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Question: How is a bundle of planes treated "Cartesianly"?

Question:How is a bundle of planes treated "Cartesianly"?

Alfred_F 665 Maple
geometry
2 hours ago
0

A bundle of planes is here defined as the set of all planes in Cartesian (x, y, z)-space that intersect along the same straight line. This line is commonly referred to as the axis of the bundle. Is there an efficient method in Maple to model a bundle of planes in a simple, symbolic way?
The background to my request for advice is the following problem (for those interested in the puzzle), dating back to 1965:
Let a surface be given in Euclidean space. Suppose that every planar section of the surface is a circle, provided the section contains more than one point. Prove that the surface is a sphere.

edited:

Simple deductions are sufficient to solve the puzzle. Complex calculations are not necessary.
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