Unrolling an Ellipse (Spiral)
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This example demonstrates the dynamic process of unrolling an ellipse into a spiral line along its circumference. It involves core mathematical concepts such as ellipse, correlation, incircle, cube, real numbers, and linear programming. The construction utilizes GeoGebra commands like Cartesian curve, length, tangent, point, and segment, along with objects like α, d, luzera, B, b, A, D, a, c, button1, and button2. Suitable for high school and above learners to understand the geometric properties and spatial transformations of ellipses.
GeoGebra Commands & Parameters
CurveCartesian((3 * cos(t)), (1.5 * sin(t)), t, 0, α) → dLength(d, 0, α) → luzeraTangent(B, d) → bPoint(b) → ASegment(B, D) → aCurveCartesian((3 * cos(t)), (1.5 * sin(t)), t, 0, (2 * π)) → c