The Simson line LN (red) of the triangle ABC with respect to point P on the circumcircle
In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear.[1] The line through these points is the Simson line of P, named for Robert Simson.[2] The concept was first published, however, by William Wallace in 1799,[3] and is sometimes called the Wallace line.[4]
The converse is also true; if the three closest points to P on three lines are collinear, and no two of the lines are parallel, then P lies on the circumcircle of the triangle formed by the three lines. Or in other words, the Simson line of a triangle ABC and a point P is just the pedal triangle of ABC and P that has degenerated into a straight line and this condition constrains the locus of P to trace the circumcircle of triangle ABC.
lines AB, AC, and BC are collinear. The line through these points is the Simsonline of P, named for Robert Simson. The concept was first published, however...
Robert Simson (14 October 1687 – 1 October 1768) was a Scottish mathematician and professor of mathematics at the University of Glasgow. The Simsonline is...
automobiles, motorcycles, and mopeds Simsonline in geometry, named for Robert SimsonSimson Provincial Park in Canada KSV Simson Bremen, German football club...
to the sides of triangle ABC are collinear and the line of collinearity is the well-known Simsonline of P. Given a point P, let the feet of perpendiculars...
on the circumcircle of the triangle, △LMN collapses to a line (the pedal line or Simsonline). The vertices of the pedal triangle of an interior point...
each of the three extended sides of the triangle are collinear in the Simsonline of the point on the circumcircle. The lines connecting the feet of the...
formula. William Wallace becomes the first to publish the concept of the Simsonline. March – The Pneumatic Institution for research into the medical implications...
geometric objects associated with triangle centers such as the Euler line, Simsonline, and nine-point circle. The chapter on areas includes both trigonometric...
The Perpendicular Bisector Construction, the Isoptic Point and the SimsonLine of a Quadrilateral, Forum Geometricorum 12: 161–189 (2012). de Villiers...
(fractal geometry) Similarity (geometry) Similarity system of triangles Simsonline Special right triangles Spieker center Spieker circle Spiral of Theodorus...
determine a degenerated circle with an infinite radius, that is a line. This is the Simsonline. If P {\displaystyle P} is the incenter of the triangle then...
the circle the result is not contained in the Elements. However, Robert Simson following Christopher Clavius demonstrated this result, sometimes called...
Simson Shorthand is a system of shorthand invented by James Simson, originally published in his 1881 book, Compend of Syllabic Shorthand: Being a Synopsis...
triangles will be lines; namely, the Simsonline of D with respect to triangle △ABC, and the other analogous Simson lines. In that case, those lines still...
have vocal parts. The ride also features clips from the show in the waiting line. Numerous video games based on the show have been produced. Some of the early...
Scotland. William Wallace becomes the first to publish the concept of the Simsonline in mathematics. 6 February – George Arnott Walker-Arnott, botanist (died...
Michelle Simson (born July 10, 1953) is a Canadian politician, who was elected to represent the Ontario electoral district of Scarborough Southwest as...
taken, the straight line between them lies wholly in that superficies (surface). The line is known as Simsonline. Lakon accepted Simson's definition of the...
three points of the concourse of opposite sides lie on a straight line. Robert Simson explained the only three propositions which Pappus indicates with...
Sauer & Sohn. Furthermore, the engineering industry was based in Suhl with Simson, a famous car and moped producer. In 1952, Suhl became one of East Germany's...
Everyday Life in Ancient Egypt, Courier Dover 2002, p.175 Compare: Najovits, Simson R. (May 2003). "The Social Context of the Egyptian Politico-Religious System"...
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