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A crossing in a knot diagram for which there exists a circle in the projection plane meeting the diagram transversely at that crossing, but not meeting the diagram at any ...

The regular skew icosahedron is a six-dimensional regular polytope that is just as symmetric as the Platonic icosahedron, but having different angles (Coxeter 1950; Coxeter ...

Given a circular table of diameter 9 feet, which is the minimal number of planks (each 1 foot wide and length greater than 9 feet) needed in order to completely cover the ...

A sphere is defined as the set of all points in three-dimensional Euclidean space R^3 that are located at a distance r (the "radius") from a given point (the "center"). Twice ...

The 120-cell is a finite regular four-dimensional polytope with Schläfli symbol {5,3,3}. It is also known as the hyperdodecahedron or hecatonicosachoron, and is composed of ...

The hypercube is a generalization of a 3-cube to n dimensions, also called an n-cube or measure polytope. It is a regular polytope with mutually perpendicular sides, and is ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...