Cylinder Cross Section Exploration
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Cross Sections
This example demonstrates the dynamic investigation of cross sections formed by slicing a cylinder at various angles and positions. It involves core mathematical concepts such as cylinder geometry, diversity of cross-sectional shapes, and analytical geometry intersection calculations. Key GeoGebra commands and objects used include Intersect, Circle, Cylinder, PointIn, If, IntersectPath, Corner, and Top, highlighting the interplay between 3D geometry and 2D representations. Suitable for high school solid geometry and analytical geometry instruction, it visually illustrates the relationship between cross-sections and spatial geometric bodies.
GeoGebra Commands & Parameters
Intersect(yAxis, zAxis) → C_1Circle(C_1, 2, zAxis) → gCylinder(g, 3.0978920006490056) → a, d, ePointIn(e) → APointIn(e) → CPointIn(e) → BCircle(C_1, 2, zAxis) → hIf(p ≟ 0, Plane[A, B, C], If[p ≟ 1, Plane[L, M, N], Plane[O, P, Q]]) → iIntersectPath(i, a) → kCorner(k) → E, F, G, HIntersectPath(i, a) → cCorner(c) → D, I, J, KTop(a) → f