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The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

Amazingly, the catacaustic of the deltoid when the rays are parallel in any direction is an astroid. In particular, for a deltoid with parametric equations x = 2cost+cos(2t) ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...

The 5.1.2 fifth-order Diophantine equation A^5=B^5+C^5 (1) is a special case of Fermat's last theorem with n=5, and so has no solution. improving on the results on Lander et ...

Let G be an algebraic group. G together with the discrete topology is a locally compact group and one may consider the counting measure as a left invariant Haar measure on G. ...

A number of attractive 2-compounds of the regular dodecahedron can be constructed. The first (left figures) has the symmetry of the cube and arises by combining two regular ...

A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function C_y(tau), spectral ...

The surface of revolution given by the parametric equations x(u,v) = cosusin(2v) (1) y(u,v) = sinusin(2v) (2) z(u,v) = sinv (3) for u in [0,2pi) and v in [-pi/2,pi/2]. It is ...

The evolute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_e = (a^2-b^2)/acos^3t (3) y_e = (b^2-a^2)/bsin^3t. ...

The pedal curve of an ellipse with parametric equations x = acost (1) y = bsint (2) and pedal point (x_0,y_0) is given by f = ...