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# geometry

## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The mathematics of the properties, measurement, and relationships of points, lines, angles, surfaces, and solids.
• noun A system of geometry.
• noun A geometry restricted to a class of problems or objects.
• noun A book on geometry.
• noun Configuration; arrangement.
• noun A surface shape.
• noun A physical arrangement suggesting geometric forms or lines.

### from The Century Dictionary.

• noun That branch of mathematics which deduces the properties of figures in space from their defining conditions, by means of assumed properties of space. Abbreviated geometry
• noun A text-book of geometry.
• noun Modern projective geometry, commonly written in German Geometrie der Lage, to distinguish it from .
• noun Higher synthetic geometry in general.
• noun The art of geometrical drawing.
• noun Geometry of three dimensions.
• noun The oldest classification of geometry is , that in which it is divided according to the method of logical procedure, namely into synthetic and analytic, the method of geometrical analysis having been invented or taught by Plato. In modern times this classification intertwines with another, namely , that which is based on the mental instrument or equipment used, giving: pure or synthetic geometry; rational; descriptive; projective; algebraic, algorithmic, analytical, Cartesian, or coördinate; differential, infinitesimal, natural, or intrinsic; enumerative or denumerative. Some of these are subdivided on the same principle, as: (α) geometry of the ruler or straight-edge; (β) of the ruler and sect-carrier; (γ) of the ruler and unitsect-carrier; (δ) of the compasses; of the ruler and compasses; (ζ) of linkages. Further divisions are: By dimensionality: geometry on the straight or on the line; two-dimensional geometry; (α) plane geometry; (β) spherics; (γ) pseudo-spherics; tri-dimensional geometry: (α) geometry of planes; (β) solid geometry; (γ) spherics; four-dimensional geometry: (α) geometry of straight?; (β) of hyperspace; n-dimeimonal geometry. By elements: point geometry; straight or line; plane; point, straight, and plane; straightest or geodesic; geometry of the sphere; of other elements, By subject-matter: pure descriptive, pure projective, or pure positional geometry, or geometry of position; topologic geometry; metric geometry; geometry of curves; of surfaces; of solids; of hyper-solids; of numbers; of motion or kinematic. By assumptions made, omitted, or denied: Euclidean geometry; non-Euclidean; metageometry, or pan-geometry; finite geometry; semi-Euclidean; non-Legendrian; Archimedean; non-Archimedean; non-Arguesian; non-Pascalian. By the kind of space or universe of the geometry: Euclidean or parabolic geometry; Bolyaian, Lobachevskian, Bolyai-Lobachevskian, absolute, or hyperbolic; Riemannian, spherical, or double elliptic; Killing's, single elliptic, or simple elliptic; Clifford's or Clifford-Kleinian. By the complexity or difficulty of the part treated: elementary geometry; higher, By the period of its development: ancient or the antique geometry; modern; recent, of the triangle, or the Lemoine-Brocard.

### from the GNU version of the Collaborative International Dictionary of English.

• noun That branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.
• noun A treatise on this science.
• noun that branch of mathematical analysis which has for its object the analytical investigation of the relations and properties of geometrical magnitudes.
• noun that part of geometry which treats of the graphic solution of all problems involving three dimensions.
• noun that part of geometry which treats of the simple properties of straight lines, circles, plane surface, solids bounded by plane surfaces, the sphere, the cylinder, and the right cone.
• noun that pert of geometry which treats of those properties of straight lines, circles, etc., which are less simple in their relations, and of curves and surfaces of the second and higher degrees.

• noun mathematics, uncountable the branch of mathematics dealing with spatial relationships
• noun mathematics, countable a type of geometry with particular properties
• noun countable the spatial attributes of an object, etc.

• noun the pure mathematics of points and lines and curves and surfaces

## Etymologies

### from The American Heritage® Dictionary of the English Language, 4th Edition

[Middle English geometrie, from Old French, from Latin geōmetria, from Greek geōmetriā, from geōmetrein, to measure land : geō-, geo- + metron, measure; see mē- in Indo-European roots.]

From Ancient Greek γεωμετρία (geometría, "geometry, land-survey"), from γεωμετρέω (geometréo, "to practice or to profess geometry, to measure, to survey land"), back-formation from γεωμέτρης (geométrēs, "land measurer"), from γῆ (gē, "earth, land, country") + μετρέω (metréō, "to measure, to count") or -μετρία (-metria, "measurement"), from μέτρον (metron, "a measure").

## Examples

• If you cram twice as many photosites onto a sensor, that halves (quarters? my geometry is a bit weak) the size of each photosite.

• Thales kept the Egyptian name “earth measurement” for his mathematics, but being Greek, used the Greek word geometry.

Euclid’s Window Leonard Mlodinow 2001

• Thales kept the Egyptian name “earth measurement” for his mathematics, but being Greek, used the Greek word geometry.

Euclid’s Window Leonard Mlodinow 2001

• Thales kept the Egyptian name “earth measurement” for his mathematics, but being Greek, used the Greek word geometry.

Euclid’s Window Leonard Mlodinow 2001

• The best known of these men was Euclid, who perfected the mathematics which we call geometry, and Ptolemy, whose ideas about geography and the shape and size of the globe Columbus carefully studied before he set out on his great voyage.

Introductory American History Elbert Jay Benton

• Centuries later, Jews would repay the compliment by appropriating the Greek word geometry and creating the word gematria, which is Hebrew for

• Gautier based his refutation of Newton in geometry, as Castel had; a style of argument typical of Jesuit science in the eighteenth century and especially in France. 17 The techniques and terminology common to mathematical proofs are the basis of Gautier's explanation, although, as Étienne Montucla complained in the Journal œconomique, his understanding of geometry is even less exact than his understanding of Newtonian optics. 18 The foundations are similar, but he draws, as part of his proofs, more analogies to interpretations or beliefs common among painters.

• Procedural geometry is quite a wide field, do you plan to specialise in procedural people, environments (trees etc) or something else?

• The point about geometry is roughly analogous with the principle of universality: the laws of geometry are universal principles that no bridge can do without.

• Atoms come together to form compounds; the geometry is determined by the orientations of the chemical bonds, which are mergers of electron orbitals.