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  2. Auxiliary line - Wikipedia

    en.wikipedia.org/wiki/Auxiliary_line

    Other common auxiliary constructs in elementary plane synthetic geometry are the helping circles. As an example, a proof of the theorem on the sum of angles of a triangle can be done by adding a straight line parallel to one of the triangle sides (passing through the opposite vertex).

  3. Angle bisector theorem - Wikipedia

    en.wikipedia.org/wiki/Angle_bisector_theorem

    Consider a triangle ABC.Let the angle bisector of angle ∠ A intersect side BC at a point D between B and C.The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC:

  4. Proof without words - Wikipedia

    en.wikipedia.org/wiki/Proof_without_words

    Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.

  5. List of mathematical proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_proofs

    Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges

  6. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis) Fundamental theorem of arbitrage-free pricing (financial mathematics) Fundamental theorem of arithmetic (number theory) Fundamental theorem of calculus ; Fundamental theorem on homomorphisms (abstract algebra)

  7. Constructible polygon - Wikipedia

    en.wikipedia.org/wiki/Constructible_polygon

    Gauss stated without proof that this condition was also necessary, [2] but never published his proof. A full proof of necessity was given by Pierre Wantzel in 1837. The result is known as the Gauss–Wantzel theorem : A regular n -gon can be constructed with compass and straightedge if and only if n is the product of a power of 2 and any number ...

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  9. Crossbar theorem - Wikipedia

    en.wikipedia.org/wiki/Crossbar_theorem

    This result is one of the deeper results in axiomatic plane geometry. [2] It is often used in proofs to justify the statement that a line through a vertex of a triangle lying inside the triangle meets the side of the triangle opposite that vertex. This property was often used by Euclid in his proofs without explicit justification. [3]

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