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  2. 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.

  3. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Fubini's theorem on differentiation (real analysis) Fuchs's theorem (differential equations) Fuglede's theorem (functional analysis) Full employment theorem (theoretical computer science) Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis)

  4. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases ...

  5. Mathematical object - Wikipedia

    en.wikipedia.org/wiki/Mathematical_object

    Mathematical constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then ...

  6. 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

  7. Pascal's theorem - Wikipedia

    en.wikipedia.org/wiki/Pascal's_theorem

    A short elementary proof of Pascal's theorem in the case of a circle was found by van Yzeren (1993), based on the proof in (Guggenheimer 1967). This proof proves the theorem for circle and then generalizes it to conics. A short elementary computational proof in the case of the real projective plane was found by Stefanovic (2010).

  8. Mathematical beauty - Wikipedia

    en.wikipedia.org/wiki/Mathematical_beauty

    A proof that is based on new and original insights. A method of proof that can be easily generalized to solve a family of similar problems. In the search for an elegant proof, mathematicians may search for multiple independent ways to prove a result, as the first proof that is found can often be improved.

  9. Van Hiele model - Wikipedia

    en.wikipedia.org/wiki/Van_Hiele_model

    The object of thought is deductive reasoning (simple proofs), which the student learns to combine to form a system of formal proofs (Euclidean geometry). Learners can construct geometric proofs at a secondary school level and understand their meaning. They understand the role of undefined terms, definitions, axioms and theorems in Euclidean ...

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