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Fifth Egg

Fifth Egg
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2020-04-12 16:05
FunctionTrigonometrySequenceSolid GeometryParametric Equation
This example demonstrates the dynamic construction of spherical surfaces and parametric surfaces using GeoGebra. Core mathematical concepts include surfaces, logarithmic functions, statistical characteristics, conditional probability, cubes, and similarity transformations. Key GeoGebra commands and objects used in the construction are Sequence, Sphere, and Surface, as outlined in the construction summary. It is suitable for high school and above learners to explore the interaction between spatial geometry and function graphs.

GeoGebra Commands & Parameters

  1. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), y(O) + ((R * sin(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), z(O) + (R * sin(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste2
  2. Sphere(O, R) → c
  3. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + ((R + h) * sin(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste1
  4. Sequence(CurveCartesian[x(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (((R + h) * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste3
  5. Sequence(CurveCartesian[x(O) + (R * sin(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), y(O) + ((R * sin(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), z(O) + (((R + h) * cos(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste4
  6. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (((R + h) * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste5
  7. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), y(O) + (R * sin(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), z(O) + (((R + h) * sin(t)) * cos(i + (π / ((2 * n)) * ff((m * t) + (2 * π))))), t, 0, 6.28319], i, -1.5708, 1.5708, π / n) → liste6
  8. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + ((R * cos(i)) * sin(j)), z(O) + ((R + h) * sin(i)), i, 0, (2 * π), j, 0, (2 * π)) → d