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In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
The utility of Abel's theorem is that it allows us to find the limit of a power series as its argument (that is, ) approaches from below, even in cases where the radius of convergence, , of the power series is equal to and we cannot be sure whether the limit should be finite or not.
Spherical version of Malfatti's problem: [4] The triangle is a spherical one. Essential tools for investigations on circles are the radical axis of two circles and the radical center of three circles. The power diagram of a set of circles divides the plane into regions within which the circle minimizing the power is constant.
The power diagram of a set of n circles C i is a partition of the plane into n regions R i (called cells), such that a point P belongs to R i whenever circle C i is the circle minimizing the power of P. [2] [3] [4] The radical axis of two intersecting circles. The power diagram of the two circles is the partition of the plane into two ...
In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem.It was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n many k th powers of positive integers is itself a k th power, then n is greater than or equal to k:
Download as PDF; Printable version; Appearance. move to sidebar hide. From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Maximum power transfer theorem;
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
A variant, Stone's representation theorem for distributive lattices, states that every distributive lattice is isomorphic to a sublattice of the power set lattice of some set. Another variant, Stone's duality , states that there exists a duality (in the sense of an arrow-reversing equivalence) between the categories of Boolean algebras and that ...