Search results
Results From The WOW.Com Content Network
Concurrent lines arise in the dual of Pappus's hexagon theorem. For each side of a cyclic hexagon, extend the adjacent sides to their intersection, forming a triangle exterior to the given side. Then the segments connecting the circumcenters of opposite triangles are concurrent.
Ceva's theorem, case 1: the three lines are concurrent at a point O inside ABC Ceva's theorem, case 2: the three lines are concurrent at a point O outside ABC. In Euclidean geometry, Ceva's theorem is a theorem about triangles.
Variants of this concept exist for a quadruple of concurrent lines on the projective plane and a quadruple of points on the Riemann sphere. In the Cayley–Klein model of hyperbolic geometry, the distance between points is expressed in terms of a certain cross-ratio.
Commandino's theorem, named after Federico Commandino (1509–1575), states that the four medians of a tetrahedron are concurrent at a point S, which divides them in a 3:1 ratio. In a tetrahedron a median is a line segment that connects a vertex with the centroid of the opposite face – that is, the centroid of the opposite triangle.
(Concurrent means that the lines pass through one point.) Pappus's theorem is a special case of Pascal's theorem for a conic—the limiting case when the conic degenerates into 2 straight lines. Pascal's theorem is in turn a special case of the Cayley–Bacharach theorem .
Given any line l, let P, Q, R be the feet of perpendiculars from the vertices A, B, C of triangle ABC to l. The lines through P. Q, R perpendicular respectively to the sides BC, CA, AB are concurrent and the point of concurrence is the orthopole of the line l with respect to the triangle ABC. In modern triangle geometry, there is a large body ...
Concurrent lines, in geometry, multiple lines or curves intersecting at a single point Concurrency (road) , an instance of one physical road bearing two or more different route numbers Concurrent (Easter) , the weekday of 24 March Julian used to calculate Julian Easter
In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors.