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CPCTC (triangle geometry) Cameron–Erdős theorem (discrete mathematics) Cameron–Martin theorem (measure theory) Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers) Cantor's intersection theorem (real analysis) Cantor's isomorphism theorem (order theory) Cantor's theorem (set theory, Cantor's diagonal argument)
Xuan tu or Hsuan thu (simplified Chinese: 弦图; traditional Chinese: 絃圖; pinyin: xuántú; Wade–Giles: hsüan 2 tʻu 2) is a diagram given in the ancient Chinese astronomical and mathematical text Zhoubi Suanjing indicating a proof of the Pythagorean theorem. [1] Zhoubi Suanjing is one of the oldest Chinese texts on mathematics. The ...
Archimedes gives two proofs of the main theorem: one using abstract mechanics and the other one by pure geometry. In the first proof, Archimedes considers a lever in equilibrium under the action of gravity, with weighted segments of a parabola and a triangle suspended along the arms of a lever at specific distances from the fulcrum. [4]
The last step of the proof fails if the projective space has dimension less than 3, as in this case it is not possible to find a point not in the plane. Monge's theorem also asserts that three points lie on a line, and has a proof using the same idea of considering it in three rather than two dimensions and writing the line as an intersection ...
Lexell's proof by breaking the triangle A ∗ B ∗ C into three isosceles triangles. The main idea in Lexell's c. 1777 geometric proof – also adopted by Eugène Catalan (1843), Robert Allardice (1883), Jacques Hadamard (1901), Antoine Gob (1922), and Hiroshi Maehara (1999) – is to split the triangle into three isosceles triangles with common apex at the circumcenter and then chase angles ...
Proof using similar triangles. This proof is based on the proportionality of the sides of three similar triangles, that is, upon the fact that the ratio of any two corresponding sides of similar triangles is the same regardless of the size of the triangles. Let ABC represent a right triangle, with the right angle located at C, as shown on the ...
Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
Similar triangles provide the basis for many synthetic (without the use of coordinates) proofs in Euclidean geometry. Among the elementary results that can be proved this way are: the angle bisector theorem , the geometric mean theorem , Ceva's theorem , Menelaus's theorem and the Pythagorean theorem .
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