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  2. Schoenflies problem - Wikipedia

    en.wikipedia.org/wiki/Schoenflies_problem

    Make the construction of the second step with tiles of diameter less than ε 1 and take C i to be the points on the polygonal curve Γ 1 intersecting A i B i. Take the points f(A i) on the triangle. Fix an origin in the triangle Δ and scale the triangle to get a smaller one Δ 1 at a distance less than ε 1 from the original triangle.

  3. Langley's Adventitious Angles - Wikipedia

    en.wikipedia.org/wiki/Langley's_Adventitious_Angles

    In 2015, an anonymous Japanese woman using the pen name "aerile re" published the first known method (the method of 3 circumcenters) to construct a proof in elementary geometry for a special class of adventitious quadrangles problem. [7] [8] [9] This work solves the first of the three unsolved problems listed by Rigby in his 1978 paper. [5]

  4. Generalized trigonometry - Wikipedia

    en.wikipedia.org/wiki/Generalized_trigonometry

    Ordinary trigonometry studies triangles in the Euclidean plane ⁠ ⁠.There are a number of ways of defining the ordinary Euclidean geometric trigonometric functions on real numbers, for example right-angled triangle definitions, unit circle definitions, series definitions [broken anchor], definitions via differential equations [broken anchor], and definitions using functional equations.

  5. 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).

  6. Conway circle theorem - Wikipedia

    en.wikipedia.org/wiki/Conway_circle_theorem

    In plane geometry, the Conway circle theorem states that when the sides meeting at each vertex of a triangle are extended by the length of the opposite side, the six endpoints of the three resulting line segments lie on a circle whose centre is the incentre of the triangle.

  7. Everybody Should Try This Trick to Making Perfectly Round Cookies

    www.aol.com/everybody-try-trick-making-perfectly...

    The next time you bake a batch of cookies, try this easy trick to making drop cookies perfectly round. All you need is a mug or glass to get started.

  8. Israel and Lebanon trade accusations of ceasefire violations ...

    www.aol.com/israel-agreed-truce-lebanon-means...

    The violations of the 2006 truce allowed Hezbollah to strengthen its forces tremendously, while Israel gathered intelligence on the militant group that would prove to be a game-changer in the 2024 ...

  9. Bretschneider's formula - Wikipedia

    en.wikipedia.org/wiki/Bretschneider's_formula

    Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]

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