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1The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.

*‘By spherical geometry, we mean geometry on the surface of a sphere, where the great circles are taken as lines.’**‘As analysis began to mix inextricably with geometry and the other branches of mathematics, the curiosities multiplied.’**‘A notable feature of advanced mathematics is that much of it is concerned with geometry in more than three dimensions.’**‘Most of the features for surfaces appearing in this book are closely related to topological geometry.’**‘Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics.’**‘He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well.’**‘He worked on the borderline between geometry and set theory, both of which are kind of nineteenth century.’**‘It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.’**‘Let us first comment on the three volume work, which was the biggest treatise ever to be written on line geometry.’**‘Simson also made many discoveries of his own in geometry and the Simson line is named after him.’**‘He goes on to consider solid geometry giving results on prisms, cylinders, and spheres.’**‘You can still access the underlying curve and surface geometry that makes up the solid.’**‘Speculative geometry contains elementary geometry which is not all based on Euclid.’**‘Low-income students who took algebra and geometry were almost three times as likely to attend college as those who did not.’**‘At this point the Greeks gave up algebra and turned to geometry.’**‘He clearly was trying to argue against the notions current at the time on using algebra to study geometry.’**‘Galileo's idea was to overcome this subjectivity and relativity by applying pure geometry and the mathematics of the pure form of space-time to nature.’**‘This requires at least some understanding of spherical geometry and trigonometry.’**‘The computer programs implement basic mathematical principles such as basic geometry and fractional math.’**‘His writings on geometry included several important papers on parallel curves and surfaces.’*

- 1.1A particular system of geometry.
*‘non-Euclidean geometries’**‘He also realised that there were an infinite number of non-euclidean geometries and this, Taurinus claimed, was highly significant.’**‘The trend toward trophic specialization is also correlated with stereotyped geometries in the locomotor system.’**‘The same issues apply more generally to other photonic crystal systems in non-fiber geometries.’**‘Similar stratal geometries have been described from comparable levels in the Chalk of the North Sea, and in outcrop in Britain and France.’**‘He also studied birational contact transformations and non-euclidean and non-archimedean geometries.’**‘It was not until the 19th century that this postulate was dropped and non-euclidean geometries were studied.’**‘His interests in research relate to finite geometries and the group theory related to them, to Cremona transformations related to the Galois theory of equations.’**‘His work on non-euclidean geometries was used by Einstein in his general theory of relativity.’**‘Geometry had began to lose its 'metric' character with projective and non-euclidean geometries being studied.’**‘Weil's work on bringing together number theory and algebraic geometry was highly fruitful.’**‘He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.’**‘His main mathematical interests were in algebraic geometry and differential geometry.’**‘His derivation of the estimates is a tour de force and the applications in algebraic geometry are beautiful.’**‘This work led to a thesis on algebraic geometry in which he introduced rings which are now named after him.’**‘The apparatus of algebraic geometry is built upon polars, and these upon distances.’**‘Under Lane she studied projective differential geometry and submitted her dissertation on Singularities of Space Curves.’**‘Note, of course, that the use of such positional grids are an early form of Cartesian geometry.’**‘Something that exists nowhere and exists along the lines of Euclidean geometry, judging by what I understand of it, cannot exist.’**‘Van Schooten was one of the main people to promote the spread of Cartesian geometry.’**‘He has written on stochastic geometry and its applications, and the statistical theory of shape.’*

- 1.2in singular The shape and relative arrangement of the parts of something.
*‘the geometry of spiders' webs’**‘Perhaps this intimate knowledge of the geometry of letterforms is why even today so many architects are partial to Futura.’**‘Modern artists long ago discovered and assimilated the geometry, line and shapes of African sculpture.’**‘At the same time, anatomical data that include the torso geometry and the shape and location of the heart are obtained via a CT scan.’**‘It connects us to the geometry of the body - the square, the circle and the triangle - and to the purity of line.’**‘I can't help it: where some see visionary lines and inspired angles I see the geometry of a madman.’**‘In the first place, chemical solutions can conform to the geometry of the sample vessel or object being irradiated.’**‘The geometry or shape of individual grains appears to be a property inherited from the original crystals of the silicate minerals in the source rock.’**‘This is used in ophthalmic surgery to maintain the geometry of the eye, and can also be used for therapeutic treatments involving osteoarthritis and wound healing.’**‘‘I was fascinated by the geometry of the ruined monuments I looked at,’ Ghosh explains.’**‘The main living area is open plan and bathed in light from the tall windows, and the geometry of this window formation is echoed within the structure of the space.’**‘I read it in my early twenties and thought, I will never, so long as I live, know as much about the geometry of the human heart.’**‘I eyed up the chest of drawers but the geometry seemed wrong somehow.’**‘In fact, the cornerstone setting lets you tweak the geometry of the picture to your heart's content.’**‘Once again, daguerreotypy was reduced to a geometry of abstract markings.’**‘Finally, we indicate the source of such inconsistent analysis, namely, an effect due to the geometry of tumors, and how to fix it.’**‘The overburden can be divided into three packages based on the geometry of the seismic reflections.’**‘This long-term effective population size is affected by the local dispersal behavior as well as the geometry of the habitat.’**‘His buildings are radical, from the geometry of their floor plans to the perforated walls that filter light into the interiors.’**‘In Eagle Creek, Columbia River, the different geometries of man and nature continually make rhymes with one another.’**‘We use facing directions to highlight the profoundly different structural geometries that exist on various scales in different parts of the coastal section.’*

Middle English via Old French from Latin geometria, from Greek, from gē ‘earth’ + metria (see -metry).

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