In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by d 2 = R ( R − 2 r ) {\displaystyle...

length Euler squares, usually called Graeco-Latin squares Euler's theorem in geometry, relating the circumcircle and incircle of a triangle Euler's quadrilateral...

In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence...

polyhedron theorem (polyhedra) Euler's quadrilateral theorem (geometry) Euler's rotation theorem (geometry) Euler's theorem (differential geometry) Euler's theorem...

In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains...

In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

which has Euler characteristic 2. This viewpoint is implicit in Cauchy's proof of Euler's formula given below. There are many proofs of Euler's formula...

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive...

Equidissection Equilateral triangle Euler's line Euler's theorem in geometry Erdős–Mordell inequality Exeter point Exterior angle theorem Fagnano's problem Fermat...

eigenvalue comparison theorem Clifford's theorem on special divisors Cohn-Vossen's inequality Erdős–Mordell inequality Euler's theorem in geometry Gromov's inequality...

published in Acta Eruditorum, 1744 The title page of Euler's Methodus inveniendi lineas curvas Euler's 1760 world map Euler's 1753 map of Africa Euler is listed...

In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature...

the geometry of the sphere, and Menelaus of Alexandria, who wrote a book on spherical trigonometry called Sphaerica and developed Menelaus' theorem. The...

known as Euler's theorem. Later in the 1700s, the new French school led by Gaspard Monge began to make contributions to differential geometry. Monge made...

the Euler characteristic of the 2-sphere is two. Therefore, there must be at least one zero. This is a consequence of the Poincaré–Hopf theorem. In the...

sphere are concentric with each other and with the sphere. By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle...

The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...

dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss's Theorema Egregium ("remarkable theorem") that asserts roughly...

Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...

one third the length of the longest median of the triangle. By Euler's theorem in geometry, the squared distance from the incenter I to the circumcenter...

In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...

the theorem is still unproven in the 24th century. The proof was released five years after the episode originally aired. Mathematics portal Euler's sum...

algebraic geometry are ideal tools to study these equations. Diophantine geometry is part of the broader field of arithmetic geometry. Four theorems in Diophantine...

sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant,...

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel...

geometry topics Glossary of Riemannian and metric geometry What follows is an incomplete list of the most classical theorems in Riemannian geometry....

The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded...

In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...

the Gauss-Codazzi equations. A major theorem, often called the fundamental theorem of the differential geometry of surfaces, asserts that whenever two...