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The term apex may used in different contexts: In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side. [1] Here the point A is the apex. In a pyramid or cone, the apex is the vertex at the "top" (opposite the base). In a pyramid, the vertex is the point that is part of all the ...
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 ...
In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called an apex of the graph. It is an apex, not the apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs K 5 or K 3,3, every vertex is an apex. The ...
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
[2]: p. 30 In the fifth century BCE, Hippias used a curve that he called a quadratrix to both trisect the general angle and square the circle, and Nicomedes in the second century BCE showed how to use a conchoid to trisect an arbitrary angle; [2]: p. 37 but these methods also cannot be followed with just straightedge and compass.
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]
For an equilateral triangle, these are the same point, which lies at the intersection of the three axes of symmetry of the triangle, one third of the distance from its base to its apex. A strict definition of a triangle centre is a point whose trilinear coordinates are f ( a , b , c ) : f ( b , c , a ) : f ( c , a , b ) where f is a function of ...
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