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Picture of the month

Credit: Kieff

Villarceau circles 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. The cut that produces Villarceau circles is shown above in the animation. They are named after the French astronomer and mathematician Yvon Villarceau (1813–1883).

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