Find link

language:

Find link is a tool written by Edward Betts.

Longer titles found: Descartes' theorem (disambiguation) (view)

searching for Descartes' theorem 10 found (33 total)

Angular defect (836 words) [view diff] no match in snippet view article find links to article

In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such

Gauss–Bonnet theorem (1,842 words) [view diff] exact match in snippet view article find links to article

proportional to its defect, as established by Johann Heinrich Lambert. Descartes' theorem on total angular defect of a polyhedron is the polyhedral analog:

Vertex configuration (1,675 words) [view diff] exact match in snippet view article find links to article

the angle defect can be used to compute the number of vertices. Descartes' theorem states that all the angle defects in a topological sphere must sum

Descartes on Polyhedra (882 words) [view diff] exact match in snippet view article find links to article

notation. In De solidorum elementis, Descartes states (without proof) Descartes' theorem on total angular defect, a discrete version of the Gauss–Bonnet theorem

Alexandrov's uniqueness theorem (1,730 words) [view diff] exact match in snippet view article find links to article

Similarly, a cube has a defect of π/2 at each of its eight vertices. Descartes' theorem on total angular defect (a form of the Gauss–Bonnet theorem) states

Convex Polyhedra (book) (763 words) [view diff] exact match in snippet view article

except at a finite set of points of positive angular defect, obeying Descartes' theorem on total angular defect that the total angular defect should be 4

Euler characteristic (3,449 words) [view diff] exact match in snippet view article find links to article

the general case. A discrete analog of the Gauss–Bonnet theorem is Descartes' theorem that the "total defect" of a polyhedron, measured in full circles

Platonic solid (5,615 words) [view diff] exact match in snippet view article find links to article

an angle defect. A 0° angle defect will fill the Euclidean plane with a regular tiling. By Descartes' theorem, the number of vertices is 720°/defect.

Curvature (6,461 words) [view diff] exact match in snippet view article find links to article

the (angular) defect; the analog for the Gauss–Bonnet theorem is Descartes' theorem on total angular defect. Because (Gaussian) curvature can be defined

Polyhedron (10,118 words) [view diff] exact match in snippet view article find links to article

rediscovered until the 19th century. One of its contributions was Descartes' theorem on total angular defect, which is closely related to Euler's polyhedral