TL;DR
This paper provides a straightforward, calculus-free explanation of the cubic surface of revolution defined by x^3+y^3+z^3-3xyz=1, including a second elementary proof of its rotational symmetry.
Contribution
It offers a direct, elementary exposition and an additional proof that the cubic surface is of revolution, simplifying understanding of this classical surface.
Findings
The surface is of revolution, confirmed by two elementary proofs.
The exposition avoids calculus, making the concepts accessible.
The paper clarifies the geometric nature of the cubic surface.
Abstract
We develop a direct and elementary (calculus-free) exposition of the famous cubic surface of revolution x^3+y^3+z^3-3xyz=1.12 pages. We have added a second elementary proof that the surface is of revolution.
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