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Greek mathematics constitutes an important period in the history of mathematics: fundamental in respect of geometry and for the idea of formal proof. [44] Greek mathematicians also contributed to number theory, mathematical astronomy, combinatorics, mathematical physics, and, at times, approached ideas close to the integral calculus. [45] [46]
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
Geometry (from the Ancient Greek: γεωμετρία; geo-"earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers . Classic geometry was focused in compass and straightedge constructions.
For the most part, straightedge and compass constructions dominated ancient Greek mathematics and most theorems and results were stated and proved in terms of geometry. These proofs involved a straightedge (such as that formed by a taut rope), which was used to construct lines, and a compass, which was used to construct circles.
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.
The book is written for a general audience, unlike a follow-up work published by Knorr, Textual Studies in Ancient and Medieval Geometry (1989), which is aimed at other experts in the close reading of Greek mathematical texts. [1] Nevertheless, reviewer Alan Stenger calls The Ancient Tradition of Geometric Problems "very specialized and ...
Hutton's definitions in 1795 [4]. The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια (trapezia [5] literally 'table', itself from τετράς (tetrás) 'four' + πέζα (péza) 'foot ...
Based on ancient Greek methods, an axiomatic system is a formal description of a way to establish the mathematical truth that flows from a fixed set of assumptions. Although applicable to any area of mathematics, geometry is the branch of elementary mathematics in which this method has most extensively been successfully applied.