MathPlotAI Logo MathPlotAI

Happy and Sad Numbers

Happy and Sad Numbers
Loading the math board and drawing, please wait…
2017-06-07 16:26
SequenceProbability & Statistics
This example demonstrates the concept of happy and sad numbers. A happy number is one that, when the sum of the squares of its digits is repeatedly calculated, eventually reaches 1; sad numbers do not. Key mathematical concepts include sequences and cycles. It uses GeoGebra commands such as Mod, Vector, and Point for construction. Suitable for middle school and above students to learn about sequences and cycles.

GeoGebra Commands & Parameters

  1. Mod(floor(A1 / 10)^(2) + Mod[A1, 10]^(2) + B1^(2), 10) → B2
  2. Mod(floor(A2 / 10)^(2) + Mod[A2, 10]^(2) + B2^(2), 10) → B3
  3. Mod(floor(A3 / 10)^(2) + Mod[A3, 10]^(2) + B3^(2), 10) → B4
  4. Mod(floor(A4 / 10)^(2) + Mod[A4, 10]^(2) + B4^(2), 10) → B5
  5. Mod(floor(A5 / 10)^(2) + Mod[A5, 10]^(2) + B5^(2), 10) → B6
  6. Mod(floor(A6 / 10)^(2) + Mod[A6, 10]^(2) + B6^(2), 10) → B7
  7. Mod(floor(A7 / 10)^(2) + Mod[A7, 10]^(2) + B7^(2), 10) → B8
  8. Mod(floor(A8 / 10)^(2) + Mod[A8, 10]^(2) + B8^(2), 10) → B9
  9. Mod(floor(A9 / 10)^(2) + Mod[A9, 10]^(2) + B9^(2), 10) → B10
  10. Mod(floor(A10 / 10)^(2) + Mod[A10, 10]^(2) + B10^(2), 10) → B11
  11. Mod(floor(A11 / 10)^(2) + Mod[A11, 10]^(2) + B11^(2), 10) → B12
  12. Mod(floor(A12 / 10)^(2) + Mod[A12, 10]^(2) + B12^(2), 10) → B13
  13. Mod(floor(A13 / 10)^(2) + Mod[A13, 10]^(2) + B13^(2), 10) → B14
  14. Mod(floor(A14 / 10)^(2) + Mod[A14, 10]^(2) + B14^(2), 10) → B15
  15. Mod(floor(A15 / 10)^(2) + Mod[A15, 10]^(2) + B15^(2), 10) → B16
  16. Mod(floor(A16 / 10)^(2) + Mod[A16, 10]^(2) + B16^(2), 10) → B17
  17. Mod(floor(A17 / 10)^(2) + Mod[A17, 10]^(2) + B17^(2), 10) → B18
  18. Mod(floor(A18 / 10)^(2) + Mod[A18, 10]^(2) + B18^(2), 10) → B19
  19. Mod(floor(A19 / 10)^(2) + Mod[A19, 10]^(2) + B19^(2), 10) → B20
  20. Mod(floor(A20 / 10)^(2) + Mod[A20, 10]^(2) + B20^(2), 10) → B21
  21. Mod(floor(A21 / 10)^(2) + Mod[A21, 10]^(2) + B21^(2), 10) → B22
  22. Mod(floor(A22 / 10)^(2) + Mod[A22, 10]^(2) + B22^(2), 10) → B23
  23. Vector(A_1, A_2) → u
  24. Vector(A_2, A_3) → v
  25. Vector(A_3, A_4) → w
  26. Vector(A_4, A_5) → e
  27. Vector(A_5, A_6) → f
  28. Vector(A_6, A_7) → g
  29. Vector(A_7, A_8) → h
  30. Vector(A_8, A_9) → i
  31. Vector(B_0, B_1) → j
  32. Vector(B_1, B_2) → k
  33. Vector(B_2, B_3) → l
  34. Vector(B_3, B_4) → m
  35. Vector(A_9, B_0) → n
  36. Mod(floor(A23 / 10)^(2) + Mod[A23, 10]^(2) + B23^(2), 10) → B24
  37. Mod(floor(A24 / 10)^(2) + Mod[A24, 10]^(2) + B24^(2), 10) → B25
  38. Mod(floor(A25 / 10)^(2) + Mod[A25, 10]^(2) + B25^(2), 10) → B26
  39. Mod(floor(A26 / 10)^(2) + Mod[A26, 10]^(2) + B26^(2), 10) → B27
  40. Mod(floor(A27 / 10)^(2) + Mod[A27, 10]^(2) + B27^(2), 10) → B28
  41. Mod(floor(A28 / 10)^(2) + Mod[A28, 10]^(2) + B28^(2), 10) → B29
  42. Mod(floor(A29 / 10)^(2) + Mod[A29, 10]^(2) + B29^(2), 10) → B30
  43. Mod(floor(A30 / 10)^(2) + Mod[A30, 10]^(2) + B30^(2), 10) → B31
  44. Mod(floor(A31 / 10)^(2) + Mod[A31, 10]^(2) + B31^(2), 10) → B32
  45. Mod(floor(A32 / 10)^(2) + Mod[A32, 10]^(2) + B32^(2), 10) → B33
  46. Mod(floor(A33 / 10)^(2) + Mod[A33, 10]^(2) + B33^(2), 10) → B34
  47. Mod(floor(A34 / 10)^(2) + Mod[A34, 10]^(2) + B34^(2), 10) → B35
  48. Vector(B_6, B_7) → q
  49. Vector(B_7, B_8) → r
  50. Vector(B_8, B_9) → s
  51. Vector(B_9, C_0) → t
  52. Vector(C_0, C_1) → u_1
  53. Vector(C_1, C_2) → v_1
  54. Vector(C_2, C_3) → w_1
  55. Vector(A, B_6) → p
  56. Point(a) → L_1
  57. Point(a) → M_1