the Euler line, named after Leonhard Euler (/ˈɔɪlər/ OY-lər), is a line determined from any triangle that is not equilateral. It is a central line of the...

mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique...

{\displaystyle 4c^{4}+9a^{2}b^{2}=16m_{a}^{2}m_{b}^{2}.} In a right triangle, the Euler line contains the median on the hypotenuse—that is, it goes through both the...

have: the Euler line, the Simson lines, and central lines. For a convex quadrilateral with at most two parallel sides, the Newton line is the line that connects...

Greeks, and the only one of the four that does not in general lie on the Euler line. It is the first listed center, X(1), in Clark Kimberling's Encyclopedia...

throughout the book. The nine-point circle with the Euler line and the Spieker circle with the Nagel line are analogous to each other, but are not duals,...

which it follows that the Euler line coincides with the axis of symmetry. The incenter of the triangle also lies on the Euler line, something that is not...

and has been used to define an Euler line of a quadrilateral. The circumcenter of mass allows us to define an Euler line for simplicial polytopes. Let...

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary...

circle all lie on a single line, known as the Euler line. The center of the nine-point circle lies at the midpoint of the Euler line, between the orthocenter...

N.. "The distance from the incenter to the Euler line", Forum Geometricorum 11 (2011): 231–236. L. Euler, "Solutio facilis problematum quorundam geometricorum...

also contains the triangle's nine-point center and is a subset of the Euler line, which also contains the circumcenter outside the orthocentroidal circle...

center of the nine-point circle are collinear, all falling on a line called the Euler line. The de Longchamps point also has other collinearities. Any vertex...

Euler lines of the four possible triangles where the extended line HN is the Euler line of triangle △ABC and the extended line AN is the Euler line of...

{ON}}={\overline {NH}}.} The nine-point center N is one-fourth of the way along the Euler line from the centroid G to the orthocenter H:: p.153  H N ¯ = 3 N G ¯ . {\displaystyle...

The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They...

circumscribed sphere). These three points define the Euler line of the tetrahedron that is analogous to the Euler line of a triangle. These results generalize to...

(orange), and the circumcenter (green) all lie on a single line, known as Euler's line (red line). The center of the nine-point circle lies at the midpoint...

Euler point to the face not containing the vertex that generated the Euler point. The center T of the twelve-point sphere also lies on the Euler line...

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric...

axis of perspectivity of the △ABC and its medial triangle. The Euler line of △ABC is the line passing through the centroid, the circumcenter, the orthocenter...

algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant...

In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the...

logarithm, also commonly written as ln(x) or loge(x). Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually...

In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose...

the Euler line of its triangle, at the midpoint between that triangle's orthocenter H and circumcenter O. The centroid G also lies on the same line, 2/3...

notable points on the Euler line", pp. 380–383. Longuet-Higgins, Michael (2000), "A fourfold point of concurrence lying on the Euler line of a triangle", The...

An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the...

point as Zeeman–Gossard perspector. Let ABC be any triangle. Let the Euler line of triangle ABC meet the sidelines BC, CA and AB of triangle ABC at D...

lines X(13)X(15) and X(14)X(16) are parallel to the Euler line. The three lines meet at the Euler infinity point, X(30). The points X(13), X(14), the...