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The symmetry operation (x,y,z)->(x,y,-z), etc., which is equivalent to 2^_, where the bar denotes an improper rotation.

The set of all points x that can be put into one-to-one correspondence with sets of essentially distinct values of four homogeneous coordinates x_0:x_1:x_2:x_3, not all ...

Let M subset R^3 be a regular surface and u_(p) a unit tangent vector to M, and let Pi(u_(p),N(p)) be the plane determined by u_(p) and the normal to the surface N(p). Then ...

A cylindric section is the intersection of a plane with a right circular cylinder. It is a circle (if the plane is at a right angle to the axis), an ellipse, or, if the plane ...

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 ...

The coordinate system obtained by inversion of Cartesian coordinates, with u,v,w in (-infty,infty). The transformation equations are x = u/(u^2+v^2+w^2) (1) y = ...

The set A^2 of all ordered pairs of complex numbers.

The set P^2 is the set of all equivalence classes [a,b,c] of ordered triples (a,b,c) in C^3\(0,0,0) under the equivalence relation (a,b,c)∼(a^',b^',c^') if ...

Draw three circles in the plane, none of which lies completely inside another, and the common external tangent lines for each pair. Then points of intersection of the three ...

A crunode, also known as an ordinary double point, of a plane curve is point where a curve intersects itself so that two branches of the curve have distinct tangent lines. ...