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Let K_1 be a knot inside a torus, and knot the torus in the shape of a second knot (called the companion knot) K_2, with certain additional mild restrictions to avoid trivial ...

The scalar triple product of three vectors A, B, and C is denoted [A,B,C] and defined by [A,B,C] = A·(BxC) (1) = B·(CxA) (2) = C·(AxB) (3) = det(ABC) (4) = |A_1 A_2 A_3; B_1 ...

A Fourier series-like expansion of a twice continuously differentiable function f(x)=1/2a_0+sum_(n=1)^inftya_nJ_0(nx) (1) for 0<x<pi, where J_0(x) is a zeroth order Bessel ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

A sequent is an expression Gamma|-Lambda, where Gamma and Lambda are (possibly empty) sequences of formulas. Here, Gamma is called the antecedent and Lambda is called the ...

A correction which must be applied to the measured moments m_k obtained from normally distributed data which have been binned in order to obtain correct estimators mu^^_i for ...

The randomization of a deck of cards by repeated interleaving. More generally, a shuffle is a rearrangement of the elements in an ordered list. Shuffling by exactly ...

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function f using quadratic polynomials (i.e., parabolic arcs instead of the straight line ...

Inscribe two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 in a reference triangle DeltaABC such that A = ∠AB_1C_1=∠AC_2B_2 (1) B = ∠BC_1A_1=∠BA_2C_2 (2) C = ∠CA_1B_1=∠CB_2A_2. ...

The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...