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The equation of the curve of intersection of a torus with a plane perpendicular to both the midplane of the torus and to the plane x=0. (The general intersection of a torus ...

A term invented by B. Grünbaum in an attempt to promote concrete and precise polyhedron terminology. The word "coptic" derives from the Greek for "to cut," and acoptic ...

If the tangents at B and C to the circumcircle of a triangle DeltaABC intersect in a point K_1, then the circle with center K_1 and which passes through B and C is called the ...

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

In the hyperbolic plane H^2, a pair of lines can be parallel (diverging from one another in one direction and intersecting at an ideal point at infinity in the other), can ...

The 60 Pascal lines of a hexagon inscribed in a conic section intersect three at a time through 20 Steiner points. There is a dual relationship between the 15 Plücker lines ...

The closed plane curve that crosses itself once and consists of one lobe on each side of the intersection. It can be viewed as a circle with a half twist. The fundamental ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

A planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing," of a planar graph is an embedding in ...