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Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

The involute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_i = ...

A generalization of the helicoid to the parametric equations x(u,v) = avcosu (1) y(u,v) = bvsinu (2) z(u,v) = cu. (3) In this parametrization, the surface has first ...

The parametric equations of the evolute of an epitrochoid specified by circle radii a and b with offset h are x = ...

The extended greatest common divisor of two integers m and n can be defined as the greatest common divisor GCD(m,n) of m and n which also satisfies the constraint ...

The gear curve is a curve resembling a gear with n teeth given by the parametric equations x = rcost (1) y = rsint, (2) where r=a+1/btanh[bsin(nt)], (3) where tanhx is the ...

One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...

A hexecontahedron is a 60-faced polyhedron. Examples include the deltoidal hexecontahedron, rhombic hexecontahedron, and triakis icosahedron. Counting the faces produced by ...