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The tennis racket theorem or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with three distinct principal moments of inertia. It has also been dubbed the Dzhanibekov effect , after Soviet cosmonaut Vladimir Dzhanibekov , who noticed one of the theorem's logical consequences ...
Hyperbolic groups have a solvable word problem. They are biautomatic and automatic . [ 9 ] Indeed, they are strongly geodesically automatic , that is, there is an automatic structure on the group, where the language accepted by the word acceptor is the set of all geodesic words.
In 1985 he demonstrated stable and unstable rotation of a T-handle nut from the orbit, subsequently named the Dzhanibekov effect. The effect had been long known from the tennis racket theorem, which says that rotation about an object's intermediate principal axis is unstable while in free fall. In 1985 he was promoted to the rank of major ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The construction yields proofs of unsolvability of several algorithmic problems for word-hyperbolic groups, including the subgroup membership problem, the generation problem and the rank problem. [23] Also, with a few exceptions, the group K in the Rips construction is not finitely presentable.
When the algorithm succeeds, it effectively solves the word problem for the specified algebra. Buchberger's algorithm for computing Gröbner bases is a very similar algorithm. Although developed independently, it may also be seen as the instantiation of Knuth–Bendix algorithm in the theory of polynomial rings.
Due to the Pythagorean theorem the number () has the simple geometric meanings shown in the diagram: For a point outside the circle () is the squared tangential distance | | of point to the circle . Points with equal power, isolines of Π ( P ) {\displaystyle \Pi (P)} , are circles concentric to circle c {\displaystyle c} .
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 are integers, then
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