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Perimeter of Square and Rectangle

Perimeter of Square and Rectangle
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2017-11-13 17:22
This example demonstrates the calculation and visualization of the perimeter of squares and rectangles. It involves core mathematical concepts such as perimeter formulas, geometric properties, and variable calculations. The construction summary utilizes GeoGebra commands and objects like Sort, Polygon, Sequence, Rotate, Flatten, Max for dynamic generation and transformation of shapes. Suitable for middle school and above mathematics education, helping students understand basic geometric calculations and dynamic geometry demonstrations.

GeoGebra Commands & Parameters

  1. Sort({x(A), x(B), x(C), x(D)}) → xvalues
  2. Sort({y(A), y(B), y(C), y(D)}) → yvalues
  3. Polygon(A, D, B, C) → poly1, a, d, b, c
  4. Sequence(Point[{xmin + c - i, ymin}], i, 1, c) → list8
  5. Sequence(Point[{xmin, ymin + i}], i, 0, a) → list5
  6. Sequence(Rotate[Point[{xmin + c, ymin + a - i}], (permtimer * ((-π)) / 2), (xmin + c, ymin)], i, 1, a) → list7
  7. Rotate(list5, (permtimer * ((-π)) / 2), list7(a)) → list12
  8. Sequence(Rotate[Point[{xmin + i, ymin + a}], (permtimer * ((-π)) / 2), list7(a)], i, 1, c) → list6
  9. Rotate(list12, (permtimer * ((-π)) / 2), list6(c)) → list13
  10. Rotate(list13, (permtimer * ((-π)) / 2), F) → list14
  11. Rotate(list6, (permtimer * ((-π)) / 2), list6(c)) → list11
  12. Sequence(Point[{Min[xvalues] + i, Min[yvalues] - 4}], i, 0, Area - 1) → arealist
  13. Flatten(Sequence[Sequence[Point[{Min[xvalues] + i, Min[yvalues] + j}], i, 0, c - 1], j, 0, a - 1]) → list1
  14. Sequence((list1(i) * (1 - areatimer)) + (arealist(i) * areatimer), i, 1, Area) → list2
  15. Sequence(Polygon[list2(i), list2(i) + (1, 0), 4], i, 1, Area) → list3
  16. Sequence(Polygon[arealist(i), arealist(i) + (1, 0), 4], i, 1, Area) → list4
  17. Sequence(Text[i, arealist(i) + (0.1, 0.2)], i, 1, Area) → areanumbers
  18. Flatten({Reverse[list8], Reverse[list7], Reverse[list11], Reverse[list14]}) → list9
  19. Sequence(Point[{Min[xvalues] + i, Min[yvalues] - 2}], i, 0, perm) → permlist
  20. Sequence((permlist(i) * permmover) + (list9(i) * (1 - permmover)), i, 1, Length[list9]) → list10
  21. Sequence(Segment[list10(i), list10(i + 1)], i, 1, perm) → list15
  22. Max(a + 1, ((R - L) * 17.4 / 32) + BOT) → T

AI Drawing Prompt Reference

Create a dynamic visualization showing the perimeter of squares and rectangles, highlighting perimeter formulas and geometric properties. The image should include multiple shapes that are dynamically generated and transformed through rotations and displacements, forming a complex pattern. Start with basic squares and rectangles, then generate multiple shapes by rotating and displacing them, and finally connect these shapes with lines to demonstrate the dynamic perimeter effectively.
The prompt above was compiled from the original drawing commands and is for reference only.