In geometry, Villarceau circles ( /viːlɑrˈsoʊ/) are a pair of circles produced by cutting a torus diagonally through the center at the correct angle. Given an arbitrary point on a torus, four circles can be drawn through it. One is in the plane (containing the point) parallel to the equatorial plane of the torus. Another is perpendicular to it. The other two are Villarceau circles. They are named after the French astronomer and mathematician Yvon Villarceau (1813–1883). Mannheim (1903) showed that a the Villarceau circles meet all of the parallel circular cross-sections of the torus at the same angle, a result that he said a Colonel Schoelcher had presented at a congress in 1891.
Read more about Villarceau Circles: Example, Existence and Equations, Filling Space
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“Before the birth of the New Woman the country was not an intellectual desert, as she is apt to suppose. There were teachers of the highest grade, and libraries, and countless circles in our towns and villages of scholarly, leisurely folk, who loved books, and music, and Nature, and lived much apart with them. The mad craze for money, which clutches at our souls to-day as la grippe does at our bodies, was hardly known then.”
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