geometries
Studies of space
Geometries is the plural of geometry, which at its core is the branch of mathematics dealing with shapes, sizes, and spatial relationships.
The plural appears when discussing different geometric systems or frameworks: Euclidean and non-Euclidean geometries operate under different assumptions about parallel lines.
It also refers to specific spatial arrangements or configurations: The geometries of these crystal structures vary significantly.
Flat-space geometry type
- non-EuclideanGeometry without parallel postulate
- hyperbolicExaggerated beyond reason
- projectiveRelating to mapping transformations
- affineRelative by marriage
differential · algebraic · analytic · fractal · topology · manifolds · theorems · proofs
Measurable extent or scope
- volumeAmount of space filled
- areaExtent of surface
- distanceSpace between two points
- orientationPosition relative to surroundings
coordinates · planes · axes · vertices · edges · surfaces · depth · width
Curved closed shape
- triangleThree-sided plane figure
- squareRhombus with right angles
- polygonMultisided plane figure
- pentagonFive-sided closed figure
hexagon · octagon · ellipse · rhombus · trapezoid · parallelogram · sphere · cube
Involving two parties
- radialEmanating from center
- rotationalConcerning circular movement
- translationalRelating to straight movement
- reflectionReturned light or thought
mirror · axis · invariance · congruence · proportion · tessellation · patterns · crystallographic
Deceptive outward appearance
- columnVertical structural element
- archCurved spanning structure
- domeRounded vault forming roof
- vaultSecure storage chamber
buttress · atrium · geodesic · cantilever · truss · vaulting · floorplan · elevation
Spatial arrangement of elements
- compositionArranged elements forming whole
- gridFramework of intersecting lines
- proportionComparative relation of parts
- golden ratioPhi, roughly 1.618
balance · alignment · spacing · modular · parametric · generative · pattern · motif
Circular spiritual diagram
- labyrinthIntricate passage network
- vesica piscisLens from intersecting circles
- golden ratioPhi, roughly 1.618
- spiralsCurves circling a center
proportions · temple · cathedral · cosmological · symbolic · ritual · ancient · harmonic
Euclidean
Flat-space geometry type
- non-EuclideanGeometry without parallel postulate
- hyperbolicExaggerated beyond reason
- projectiveRelating to mapping transformations
affine · differential · algebraic · analytic · fractal · topology · manifolds · theorems · proofs · axioms
dimension
Measurable extent or scope
orientation · coordinates · planes · axes · vertices · edges · surfaces · depth · width · height
circle
Curved closed shape
pentagon · hexagon · octagon · ellipse · rhombus · trapezoid · parallelogram · sphere · cube · cylinder
bilateral
Involving two parties
- radialEmanating from center
- rotationalConcerning circular movement
- translationalRelating to straight movement
reflection · mirror · axis · invariance · congruence · proportion · tessellation · patterns · crystallographic · glide
facade
Deceptive outward appearance
vault · buttress · atrium · geodesic · cantilever · truss · vaulting · floorplan · elevation · structural
layout
Spatial arrangement of elements
- compositionArranged elements forming whole
- gridFramework of intersecting lines
- proportionComparative relation of parts
golden ratio · balance · alignment · spacing · modular · parametric · generative · pattern · motif · form
mandala
Circular spiritual diagram
- labyrinthIntricate passage network
- vesica piscisLens from intersecting circles
- golden ratioPhi, roughly 1.618
spirals · proportions · temple · cathedral · cosmological · symbolic · ritual · ancient · harmonic
geometriesalgebra
Math using symbols
algebras · arithmetic · number theory · analysis · calculus
geometriesempiricism
Knowledge through observation
materiality · physicality · concreteness · randomness · chaos
- geometric shapesForms with defined boundaries
- geometric patternsArrangements of regular shapes
- geometric progressionSeries multiplying by constant
- geometric designArrangement of mathematical shapes
- geometric proofsLogical arguments about shapes
- geometric formsMathematically defined figures