Spherical Triangle

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2014-06-23 05:55

In collections Spherical Geometry Ideas

This example demonstrates the geometry of a spherical triangle, including its vertices, edges, and angles on a spherical surface. It involves core concepts like spherical geometry, angle measurement, and triangle inequalities. Constructed using commands such as Sphere, PointIn, Plane, OrthogonalLine, Intersect, Angle, IntersectPath, and CurveCartesian, it is suitable for high school students and math enthusiasts exploring solid geometry and trigonometry applications.

GeoGebra Commands & Parameters

Sphere((0, 0, 0), 1) → a
PointIn(a) → B
PointIn(a) → C
Plane(B, C_1, C) → i
OrthogonalLine(C_1, i) → j
Intersect(j, a, 2) → F
PointIn(a) → A
Angle(A, (0, 0, 0), B) → α
Plane(A, B, (0, 0, 0)) → c
IntersectPath(c, a) → d
OrthogonalLine(C_1, c) → e
Intersect(e, a, 1) → D
CurveCartesian((A1 * cos(t)) + (A3 * sin(t)), (B1 * cos(t)) + (B3 * sin(t)), (C1 * cos(t)) + (C3 * sin(t)), t, 0, Angle[A, C_1, B]) → f
Plane(C_1, C, A) → b
OrthogonalLine(C_1, b) → g
Intersect(g, a, 1) → E
CurveCartesian((A1 * cos(t)) + (A6 * sin(t)), (B1 * cos(t)) + (B6 * sin(t)), (C1 * cos(t)) + (C6 * sin(t)), t, 0, Angle[A, (0, 0, 0), C]) → h
CurveCartesian((A4 * cos(t)) + (A9 * sin(t)), (B4 * cos(t)) + (B9 * sin(t)), (C4 * cos(t)) + (C9 * sin(t)), t, 0, Angle[B, (0, 0, 0), C]) → k

AI Drawing Prompt Reference

Draw a spherical triangle on a sphere, marking its three vertices and edges, and measuring the angles at each vertex. Start by drawing a sphere, then randomly select three points on the sphere as the triangle's vertices. Next, draw planes through these vertices and find their intersections with the sphere. Finally, connect these intersection points with curves to form the edges of the spherical triangle, and label the angles at each vertex.

The prompt above was compiled from the original drawing commands and is for reference only.