geometry
Pluralgeometries (some meanings)
- 1The branch of mathematics that studies spatial relationships, such as the lengths, angles, and positions of lines and figures.
Architects use geometry to work out the angles and lengths of a sloping roof.
She took geometry in tenth grade and loved writing proofs.
Note
The name remembers where the subject began: Greek geōmetría joined gê, "earth, land", to -metría, "measurement", and could also mean a land survey. Naming the subject, the word takes no article and no plural (she took geometry; geometry is hard). The plural geometries belongs to systems built on particular axioms.
- 2The spatial features of an object or system, such as its shape, size, and layout, whether measured or specified.
Engineers changed the geometry of the wing to cut drag at high speed.
Mountain bikes and road bikes have very different frame geometries.
Similarshape, configuration, design, layout
Note
Scientists and engineers use the word for one thing's layout rather than for the subject: the geometry of the samples, a drive's geometry, or, in Roger Penrose's 2018 tribute to Stephen Hawking, the physics and the geometry of the universe. It usually belongs to something, so it comes with of, a possessive or a noun in front.
- 3A mathematical system of spatial relationships built on its own set of axioms; also, the part of geometry that studies one or more systems of that kind.
On the surface of a sphere, spherical geometry treats great circles as its straight lines.
Nineteenth-century mathematicians showed that consistent non-Euclidean geometries could exist.
Note
The countable sense usually arrives with a qualifier naming the system: Euclidean, hyperbolic, spherical, finite, even taxicab geometry, which takes its cue from real-world city streets. Each starts from its own axioms, so a rule that holds in one, such as exactly one parallel through a point off a line, can fail in another.
- 4In algebraic geometry, a mathematical object made up of representations of a space together with its spatial relationships.
Practice
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Origin
From Middle English gemetry, geometrie, from Old French geometrie, from Latin geōmetria, from Ancient Greek γεωμετρία (geōmetría, "geometry, land-survey"), from γεωμέτρης (geōmétrēs, "geometer, land measurer"), from γῆ (gê, "earth, land, country") + -μετρία (-metría, "measurement"), from μέτρον (métron, "a measure"). It is a doublet of gematria.