Interactive Plane Cutting a Sphere

Loading the math board and drawing, please wait…

2020-04-13 21:37

In collections Cutting solids by a plane

This example demonstrates how an interactive plane intersects a sphere, showing the dynamic changes in the cross-sectional circle. It involves core mathematical concepts like sphere, circle, spatial geometry, and intersection. Construction highlights include commands like Point, Sphere, Plane, Intersect from GeoGebra, emphasizing geometric visualization. Suitable for high school solid geometry education, illustrating the relationship between cross-sections and parameters.

GeoGebra Commands & Parameters

Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
Cube(A, B, C) → a, D, faceCDHG, faceEFGH, arêteAD, arêteAB, arêteBC, arêteCD, arêteAE, arêteDH, arêteEH, arêteEF, E, arêteBF, arêteFG, arêteCG, arêteGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
Midpoint(C, A) → I
Midpoint(F, H) → J
Line(J, I) → f
Circle(I, Distance[A, B], f) → c
Point(c) → K
Midpoint(F, C) → M
Mirror(K, I) → K'
Line(K', K) → g
Circle(I, (1.2 * Distance[A, B]), g) → d
Point(d) → L
Plane(L, K, K') → p
Circle(K', L, K) → e
Center(e) → N
OrthogonalLine(N, p) → h
Point(h) → O
Vector(I, O) → u
Translate(p, u) → p'
Segment(K', K) → b
Line(L, b) → f_1
Point(arêteEF) → D_1
OrthogonalLine(K, p) → h_1
Plane(K', h_1) → p_1
OrthogonalLine(K, p_1) → k_1
Line(K', k_1) → l_1
Intersect(f_1, l_1) → E_1
Intersect(k_1, f_1) → F_1
Mirror(F_1, K) → G_1
Mirror(E_1, K') → H_1
Polygon(F_1, E_1, H_1, G_1) → q2, m_1, e_1, n_1, q_1
Translate(q2, u) → q2'
Circle(I, Distance[I, A], f) → q
Point(f) → S
Segment(A, I) → i
Segment(I, S) → j
Sphere(I, A) → k
IntersectPath(p', k) → r
IntersectPath(p', k) → s