Grilled Cheese

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Grilled Cheese is a product of Village Compute

Version devBuilt at: 2026-10-17 03:54:26 EDT

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Photographic portrait of William Thurston, and a quote : "It's interesting that although "or", "and" and "implies" have identical formal usage, we think of "or" and "and" as conjunctions and "implies" as a verb."
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Selfie of Sarah, Anna, Cleo and Katerina
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Cotes’ Harmonic Means Theorem in Geometry : In the plane, let f (x, y) = 0 be an algebraic curve of degree d, denoted by C, and let p be a point not on C. For a straight line L through p, and a second point q on L, denote by pq the distance from p to q, signed + or − consistent with some fixed orientation of L. Let r1, . . . , rd be the d points of intersection of L with C and let pL be the point on L satisfying d/ppL = 1/pr1 + ... + 1/prd (1) Then the following subset of the plane is a straight line ∪L{pL | pL satisfies equation (1)}, the union being taken over all straight lines L through p.
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