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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. List of data structures. List of derivatives and integrals in alternative calculi. List of equations.
Ceva's theorem is a theorem of affine geometry, in the sense that it may be stated and proved without using the concepts of angles, areas, and lengths (except for the ratio of the lengths of two line segments that are collinear). It is therefore true for triangles in any affine plane over any field. A slightly adapted converse is also true: If ...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic ...
C. Campbell's theorem (geometry) Castelnuovo–de Franchis theorem. Castelnuovo's contraction theorem. Chow–Rashevskii theorem. Collage theorem. Commandino's theorem.
Diagram of Stewart's theorem. Let a, b, c be the lengths of the sides of a triangle. Let d be the length of a cevian to the side of length a.If the cevian divides the side of length a into two segments of length m and n, with m adjacent to c and n adjacent to b, then Stewart's theorem states that + = (+).
B. Base change theorems. Beauville–Laszlo theorem. Behrend's trace formula. Belyi's theorem. Bézout's theorem. Birkhoff–Grothendieck theorem. Bogomolov–Sommese vanishing theorem. Borel fixed-point theorem.
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin( α + β ) = sin α cos β + cos α sin ...
Download as PDF; Printable version ... Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish ...
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