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The inner and outer spheres tangent internally to a cone and also to a plane intersecting the cone are called Dandelin spheres. The spheres can be used to show that the ...

A spheric section is the curve formed by the intersection of a plane with a sphere. Excluding the degenerate cases of the plane tangent to the sphere or the plane not ...

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

The surface corresponding to the region of obscuration when a solid is illuminated from a point light source (located at the radiant point). A disk is the shadow of a sphere ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f ...

How many times can a shape be completely surrounded by copies of itself without being able to tile the entire plane, i.e., what is the maximum (finite) Heesch number?

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

Increasing a plane figure's linear dimensions by a scale factor s increases the perimeter p^'->sp and the area A^'->s^2A.

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...