MathPlotAI Logo MathPlotAI

Sphere to Pyramid Transformation

Sphere to Pyramid Transformation
Loading the math board and drawing, please wait…
2017-03-13 18:51
Solid GeometryTransformationGeometric Construction
This example demonstrates the geometric transformation from a sphere to a pyramid. It involves core mathematical concepts such as solid geometry, spatial transformation, and geometric construction. Key GeoGebra commands used include Rotate, Line, Intersect, Circle, Distance, and Sequence. It is suitable for high school and above students to learn and understand spatial geometric transformations and geometric constructions.

GeoGebra Commands & Parameters

  1. Rotate(F, (2 * π / n)) → E
  2. Line(E, F) → l
  3. Intersect(yAxis, l) → G
  4. Circle((0, 0), 1) → c
  5. Distance(E, F) → EF
  6. Sequence(Surface[((((1 - p + (p * r(u))) * (1 - p + (p * r(v)))) * cos(u)) * ((cos(v) * cos(i)) - (sin(i) * sin(v)))), ((((1 - p + (p * r(u))) * (1 - p + (p * r(v)))) * cos(u)) * ((cos(v) * sin(i)) + (cos(i) * sin(v)))), ((1 - p + ((p * h) * r(u))) * sin(u)), u, 0, π / 2, v, 0, (2 * π / n)], i, (2 * π / n), (2 * π), (2 * π / n)) → liste2
  7. Sequence(Rotate[CurveCartesian[((1 - p + (p * r(t))) * cos(t)), ((1 - p + (p * r(t))) * sin(t)), t, 0, (2 * π / n)], i], i, (2 * π / n), (2 * π), (2 * π / n)) → liste1