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To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

Given a general second tensor rank tensor A_(ij) and a metric g_(ij), define theta = A_(ij)g^(ij)=A_i^i (1) omega^i = epsilon^(ijk)A_(jk) (2) sigma_(ij) = ...

The Kenmotu circle is the circle passing through the six contact points of the congruent squares used in the construction of the Kenmotu point with the triangle sides. It is ...

Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then ds_N^2=ds_T^2+ds_B^2, (1) where ds_N^2 = ...

For an infinite population with mean mu, variance sigma^2, skewness gamma_1, and kurtosis excess gamma_2, the corresponding quantities for the distribution of means are ...

To find the minimum distance between a point in the plane (x_0,y_0) and a quadratic plane curve y=a_0+a_1x+a_2x^2, (1) note that the square of the distance is r^2 = ...

The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1. A full angle is ...

A related rates problem is the determination of the rate at which a function defined in terms of other functions changes. Related rates problems can be solved by computing ...

The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...