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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.
Saccheri quadrilaterals. A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base.It is named after Giovanni Gerolamo Saccheri, who used it extensively in his 1733 book Euclides ab omni naevo vindicatus (Euclid freed of every flaw), an attempt to prove the parallel postulate using the method reductio ad absurdum.
The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry ...
The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane (plane geometry) and the three-dimensional Euclidean space. [b] [20]
The geometry of the Euclidean plane is the common elementary geometry taught in schools. Subcategories This category has the following 11 subcategories, out of 11 total.
Egyptian geometry; Ancient Greek geometry Euclidean geometry. Pythagorean theorem; Euclid's Elements; Measurement of a Circle; Indian mathematics. Bakhshali manuscript; Modern geometry History of analytic geometry. History of the Cartesian coordinate system; History of non-Euclidean geometry; History of topology; History of algebraic geometry ...
In addition, the Euclidean geometry (which has zero curvature everywhere) is not the only geometry that the plane may have. The plane may be given a spherical geometry by using the stereographic projection. This can be thought of as placing a sphere tangent to the plane (just like a ball on the floor), removing the top point, and projecting the ...
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