Definition of geometry in US English:



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

    • ‘Most of the features for surfaces appearing in this book are closely related to topological geometry.’
    • ‘Let us first comment on the three volume work, which was the biggest treatise ever to be written on line geometry.’
    • ‘He goes on to consider solid geometry giving results on prisms, cylinders, and spheres.’
    • ‘He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well.’
    • ‘It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.’
    • ‘As analysis began to mix inextricably with geometry and the other branches of mathematics, the curiosities multiplied.’
    • ‘At this point the Greeks gave up algebra and turned to geometry.’
    • ‘He worked on the borderline between geometry and set theory, both of which are kind of nineteenth century.’
    • ‘Low-income students who took algebra and geometry were almost three times as likely to attend college as those who did not.’
    • ‘He clearly was trying to argue against the notions current at the time on using algebra to study geometry.’
    • ‘Speculative geometry contains elementary geometry which is not all based on Euclid.’
    • ‘You can still access the underlying curve and surface geometry that makes up the solid.’
    • ‘The computer programs implement basic mathematical principles such as basic geometry and fractional math.’
    • ‘A notable feature of advanced mathematics is that much of it is concerned with geometry in more than three dimensions.’
    • ‘By spherical geometry, we mean geometry on the surface of a sphere, where the great circles are taken as lines.’
    • ‘This requires at least some understanding of spherical geometry and trigonometry.’
    • ‘Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics.’
    • ‘His writings on geometry included several important papers on parallel curves and surfaces.’
    • ‘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.’
    • ‘Simson also made many discoveries of his own in geometry and the Simson line is named after him.’
    1. 1.1 A particular system of geometry.
      ‘non-Euclidean geometries’
      • ‘It was not until the 19th century that this postulate was dropped and non-euclidean geometries were studied.’
      • ‘His main mathematical interests were in algebraic geometry and differential geometry.’
      • ‘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.’
      • ‘He also studied birational contact transformations and non-euclidean and non-archimedean geometries.’
      • ‘He has written on stochastic geometry and its applications, and the statistical theory of shape.’
      • ‘The same issues apply more generally to other photonic crystal systems in non-fiber geometries.’
      • ‘He also realised that there were an infinite number of non-euclidean geometries and this, Taurinus claimed, was highly significant.’
      • ‘He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.’
      • ‘Similar stratal geometries have been described from comparable levels in the Chalk of the North Sea, and in outcrop in Britain and France.’
      • ‘His derivation of the estimates is a tour de force and the applications in algebraic geometry are beautiful.’
      • ‘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.’
      • ‘Weil's work on bringing together number theory and algebraic geometry was highly fruitful.’
      • ‘This work led to a thesis on algebraic geometry in which he introduced rings which are now named after him.’
      • ‘His work on non-euclidean geometries was used by Einstein in his general theory of relativity.’
      • ‘Something that exists nowhere and exists along the lines of Euclidean geometry, judging by what I understand of it, cannot exist.’
      • ‘The trend toward trophic specialization is also correlated with stereotyped geometries in the locomotor system.’
      • ‘Geometry had began to lose its 'metric' character with projective and non-euclidean geometries being studied.’
      • ‘Van Schooten was one of the main people to promote the spread of Cartesian geometry.’
      • ‘Note, of course, that the use of such positional grids are an early form of Cartesian geometry.’
    2. 1.2in singular The shape and relative arrangement of the parts of something.
      ‘the geometry of spiders' webs’
      • ‘This long-term effective population size is affected by the local dispersal behavior as well as the geometry of the habitat.’
      • ‘Perhaps this intimate knowledge of the geometry of letterforms is why even today so many architects are partial to Futura.’
      • ‘Once again, daguerreotypy was reduced to a geometry of abstract markings.’
      • ‘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.’
      • ‘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.’
      • ‘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.’
      • ‘His buildings are radical, from the geometry of their floor plans to the perforated walls that filter light into the interiors.’
      • ‘In the first place, chemical solutions can conform to the geometry of the sample vessel or object being irradiated.’
      • ‘In Eagle Creek, Columbia River, the different geometries of man and nature continually make rhymes with one another.’
      • ‘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.’
      • ‘We use facing directions to highlight the profoundly different structural geometries that exist on various scales in different parts of the coastal section.’
      • ‘It connects us to the geometry of the body - the square, the circle and the triangle - and to the purity of line.’
      • ‘Modern artists long ago discovered and assimilated the geometry, line and shapes of African sculpture.’
      • ‘I can't help it: where some see visionary lines and inspired angles I see the geometry of a madman.’
      • ‘‘I was fascinated by the geometry of the ruined monuments I looked at,’ Ghosh explains.’
      • ‘In fact, the cornerstone setting lets you tweak the geometry of the picture to your heart's content.’
      • ‘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.’
      • ‘The overburden can be divided into three packages based on the geometry of the seismic reflections.’
      • ‘Finally, we indicate the source of such inconsistent analysis, namely, an effect due to the geometry of tumors, and how to fix it.’
      • ‘I eyed up the chest of drawers but the geometry seemed wrong somehow.’


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