Search Results for ""

Let T be a linear operator on a separable Hilbert space. The spectrum sigma(T) of T is the set of lambda such that (T-lambdaI) is not invertible on all of the Hilbert space, ...

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

The principal theorem of axonometry, first published without proof by Pohlke in 1860. It states that three segments of arbitrary length a^'x^', a^'y^', and a^'z^' which are ...

A curve alpha on a regular surface M is a principal curve iff the velocity alpha^' always points in a principal direction, i.e., S(alpha^')=kappa_ialpha^', where S is the ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

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 ...

A polyhedron or plane tessellation is called semiregular if its faces are all regular polygons and its corners are alike (Walsh 1972; Coxeter 1973, pp. 4 and 58; Holden 1991, ...

The standard form of a line in the Cartesian plane is given by ax+by=c for real numbers a,b,c in R. This form can be derived from any of the other forms (point-slope form, ...

The tangram is a combination of plane polygonal pieces such that the edges of the polygons are coincident. There are 13 convex tangrams (where a "convex tangram" is a set of ...