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Plane and Integral Interaction Demo

Plane and Integral Interaction Demo
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2015-08-23 01:14
CalculusIntegral
This example demonstrates the interaction between planes, integrals, and tangent lines by dynamically adjusting parameters to observe geometric changes. Core math concepts include planes, geometric distribution, tangent lines, integral calculus, and incircle. It uses GeoGebra commands like Surface and Sequence, with objects a, h, U, V, UU, b, d, n, liste1, liste2. Suitable for high school and above students learning calculus and geometric constructions.

GeoGebra Commands & Parameters

  1. Surface(((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), u, π - UU, π + UU - U, v, -1.5708, V) → b
  2. Surface(((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), u, 0.01 + π - UU, π + UU - U, v, -1.5708, V) → d
  3. Sequence(CurveCartesian[((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), u, π - UU, π + UU - U], v, -1.5708, V, π / n) → liste1
  4. Sequence(CurveCartesian[((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), v, -1.5708, V], u, π - UU, π + UU - U, (2 * π / n)) → liste2