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Pascal's triangle, rows 0 through 7. The hockey stick identity confirms, for example: for n =6, r =2: 1+3+6+10+15=35. In combinatorics , the hockey-stick identity , [ 1 ] Christmas stocking identity , [ 2 ] boomerang identity , Fermat's identity or Chu's Theorem , [ 3 ] states that if n ≥ r ≥ 0 {\displaystyle n\geq r\geq 0} are integers, then
Iron(III) azide, also called ferric azide, is a chemical compound with the formula Fe(N 3) 3. It is an extremely explosive, impact-sensitive, hygroscopic dark brown solid. This compound is used to prepare various azidoalkanes, such as n -butyl azide, from alkenes via formation of alkylboranes and subsequent anti-Markovnikov addition of azide group.
Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times).
In chemistry, azide (/ ˈ eɪ z aɪ d /, AY-zyd) is a linear, polyatomic anion with the formula N − 3 and structure − N=N + =N −. It is the conjugate base of hydrazoic acid HN 3 . Organic azides are organic compounds with the formula RN 3 , containing the azide functional group . [ 1 ]
CYK algorithm: an O(n 3) algorithm for parsing context-free grammars in Chomsky normal form; Earley parser: another O(n 3) algorithm for parsing any context-free grammar; GLR parser: an algorithm for parsing any context-free grammar by Masaru Tomita. It is tuned for deterministic grammars, on which it performs almost linear time and O(n 3) in ...
Lead azide was a component of the six .22 (5.6 mm) caliber Devastator rounds fired from a Röhm RG-14 revolver by John Hinckley, Jr. in his assassination attempt on U.S. President Ronald Reagan on March 30, 1981. The rounds consisted of lead azide centers with lacquer-sealed aluminum tips designed to explode upon impact.
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]