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  • geometry - Different proofs of the Pythagorean theorem? - Mathematics . . .
    Some popular dissection proofs of the Pythagorean Theorem --such as Proof #36 on Cut-the-Knot-- demonstrate a specific, clear pattern for cutting up the figure's three squares, a pattern that applies to all right triangles I have yet to find a similarly straightforward cutting pattern that would apply to all triangles and show that my same
  • A new pythagorean proof - Mathematics Stack Exchange
    $\begingroup$ 1) Another site where you can find many proofs of Pythagoras theorem ; yours has some few similarities with proof #116 2) Abourt your last question : no, even if you find a type of dissection superimposition corresponding to the geometry of your figure, you have the originality to apply it to Pythagorean theorem $\endgroup$
  • What is the simplest proof of the pythagorean theorem you know?
    $\begingroup$ Any explanation of the Pythagorean Theorem that can be understood by children cannot be called a ‘proof’ in the strictest sense of the word It is at best a ‘demonstration’ $\endgroup$
  • Are there any calculus complex numbers etc proofs of the pythagorean . . .
    $\begingroup$ Echoing Qiaochu: it really depends on what tools you have For example, there is a "Pythagorean Theorem" that holds for any inner product space (in particular, for the real and complex planes): if $\langle \mathbf{x},\mathbf{y}\rangle = 0$ (if $\mathbf{x}$ and $\mathbf{y}$ are orthogonal), then $$\lVert \mathbf{x}\rVert^2 + \lVert \mathbf{y}\rVert^2 = \lVert \mathbf{x}+\mathbf{y
  • Is this a valid proof of Pythagoras theorem using complex numbers?
    What are some proofs of the Pythagorean theorem that use imaginary numbers? Related 3
  • What is Trigonometric Proof of Pythagoras Theorem?
    Loomis was an accomplished mathematician who, nearly 100 years ago, published a collection of 300+ proofs of the Pythagorean Theorem ranging from geometric constructs to magic squares The book is in the public domain and can be found on Google Books
  • Is Pythagoras Theorem a theorem? - Mathematics Stack Exchange
    If you study any of the non-Euclidean geometries in which the parallel postulate fails, the Pythagorean Theorem will fail there too To connect the geometric content of the Pythagorean Theorem to the notion of distance between points given in the usual coordinate system in the plane you have to define a coordinate system
  • which axiom (s) are behind the Pythagorean Theorem
    Sure, the Pythagorean theorem is an item in the theory of Euclidean geometry, and it can be derived from the modern axioms of Euclidean geometry A full set of Euclidean geometry axioms contains the information about similarity and area that are sufficient to prove the Pythagorean theorem "synthetically," that is, directly from the axioms
  • Is there an infinite number of proofs for the Pythagorean Theorem?
    It seems there are many, many proofs for the Pythagorean Theorem, but is there an actual upper limit? It seems every type of math has several different proofs for it, and there seems to always be new ways I've seen books with over 300+ proofs Is it possible there may not an upper limit?
  • soft question - Most complicated proof of Pythagoras - Mathematics . . .
    $\begingroup$ Let $\phi$ be Pythagoras' Theorem and let $\psi$ be a statement, all of whose currently known proofs are insanely long and complicated Then any proof of $\psi \wedge \phi$ is a a proof of Pythagoras' Theorem and (at least currently) insanely long and complicated $\endgroup$ –





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