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A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

The curve y=1-e^(ax), illustrated above.

A one-dimensional map whose increments are distributed according to a normal distribution. Let y(t-Deltat) and y(t+Deltat) be values, then their correlation is given by the ...

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.

A connection defined on a smooth algebraic variety defined over the complex numbers.

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m>2. If n/m<2, the curve is a hypoellipse.

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m<2. If n/m>2, the curve is a hyperellipse.

Let a plane figure have area A and perimeter p. Then Q=(4piA)/(p^2)<=1, where Q is known as the isoperimetric quotient. The equation becomes an equality only for a circle.

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

A sphere is rigid.