生成整数点。使用线段连接相邻的整数点，形成数轴上的整数序列。最后，添加一些辅助线和标记，如垂直线、水平线、圆和圆弧，以增强数轴的可读性和互动性。
以上提示语为根据原始绘图命令整理而来，仅供参考。