geometry

plural geometries

1. uncountablemathematicsThe branch of mathematics dealing with spatial relationships.

   ANY problem in geometry can easily be reduced to such terms that a knowledge of the lengths of certain straight lines is sufficient for its construction.

   1925, René Descartes, “The Geometry of Rene Descartes”, in David Eugene Smith, Marcia Latham, transl., [1637, La Géométrie], Cosimo Classics, published 2007, page 2

2. countableoften qualified in combinationmathematicsA mathematical system that deals with spatial relationships and that is built on a particular set of axioms; a subbranch of geometry which deals with such a system or systems.

   1975 [Addison-Wesley], Eugene F. Krause, Taxicab Geometry, 1986, Dover, page 64, Entire new geometries are also suggested by real-world cities.

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   Finite geometries were developed in the late nineteenth century, in part to demonstrate and test the axiomatic properties of completeness, consistency, and independence.

   2004, Judith Cederberg, A Course in Modern Geometries, Springer, page 1

   Previous theorists have often tried to test whether visual space is best described by a small set of traditional geometries, such as the Euclidean geometry most of us studied in High School or the hyperbolic and spherical geometries introduced by 19ᵗʰ-century mathematicians.

   2006, Mark Wagner, The Geometries of Visual Space, Lawrence Erlbaum Associates, page ix

3. countableThe observed or specified spatial attributes of an object, etc.

   The inset of figure 1 shows the geometry of the samples. They are 4.6 mm long and 0.4 mm wide.

   1990, M. E. Cage, D. Y. Yu, G. Marullo Reedtz, “Observation and an Explanation of Breakdown of the Quantum Hall Effect”, in Journal of Research of the National Institute of Standards and Technology, volume 95, number 1

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   Also, certain SCSI controllers need to be told where to find drive geometry in order for Linux to recognize the layout of your drive.

   2003, Matt Welsh, Running Linux, page 74

   He was extremely highly regarded, in view of his many greatly impressive, sometimes revolutionary, contributions to the understanding of the physics and the geometry of the universe.

   2018 March 14, Roger Penrose, “'Mind over matter': Stephen Hawking – obituary”, in The Guardian

4. countablealgebraic geometryA mathematical object comprising representations of a space and of its spatial relationships.