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Spiral of Prisms

Spiral of Prisms
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2020-01-21 02:20
TriangleSequenceSolid GeometryGraphing
This example demonstrates the construction and visualization of a spiral of prisms. It involves core mathematical concepts such as prisms, triangles, sequences, surface area, and volume calculations. The construction uses GeoGebra commands like CurveCartesian and Sequence, along with objects like sliders for animation. Suitable for high school solid geometry instruction and exploratory learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(x1(t), y1(t), 0, t, 0, (delta * 40)) → a
  2. Sequence(Polygon[a((delta * (i + 1 / (2 + (2 * i / n))))), a((delta * i)), m, xOyPlane], i, 0, n) → liste1
  3. Sequence(Prism[Element[liste1, i], (h * i / 5)], i, 1, Length[liste1]) → liste2
  4. Sequence(Centroid[Element[liste1, i]] + (0, 0, (h * i / 10)), i, 1, Length[liste1]) → l1
  5. Sequence(Line[Element[l1, i], xAxis], i, 1, Length[l1]) → l3
  6. Sequence(Rotate[Element[liste2, i], c, Element[l3, i]], i, 1, Length[l1]) → l2
  7. Sequence(Rotate[Element[liste2, i], c, Element[l3, i]], i, 1, Length[l1]) → liste3