Intersection of Cylinder and Sphere
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This example demonstrates the curve formed by the intersection of a sphere and a cylinder. Key mathematical concepts include curve discussion in coordinate geometry and solid geometry. Using the CurveCartesian command, the parametric equation of the intersection curve is constructed. Suitable for high school students studying coordinate geometry and solid geometry.
GeoGebra Commands & Parameters
CurveCartesian(((R + m_1^(2) + m_3^(2) - ((2 * m_3) * t) - r + t^(2)) / 2 / m_1, ((-sqrt((-R^(2)) + ((2 * R) * m_1^(2)) - ((2 * R) * m_3^(2)) + (((4 * R) * m_3) * t) + ((2 * R) * r) - ((2 * R) * t^(2)) - m_1^(4) - ((2 * m_1^(2)) * m_3^(2)) + (((4 * m_1^(2)) * m_3) * t) + ((2 * m_1^(2)) * r) - ((2 * m_1^(2)) * t^(2)) - m_3^(4) + ((4 * m_3^(3)) * t) + ((2 * m_3^(2)) * r) - ((6 * m_3^(2)) * t^(2)) - (((4 * m_3) * r) * t) + ((4 * m_3) * t^(3)) - r^(2) + ((2 * r) * t^(2)) - t^(4)))) / ((2 * m_1)), t), t, -10, 10) → c
AI Drawing Prompt Reference
Draw the intersection curve of a sphere and a cylinder, showing its shape in 3D space, described by a parametric equation with values ranging from -10 to 10, emphasizing the mathematical concepts of the curve in coordinate and solid geometry.
The prompt above was compiled from the original drawing commands and is for reference only.