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The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

A line segment connecting nonadjacent polyhedron vertices sharing a common face in a parallelepiped or other similar solid.

Find the m×n array of single digits which contains the maximum possible number of primes, where allowable primes may lie along any horizontal, vertical, or diagonal line. For ...

For a nonzero real number r and a triangle DeltaABC, swing line segment BC about the vertex B towards vertex A through an angle rB. Call the line along the rotated segment L. ...

Orthogonal involution, also called absolute involution, is the involution on the line at infinity that maps orthogonal directions to each other.

A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

A perimeter-bisecting line segment which originates at a vertex of a polygon. The three splitters of a triangle concur in a point known as the Nagel point Na.

Given a triangle center X=l:m:n, the line mnalpha+nlbeta+lmgamma=0, where alpha:beta:gamma are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38). ...

If an infinite number of points in the plane are all separated by integer distances, then all the points lie on a straight line.