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Handshakes

Handshakes
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2014-07-28 23:48
PolygonTrigonometryGeometric Construction
This example demonstrates a regular polygon with diagonals. It involves combinatorics. Using GeoGebra commands like Point, Sequence, and Sum, you can construct a polygon with diagonals. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(x = x(A)) → B
  2. Sequence(Rotate[B, ((i * 360) * ° / n) + (180 * ° / n), A], i, 1, n) → list1
  3. Sequence(Sequence[Segment[Element[list1, i], Element[list1, i + j]], j, 1, n - i], i, 1, n - 1) → list2
  4. Sequence(Length[Element[list2, i]], i, 1, n - 1) → handshakes
  5. Sum(handshakes) → total
  6. Sequence(Segment[Element[list1, A1], Element[list1, A1 + j]], j, 1, n - A1) → B1
  7. Sequence(Segment[Element[list1, A2], Element[list1, A2 + j]], j, 1, n - A2) → B2
  8. Sequence(Segment[Element[list1, A3], Element[list1, A3 + j]], j, 1, n - A3) → B3
  9. Sequence(Segment[Element[list1, A4], Element[list1, A4 + j]], j, 1, n - A4) → B4
  10. Sequence(Segment[Element[list1, A5], Element[list1, A5 + j]], j, 1, n - A5) → B5
  11. Sequence(Segment[Element[list1, A6], Element[list1, A6 + j]], j, 1, n - A6) → B6
  12. Sequence(Segment[Element[list1, A7], Element[list1, A7 + j]], j, 1, n - A7) → B7
  13. Sequence(Segment[Element[list1, A8], Element[list1, A8 + j]], j, 1, n - A8) → B8
  14. Sequence(Segment[Element[list1, A9], Element[list1, A9 + j]], j, 1, n - A9) → B9
  15. Sequence(Segment[Element[list1, A10], Element[list1, A10 + j]], j, 1, n - A10) → B10
  16. Sequence(Segment[Element[list1, A11], Element[list1, A11 + j]], j, 1, n - A11) → B11
  17. Sequence(Segment[Element[list1, A12], Element[list1, A12 + j]], j, 1, n - A12) → B12
  18. Sequence(Segment[Element[list1, A13], Element[list1, A13 + j]], j, 1, n - A13) → B13
  19. Sequence(Segment[Element[list1, A14], Element[list1, A14 + j]], j, 1, n - A14) → B14
  20. Sequence(Segment[Element[list1, A15], Element[list1, A15 + j]], j, 1, n - A15) → B15
  21. Sequence(Segment[Element[list1, A16], Element[list1, A16 + j]], j, 1, n - A16) → B16
  22. Sequence(Segment[Element[list1, A17], Element[list1, A17 + j]], j, 1, n - A17) → B17
  23. Sequence(Segment[Element[list1, A18], Element[list1, A18 + j]], j, 1, n - A18) → B18
  24. Sequence(Segment[Element[list1, A19], Element[list1, A19 + j]], j, 1, n - A19) → B19
  25. Sequence(Segment[Element[list1, A20], Element[list1, A20 + j]], j, 1, n - A20) → B20
  26. Sequence(Segment[Element[list1, A21], Element[list1, A21 + j]], j, 1, n - A21) → B21
  27. Sequence(Segment[Element[list1, A22], Element[list1, A22 + j]], j, 1, n - A22) → B22
  28. Sequence(Segment[Element[list1, A23], Element[list1, A23 + j]], j, 1, n - A23) → B23
  29. Sequence(Segment[Element[list1, A24], Element[list1, A24 + j]], j, 1, n - A24) → B24
  30. Sum(Take[handshakes, 1, k]) → totalk

AI Drawing Prompt Reference

Draw a regular polygon and display all its diagonals. Start by identifying one vertex of the polygon and then rotate it around this vertex at specific angles to generate the remaining vertices. Next, connect each vertex to other non-adjacent vertices to form the diagonals. Finally, calculate and display the total length of all diagonals, as well as the lengths of diagonals originating from specific vertices.
The prompt above was compiled from the original drawing commands and is for reference only.