*aka “shapes + sizes”*
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*courtesy of ‘ancient greeks’ –>
γεωμετρία
geo– -> “earth”
-metron -> “measurement”
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[“geometry” is a branch of ‘mathematics’ concerned with questions of…]
*’shape’*
*’size’*
*’relative position’ of ‘figures’*
*’properties of ‘space’*
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(a mathematician who works in the field of ‘geometry’ is called a ‘geometer’)
(i like that title!)
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(‘geometry’ arose independently in a number of ‘early cultures’ as a body of ‘practical knowledge’ concerning [‘lengths’ / ‘areas’ / ‘volumes’], with elements of ‘formal mathematical science’ emerging in the ‘west’ as early as ‘thales’ (~6th centry BCE))
(by the ‘3rd century BCE’, ‘geometry’ was put into an ‘axiomatic form’ by ‘euclid’, whose treatment—’euclidean geometry’—set a standard for many centuries to follow)
(‘archimedes’ developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus)
(the field of ‘astronomy’, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia)
(in the ‘classical world’, both ‘geometry’ and ‘astronomy’ were considered to be part of the ‘Quadrivium’, a subset of the 7 liberal arts considered essential for a free citizen to master)
(the introduction of coordinates by ‘René Descartes’ and the concurrent developments of algebra marked a new stage for geometry, since geometric figures such as ‘plane curves’ could now be represented analytically in the form of functions and equations)
(this played a key role in the emergence of ‘infinitesimal calculus’ in the 17th century)
(furthermore, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of ‘projective geometry’)
(the subject of ‘geometry’ was further enriched by the study of the intrinsic structure of geometric objects that originated with ‘Euler’ and ‘Gauss’ and led to the creation of topology and ‘differential geometry’)
(in Euclid’s time, there was no clear distinction between physical and geometrical space)
(since the 19th-century discovery of non-Euclidean geometry, the concept of space has undergone a radical transformation and raised the question of which geometrical space best fits physical space)
(with the rise of formal mathematics in the 20th century, ‘space’ (whether ‘point’, ‘line’, or ‘plane’) lost its intuitive contents, so today one has to distinguish between physical space, geometrical spaces (in which ‘space’, ‘point’ etc. still have their intuitive meanings) and ‘abstract spaces’)
(contemporary geometry considers ‘manifolds’, spaces that are considerably more abstract than the familiar ‘Euclidean space’, which they only approximately resemble at small scales)
(these spaces may be endowed with additional structure which allow one to speak about length)
(modern geometry has many ties to ‘physics’ as is exemplified by the links between pseudo-Riemannian geometry and ‘general relativity’)
(one of the youngest physical theories, ‘string theory’, is also very geometric in flavor)
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(while the visual nature of ‘geometry’ makes it initially more accessible than other mathematical areas such as ‘algebra’ or ‘number theory’, ‘geometric language’ is also used in contexts far removed from its traditional euclidean provenance (for example, in ‘fractal geometry’ + ‘algebraic geometry’))
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💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥