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The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

The angular acceleration alpha is defined as the time derivative of the angular velocity omega, alpha=(domega)/(dt)=(d^2theta)/(dt^2)z^^=(a)/r.

The angular distance traveled around a circle is the number of radians the path subtends, theta=l/(2pir)2pi=l/r.

The angular velocity omega is the time derivative of the angular distance theta with direction z^^ perpendicular to the plane of angular motion, omega=(dtheta)/(dt)z^^=(v)/r.

When the Gaussian curvature K is everywhere negative, a surface is called anticlastic and is saddle-shaped. A surface on which K is everywhere positive is called synclastic. ...

Two curves which, at any point, have a common principal normal vector are called Bertrand curves. The product of the torsions of Bertrand curves is a constant.

A biflecnode, also called a biflecnodal point, is a point at which a curve crosses itself and is at the same time an inflection point. Biflecnodes are possible for curves of ...

The comass of a differential p-form phi is the largest value of phi on a p vector of p-volume one, sup_(v in ^ ^pTM,|v|=1)|phi(v)|.

Let gamma(t) be a smooth curve in a manifold M from x to y with gamma(0)=x and gamma(1)=y. Then gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x. The ...