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  2. No-three-in-line problem - Wikipedia

    en.wikipedia.org/wiki/No-three-in-line_problem

    This application was the motivation for Paul Erdős to find his solution for the no-three-in-line problem. [13] It remained the best area lower bound known for the Heilbronn triangle problem from 1951 until 1982, when it was improved by a logarithmic factor using a construction that was not based on the no-three-in-line problem. [14]

  3. Triangle inequality - Wikipedia

    en.wikipedia.org/wiki/Triangle_inequality

    The reverse triangle inequality is an equivalent alternative formulation of the triangle inequality that gives lower bounds instead of upper bounds. For plane geometry, the statement is: [19] Any side of a triangle is greater than or equal to the difference between the other two sides. In the case of a normed vector space, the statement is:

  4. Simplex - Wikipedia

    en.wikipedia.org/wiki/Simplex

    In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment,

  5. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    Generalization for arbitrary triangles, green area = blue area Construction for proof of parallelogram generalization. Pappus's area theorem is a further generalization, that applies to triangles that are not right triangles, using parallelograms on the three sides in place of squares (squares are a special case, of course). The upper figure ...

  6. Droz-Farny line theorem - Wikipedia

    en.wikipedia.org/wiki/Droz-Farny_line_theorem

    Second generalization: Let a conic S and a point P on the plane. Construct three lines d a , d b , d c through P such that they meet the conic at A, A'; B, B' ; C, C' respectively. Let D be a point on the polar of point P with respect to (S) or D lies on the conic (S).

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    Fisher-Price Wooden Activity Triangle. $20 at Walmart. Fisher-Price Busy Buddies Pop-Up . $17 at Walmart. Fisher-Price Laugh and Learn Mix & Learn DJ Activity Table. $31 at Walmart. For Toddlers.

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