geometries

Noun

geometry (countable and uncountable, plural geometries)

1. (uncountable) The 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. (countable, often qualified in combination) A 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.
3. (countable) The 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...
4. (countable) A mathematical object comprising representations of a space and of its spatial relationships.