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Simson line

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. The line through these points is the Simson line of P, named for Robert Simson. The concept was first published, however, by William Wallace in 1799, and is sometimes called the Wallace line.

Properties, Equation & Generalizations

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Overview

Equation

Properties

Generalizations

Advanced semantic analysis

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Map overview Semantic statistics

Simson line

Nodes31
Edges30
Triples48
Avg. degree1.94
Density0.064516
Components1

How this topic connects Entity context

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Simson line

Top relations

related to Generalization 1 · 16
Simson line → AB, Ap, B0, BC, BP, C0, CA, CP, If, Let A0, Let ABC, Let AP, Moreover, PH, Simson, Then A0
related to Properties · 15
Simson line → ABC, Furthermore, Given, If, In, Letting, No, PH, PQ, Simson, Steiner, The, The Simson, The Steiner, This
related to External links · 10
Simson line → Dynamic Geometry Sketches, Eric, Euler, Interactive Geometry, Jackson, MathWorld, Neuberg's Pedal, Simson, Simson-Wallace, Weisstein
related to Equation · 3
Simson line → ABC, Placing, The Simson
related to Generalization 3 · 3
Simson line → Cyclic Quadrilateral, Cyster, The Simson Lines
is a · 1
Simson line → set of points z satisfying 2 a b c z

Important terminology Word statistics

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Important terminology

simson line triangle point circumcircle points lines angle abc collinear displaystyle quadrilateral 180 circ two lies pedal geometry side circle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Simson lineis aset of points z satisfying 2 a b c z0.90text
Simson linerelated to EquationPlacing0.60section
Simson linerelated to EquationABC0.60section
Simson linerelated to EquationThe Simson0.60section
Simson linerelated to External linksJackson0.60section
Simson linerelated to External linksWeisstein0.60section
Simson linerelated to External linksEric0.60section
Simson linerelated to External linksMathWorld0.60section
Simson linerelated to External linksNeuberg's Pedal0.60section
Simson linerelated to External linksSimson-Wallace0.60section
Simson linerelated to External linksDynamic Geometry Sketches0.60section
Simson linerelated to External linksSimson0.60section

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    Connections between topic areas Semantic bridges

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    Min side: 3
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