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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.
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 compass.
Euclidean geometry was developed without change of methods or scope until the 17th century, when René Descartes introduced what is now called Cartesian coordinates. This constituted a major change of paradigm : Instead of defining real numbers as lengths of line segments (see number line ), it allowed the representation of points using their ...
This axiom is used not only in Euclidean geometry but also in the broader study of affine geometry where the concept of parallelism is central. In the affine geometry setting, the stronger form of Playfair's axiom (where "at most one" is replaced by "one and only one") is needed since the axioms of neutral geometry are not present to provide a ...
Forum Geometricorum: A Journal on Classical Euclidean Geometry was a peer-reviewed open-access academic journal that specialized in mathematical research papers on Euclidean geometry. [ 1 ] Founded in 2001, it was published by Florida Atlantic University and was indexed by Mathematical Reviews [ 2 ] and Zentralblatt MATH . [ 3 ]
Euclidean tilings are usually named after Cundy & Rollett’s notation. [1] This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons.
The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows: [1]: p. 78 Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY.
The British flag theorem can be generalized into a statement about (convex) isosceles trapezoids.More precisely for a trapezoid with parallel sides and and interior point the following equation holds:
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