In mathematical analysis, the universal chord theorem states that if a function f is continuous on [a,b] and satisfies f ( a ) = f ( b ) {\displaystyle...

decomposed into two perpendicular subspaces is a 2-distance set. The Universal chord theorem states that for any real function, the distance set of the level...

while still an undergraduate, in which he introduced the Lévy–Steinitz theorem. His teacher and advisor was Jacques Hadamard. After graduation, he spent...

Constant chord theorem (geometry) Conway circle theorem (Euclidean plane geometry) Crossbar theorem (Euclidean plane geometry) Dandelin's theorem (solid...

maximal planar graphs to a theorem of Hassler Whitney. Seymour, P. D.; Weaver, R. W. (1984), "A generalization of chordal graphs", Journal of Graph Theory...

{CM} }}=2r}  (PMCK is a parallelogram). Using the intersecting chords theorem on the chords BC and DE, we get B M ¯ ⋅ C M ¯ = D M ¯ ⋅ E M ¯ . {\displaystyle...

from its side lengths, or the inscribed angle theorem in the form that the angles subtended by a chord of a circle from other points on the circle are...

strong perfect graph theorem as being the graphs with no odd holes or odd anti-holes. The hole-free graphs are the same as the chordal graphs. homomorphic...

Bundle theorem Butterfly theorem – About the midpoint of a chord of a circle, through which two other chords are drawn Carnot's theorem – Theorem in Euclidean...

important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem on partially ordered sets, Kőnig's theorem on matchings, and...

trailing edge angle. The chord line is the straight line connecting leading and trailing edges. The chord length, or simply chord, c {\displaystyle c} ,...

made chordal if they aren't already chordal. This is the first essential step of the algorithm. It makes use of the following theorem: Theorem: For an...

Pythagorean theorem. Theorems on the lengths of chords are essentially applications of the modern law of sines. We have seen that Archimedes' theorem on the...

important theorem about Vassiliev invariants: For every knot one can compute an integral, now called the Kontsevich integral, which is a universal Vassiliev...

first the measure is available only for chords not parallel to the y-axis, but the final formula works for any chord. As a consequence, one obtains an equation...

constructs a dismantling order. They include the chordal graphs, and the graphs that contain a universal vertex. Cop-win graphs can be defined by a pursuit–evasion...

of the row's chord in the column's 4-polytope. For example, in the #3 chord row, the 600-cell's 72 great decagons contain 720 #3 chords in all. The red...

(1999), theorem 6.6.1, p. 99; Golumbic (1978), corollary 4. Brandstädt, Le & Spinrad (1999), theorem 6.6.1, p. 99; Golumbic (1978), theorem 2. Wolk (1962)...

(2005). Gödel's Theorem: An Incomplete Guide to its Use and Abuse. AK Peters. ISBN 1-56881-238-8. Alfred North Whitehead (1898) Universal Algebra Archived...

ones-- which can be seen either by direct computation, the universal coefficient theorem or even Poincaré duality. If a torus is punctured and turned...

2021) Duffin–Schaeffer theorem (Dimitris Koukoulopoulos, James Maynard, 2019) Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian...

directrix. The major axis is the chord between the two vertices: the longest chord of an ellipse, the shortest chord between the branches of a hyperbola...

vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ) is the distance AC (half of the chord). On the...

challenges — Center of gravity — Center of mass — Center of pressure — Chord — Collimated light — Compressibility — Computational fluid dynamics — Computing...

} , then the Reynolds number is essentially fixed by the Buckingham π theorem. In detail, since there are 4 quantities ρ , u , L , μ {\displaystyle \rho...

Euclid and Archimedes studied the properties of chords and inscribed angles in circles, and they proved theorems that are equivalent to modern trigonometric...

conformal equivalence. By the uniformization theorem, every compact Riemann surface has simply connected universal covering surface given by exactly one of...

\mathbb {Z} )} on the upper half-plane: a version of the Riemann–Roch theorem holds after the quotient is compactified by the addition of two orbifold...

nontrivial example of a universal attracting fixed point. It is also a transcendental number because of the Lindemann–Weierstrass theorem. The generalised case...

frequently. Greek mathematicians used the full chord and never imagined the half chord that we use today. Half chord was first used by Aryabhata which made trigonometry...