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Shonk's Reinvention

Shonk's Reinvention
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2016-04-02 23:56
CirclePolygonTrigonometryGeometric Construction
This example demonstrates the dynamic process of generating new geometric figures and their area changes by rotating and joining vertices of polygons. Core math concepts include polygons, rhombus, area calculation, fractions, incircle, and interest calculation. Construction highlights from the GeoGebra command summary involve Rotate, Join, and Sequence commands/objects. Suitable for middle school and above, ideal for geometry construction teaching and mathematical art exploration.

GeoGebra Commands & Parameters

  1. Rotate(B, (360 * ° / N), A) → B'
  2. Join(Sequence[Rotate[Sequence[B + (i / M * (B' - B)), i, 1, M], ((j * 360) * ° / N), A], j, 1, N]) → list1
  3. Rotate(Sequence[Segment[A, Element[list1, i]], i, 1, (M * N)], ((t * 360) * ° / N), A) → list2
  4. Sequence(Rotate[Mirror[list2, Line[B, B']], ((((1 + e) * i) * 360) * ° / N), A], i, 1, ceil(N / (1 + e))) → list3
  5. Sequence(Rotate[Rotate[list2, 180°, A + ((1 + f) * (B - A))], ((i * 360) * ° / N), A], i, 1, N) → list4