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Visual Proof of Sum of Odd Numbers

Visual Proof of Sum of Odd Numbers
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2020-01-29 22:02
SequenceCoordinate Geometry
This example demonstrates that the sum of odd numbers is a square number. It provides a visual explanation using geometric constructions. The construction involves creating and connecting points with GeoGebra commands. Suitable for middle school and above students to learn about sequences and geometric constructions.

GeoGebra Commands & Parameters

  1. Numeric A1(1)
  2. Numeric A2(1)
  3. Numeric A3(1)
  4. Numeric A4(1)
  5. Numeric A5(1)
  6. Numeric A6(1)
  7. Numeric A7(1)
  8. Numeric A8(1)
  9. Numeric A9(1)
  10. Numeric B1(1)
  11. Numeric B2(2)
  12. Numeric B3(3)
  13. Numeric B4(4)
  14. Numeric B5(5)
  15. Numeric B6(6)
  16. Numeric B7(7)
  17. Numeric B8(8)
  18. Numeric B9(9)
  19. Numeric A10(2)
  20. Numeric A11(2)
  21. Numeric A12(2)
  22. Numeric A13(2)
  23. Numeric A14(2)
  24. Numeric A15(2)
  25. Numeric A16(2)
  26. Numeric A17(2)
  27. Numeric A18(2)
  28. Numeric B10(1)
  29. Numeric B11(2)
  30. Numeric B12(3)
  31. Numeric B13(4)
  32. Numeric B14(5)
  33. Numeric B15(6)
  34. Numeric B16(7)
  35. Numeric B17(8)
  36. Numeric B18(9)
  37. Numeric A19(3)
  38. Numeric A20(3)
  39. Numeric A21(3)
  40. Numeric A22(3)
  41. Numeric A23(3)
  42. Numeric A24(3)
  43. Numeric A25(3)
  44. Numeric A26(3)
  45. Numeric A27(3)
  46. Numeric B19(1)
  47. Numeric B20(2)
  48. Numeric B21(3)
  49. Numeric B22(4)
  50. Numeric B23(5)
  51. Numeric B24(6)
  52. Numeric B25(7)
  53. Numeric B26(8)
  54. Numeric B27(9)
  55. Numeric A28(4)
  56. Numeric A29(4)
  57. Numeric A30(4)
  58. Numeric A31(4)
  59. Numeric A32(4)
  60. Numeric A33(4)

AI Drawing Prompt Reference

Draw a geometric diagram to prove that the sum of odd numbers is a square number. First, plot points with x-coordinates from 1 to 9 and y-coordinates of 1, then plot points with x-coordinates from 1 to 9 and y-coordinates from 2 to 10, and finally plot points with x-coordinates from 1 to 9 and y-coordinates from 3 to 11. Connect these points sequentially with line segments to form three gradually larger triangles, demonstrating the accumulation of odd numbers and ultimately forming a large square.
The prompt above was compiled from the original drawing commands and is for reference only.