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The Miller Institute knot is the 6-crossing prime knot 6_2. It is alternating, chiral, and invertible. A knot diagram of its laevo form is illustrated above, which is ...

For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

The stevedore's knot is the 6-crossing prime knot 6_1. It is implemented in the Wolfram Language as KnotData["Stevedore"]. It has braid word ...

P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether (Thomson 1869). He categorized knots in ...

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...