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Download as PDF; Printable version; In other projects ... Euclidean plane geometry (11 C, 96 P) R. Reflection groups (1 C, 8 P) S. Euclidean solid geometry (7 C, 33 P)
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions ( theorems ) from these.
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle ABC, let the lines AO, BO, CO be drawn from the vertices to a common point O (not on one of the sides of ABC), to meet opposite sides at D, E, F respectively. (The segments AD, BE, CF are known as cevians.) Then, using signed lengths of segments,
The Geometer's Sketchpad is a commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics.It was created as part of the NSF-funded Visual Geometry Project led by Eugene Klotz and Doris Schattschneider from 1986 to 1991 at Swarthmore College. [1]
Tarski's axioms are an axiom system for Euclidean geometry, specifically for that portion of Euclidean geometry that is formulable in first-order logic with identity (i.e. is formulable as an elementary theory). As such, it does not require an underlying set theory. The only primitive objects of the system are "points" and the only primitive ...
In particular, Euclidean geometry was more restrictive than affine geometry, which in turn is more restrictive than projective geometry. Klein proposed that group theory , a branch of mathematics that uses algebraic methods to abstract the idea of symmetry , was the most useful way of organizing geometrical knowledge; at the time it had already ...
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