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This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
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.
It repeatedly replaces two numbers by their arithmetic and geometric mean, in order to approximate their arithmetic-geometric mean. The version presented below is also known as the Gauss–Euler , Brent–Salamin (or Salamin–Brent ) algorithm ; [ 1 ] it was independently discovered in 1975 by Richard Brent and Eugene Salamin .
Pages in category "Theorems in geometry" The following 48 pages are in this category, out of 48 total. This list may not reflect recent changes. 0–9. 2π theorem; A.
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 ...
2008-05-20T00:47:20Z Jokes Free4Me 500x540 (13967 Bytes) {{Information |Description=Illustration to Euclid's proof of the Pythagorean theorem, including less important labels and lines. |Source=[[:Image:Illustration to Euclid's proof of the Pythagorean theorem.svg]] |Date=May 20, 2; Uploaded with derivativeFX
The formula above is a geometric series—each successive term is one fourth of the previous term. In modern mathematics, that formula is a special case of the sum formula for a geometric series. Archimedes evaluates the sum using an entirely geometric method, [8] illustrated in the adjacent picture. This picture shows a unit square which has ...
One of many examples from algebraic geometry in the first half of the 20th century: Severi (1946) claimed that a degree-n surface in 3-dimensional projective space has at most (n+2 3 )−4 nodes, B. Segre pointed out that this was wrong; for example, for degree 6 the maximum number of nodes is 65, achieved by the Barth sextic , which is more ...