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Steinmetz curve - mklabgr - 08-01-2026
Steinmetz curve
Summary
A Steinmetz curve is the three-dimensional curve formed by the intersection of two right circular cylinders whose axes meet at right angles. If the cylinders have radii (a) and (b), the curve can be described by parametric equations, making it an important object in geometry and differential geometry. When the two cylinders have the same radius, the Steinmetz curve becomes the boundary of the famous Steinmetz solid, and the intersection simplifies into two crossing ellipses.
Named after the mathematician and electrical engineer Charles Proteus Steinmetz, the curve serves as a classic example in the study of surfaces, spatial intersections, and geometric modeling, with applications in mathematics, computer graphics, and engineering.
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