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Sum of n Odd Numbers

Sum of n Odd Numbers
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2019-03-19 21:44
SequenceCoordinate GeometryGeometric Construction
This example demonstrates the pattern of the sum of n odd numbers. Key mathematical concepts include sequences and summation. Using GeoGebra commands Sequence, If, and Element, the odd number sequence and its summation process are dynamically displayed. Suitable for students at the junior high school level and above to learn about the summation of sequences.

GeoGebra Commands & Parameters

  1. Sequence((0, k), k, 0, a) → l1
  2. Sequence((1, k), k, 0, a) → l2
  3. Sequence(Polygon[Element[l1, k], Element[l1, k + 1], Element[l2, k + 1], Element[l2, k]], k, 1, a) → l3
  4. Sequence((k, 0), k, 0, a, 2) → l4
  5. Sequence(Vector[A, Element[l4, k]], k, 1, a) → l5
  6. Sequence(Sequence[Element[l3, k], k, 1, b], b, 1, a, 2) → l6
  7. Sequence(Translate[Element[l6, k], Vector[Element[l5, k]]], k, 1, a) → l7
  8. Sequence((k, 0), k, 1, c - 1) → l8
  9. Sequence(Vector[Element[l4, k + 1], Element[l8, k]], k, 1, c - 1) → l9
  10. If(0 ≤ b ≤ 1, Sequence[Dilate[Element[l9, k], b], k, 1, c - 1], If[b > 1, Sequence[Element[l9, k], k, 1, c - 1]]) → l10
  11. Element(l6, 1) → l12
  12. Sequence((k, k), k, 1, c) → Turn
  13. Sequence((k + 1, k), k, 1, c - 1) → l14
  14. Sequence((k, 0), k, 1, c) → l15
  15. Sequence(Polygon[Element[Turn, k], Element[l14, k], Element[l15, k + 1], Element[l15, k]], k, 1, a) → l16
  16. Sequence((k, k - 1), k, 1, c) → l18
  17. Sequence((k, (2 * k) + 1), k, 1, c - 1) → l13
  18. Sequence((k + 1, (2 * k) + 1), k, 1, c - 1) → l17
  19. Sequence(Polygon[Element[l13, k], Element[l17, k], Element[l18, k + 1], Element[Turn, k]], k, 1, c) → l19
  20. If(1 < b ≤ 2, Sequence[Rotate[Element[l19, k], α, Element[Turn, k]], k, 1, c], If[b > 2, Sequence[Rotate[Element[l19, k], 90°, Element[Turn, k]], k, 1, c]]) → l20
  21. If(2 < b ≤ 3, Sequence[Vector[Element[Turn, k], Element[l18, k + 1]], k, 1, c]) → l21
  22. If(2 < b ≤ 3, Sequence[Dilate[Element[l21, k], b - 2], k, 1, c]) → l22
  23. Sequence(Translate[Element[l20, k], Vector[Element[l22, k]]], k, 1, c) → l23
  24. Sequence(k, k, 1, 10) → l11
  25. Sequence(Translate[Element[l7, k + 1], Vector[Element[l10, k]]], k, 1, c) → l24

AI Drawing Prompt Reference

Draw a series of rectangles starting from 0, with each rectangle's bottom-left corner on the x-axis and the top-right corner at the corresponding odd number position. Use transformations like rotation, translation, and scaling to arrange these rectangles in a specific pattern, forming a composite shape that demonstrates the summation of odd number sequences.
The prompt above was compiled from the original drawing commands and is for reference only.