Hypotrochoids: Flowers (2)
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geometriadinamica.es
This example demonstrates the generation of hypotrochoids, a curve traced by a point attached to a circle rolling inside another circle. Key mathematical concepts include the motion of circles, parametric equations, and loci. Using GeoGebra commands such as CurveCartesian, rotación, and z, the formation of hypotrochoids is dynamically illustrated. Suitable for high school mathematics education, particularly for learning analytic geometry and parametric equations.
GeoGebra Commands & Parameters
CurveCartesian((b * cos(t)), (b * sin(t)), t, -6.28, 6.28) → dCurveCartesian((((a * abs(cos((n * t)))) + b) * cos(t + z)), (((a * abs(cos((n * t)))) + b) * sin(t + z)), t, -6.28, 6.28) → c
AI Drawing Prompt Reference
Draw two closed parametric curves on the same coordinate plane. First, plot a circle-like curve defined by x = b*cos(t) and y = b*sin(t), tracing it continuously as t ranges from -6.28 to 6.28 to obtain curve d. Next, draw a more complex hypotrochoid-style “flower” curve where the radius factor is (a*|cos(n*t)| + b), and set the coordinates to x = (a*|cos(n*t)| + b)*cos(t+z) and y = (a*|cos(n*t)| + b)*sin(t+z), again tracing for t from -6.28 to 6.28 to obtain curve c.
The prompt above was compiled from the original drawing commands and is for reference only.