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Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
The red triangle is the medial triangle of the black. The endpoints of the red triangle coincide with the midpoints of the black triangle. In Euclidean geometry, the medial triangle or midpoint triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC, BC.
The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's diameter.
10 Andrews–Curtis conjecture: combinatorial group theory: James J. Andrews and Morton L. Curtis: 358 Andrica's conjecture: number theory: Dorin Andrica: 45 Artin conjecture (L-functions) number theory: Emil Artin: 650 Artin's conjecture on primitive roots: number theory: ⇐generalized Riemann hypothesis [2] ⇐Selberg conjecture B [3] Emil ...
The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.
The "straightedge" and "compass" of straightedge-and-compass constructions are idealized versions of real-world rulers and compasses. The straightedge is an infinitely long edge with no markings on it. It can only be used to draw a line segment between two points, or to extend an existing line segment.
Morrie's law is a special trigonometric identity.Its name is due to the physicist Richard Feynman, who used to refer to the identity under that name.Feynman picked that name because he learned it during his childhood from a boy with the name Morrie Jacobs and afterwards remembered it for all of his life.
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.