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Field of mathematics dealing with three-dimensional Euclidean spaces
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional
Solid_geometry
Creating a complex 3D surface or object by combining primitive objects
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows
Constructive_solid_geometry
One of eight divisions of a Euclidean 3D coordinate system
An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It
Octant_(solid_geometry)
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Geometric shape
In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called
Cone
Mathematical model of the physical space
system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are
Euclidean_geometry
Overview of and topical guide to geometry
Constructive solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic
Outline_of_geometry
Measure in 3-dimensional geometry
In geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is
Solid_angle
Geometry of the surface of a sphere
surface embedded in 3-dimensional Euclidean space (part of the study of solid geometry), or intrinsically using methods that only involve the surface itself
Spherical_geometry
2002 British TV series or programme
Solid Geometry is a 2002 British mystery drama short film written and directed by Denis Lawson and starring his nephew Ewan McGregor and Ruth Millar. It
Solid_Geometry_(film)
Three-dimensional solid
traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a
Cylinder
Method of representing a 3D object by defining the limits of its volume
are used to create the edge circuits. Compared to the constructive solid geometry (CSG) representation, which uses only primitive objects and Boolean
Boundary_representation
Browser-based 3D modeling program
3D printing as well as an entry-level introduction to constructive solid geometry in schools. Tinkercad was founded by former Google engineer Kai Backman
Tinkercad
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
3D modeling software component
Geometry Kernel web site. SolveSpace has its own integrated parametric solid geometry kernel with a limited NURBS support. The kernel market currently is
Geometric_modeling_kernel
Set of principles for modeling solid geometry
manipulate three-dimensional geometry in a fashion that is consistent with the physical behavior of real artifacts. Solid modeling research and development
Solid_modeling
Technique of illustration
Modern orthographic projection is derived from Gaspard Monge's descriptive geometry. Monge defined a reference system of two viewing planes: horizontal H ("ground")
Multiview orthographic projection
Multiview_orthographic_projection
Coordinate system
are several variants of this mnemonic. Half-plane Octant (solid geometry) Orthant Ray (geometry) Wikimedia Commons has media related to Quadrants. Weisstein
Quadrant_(plane_geometry)
Conic solid with a polygonal base
Alsina, Claudi; Nelsen, Roger B. (2015), A Mathematical Space Odyssey: Solid Geometry in the 21st Century, Mathematical Association of America, p. 85,
Pyramid_(geometry)
Geometric model of the physical space
In geometry, a three-dimensional space is a mathematical space in which three values (termed coordinates) are required to determine the position of a point
Three-dimensional_space
Relation between sides of a right triangle
theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of
Pythagorean_theorem
Any of the five regular polyhedra
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are
Platonic_solid
Ancient Greek mathematician (fl. 300 BC)
Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated
Euclid
Intersection of cylinders
In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves
Steinmetz_solid
Polyhedron with six rhombi as faces
HSM. Regular Polytopes. Third Edition. Dover. p.26. Lines, L (1965). Solid geometry: with chapters on space-lattices, sphere-packs and crystals. Dover Publications
Rhombohedron
Mathematical treatise by Euclid
constructions, and theorems with their proofs that covers plane and solid Euclidean geometry, elementary number theory, and incommensurability. These include
Euclid's_Elements
Set of points equidistant from a center
(sphaîra) 'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from
Sphere
Planar surface that forms part of the boundary of a solid object
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object. For example, a cube has six faces in
Face_(geometry)
Number between two given numbers
ISBN 978-1-4020-1522-9 Horatio N. Robinson (1860), "Theorem 22", Elements of Geometry, and Plane and Spherical Trigonometry, with Numerous Practical Problems
Heronian_mean
Edge-joined polygons which fold into a polyhedron
polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed
Net_(polyhedron)
Cuboid with all right angles and equal opposite faces
ISBN 978-0-429-26170-1. Dupuis, Nathan Fellowes (1893). Elements of Synthetic Solid Geometry. Macmillan. Jessen, Børge (1967). "Orthogonal icosahedra". Nordisk Matematisk
Rectangular_cuboid
Solid with six equal square faces
A cube is a three-dimensional solid object in geometry. It has eight vertices and twelve straight edges of the same length, so that these edges form six
Cube
2013 video game
Geometry Dash is a 2013 side-scrolling rhythm platform video game developed by Swedish game developer Robert Topala and published by his company RobTop
Geometry_Dash
Diophantine geometry Classical Euclidean geometry see Euclidean geometry Classical geometry may refer to solid geometry or classical Euclidean geometry. See
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Geometrical concept
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional
Cross_section_(geometry)
Basic shapes represented in vector graphics
which were all that early vector graphics systems had. In constructive solid geometry, primitives are simple geometric shapes such as a cube, cylinder, sphere
Geometric_primitive
3-dimensional object
In mathematics, a solid torus is the solid formed by sweeping a disk around a circle. As a topological space, it is homeomorphic to the Cartesian product
Solid_torus
Quadrilateral with sides of equal length
In geometry, a rhombus (pl.: rhombi or rhombuses) is an equilateral quadrilateral, a quadrilateral whose four sides all have the same length. Other names
Rhombus
Free software for creating 3D objects
sums) to render a 3D model. As such, the program performs constructive solid geometry (CSG). OpenSCAD is available for Windows, Linux, and macOS. OpenSCAD
OpenSCAD
List of lists
polygons, polyhedra and polytopes List of regular polytopes and compounds Solid geometry, including table of major three-dimensional shapes Box-drawing character
Lists_of_shapes
Method for recursively subdividing a space into two subsets using hyperplanes
include: performing geometrical operations with shapes (constructive solid geometry) in CAD, collision detection in robotics and 3D video games, ray tracing
Binary_space_partitioning
Cylinder whose generatrices are perpendicular to the bases
of straw Titanium cylinder Candle Mathematics portal Cylinder Geometry Solid geometry Giovanni; Giovanni Jr.; Bonjorno (2011). Matemática fundamental:
Right_circular_cylinder
Free and open-source 3D CAD software
is a default workbench for constructing solid geometry (body) by 3D operations from 2D sketches and 3D geometry modification operations (Boolean, pattern
FreeCAD
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors
List_of_Johnson_solids
Arrangement of steering linkages
preceding "turntable" steering, Ackermann geometry gives each front wheel hub its own pivoted carrier (on solid axles this pivot is called a kingpin but
Ackermann_steering_geometry
Polyhedron defined by two triangles and three trapezoid faces
In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices. A
Wedge_(geometry)
2009 puzzle video game
3D, known in Japan as Rittai Picross (立体ピクロス, Rittai Pikurosu; lit. "Solid Geometry Picross"), is a puzzle video game developed by HAL Laboratory and published
Picross_3D
Grimes 2002 Star Wars: Episode II – Attack of the Clones Obi-Wan Kenobi Solid Geometry Phil Short film 2003 Down with Love Catcher Block Young Adam Joe Taylor
Ewan_McGregor_filmography
Computer-aided design software
BRL-CAD is a constructive solid geometry (CSG) solid modeling computer-aided design (CAD) system. It includes an interactive geometry editor, ray tracing support
BRL-CAD
Bisection of Euclidean space by a hyperplane
Hemisphere (geometry) Line (geometry) Nef polygon, construction of polyhedra using half-spaces Poincaré half-plane model Quadrant (solid geometry) Siegel
Half-space_(geometry)
mathematical subjects of the time, such as number theory, algebra and solid geometry, including proofs that the square root of two is irrational and that
History_of_mathematics
Archimedean solid with 62 faces
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types
Rhombicosidodecahedron
Form of an object
with metaphorical names Lists of shapes Shape factor Size Skew polygon Solid geometry Region (mathematics) Kendall, D.G. (1984). "Shape Manifolds, Procrustean
Shape
German astronomer and mathematician (1571–1630)
vinariorum / New solid geometry of wine barrels. Accessit stereometriæ Archimedeæ supplementum / A supplement to the Archimedean solid geometry has been added
Johannes_Kepler
British novelist and screenwriter (born 1948)
achieved notoriety in 1979 when the BBC suspended production of his play Solid Geometry because of its supposed obscenity. His second collection of short stories
Ian_McEwan
Curve from a cone intersecting a plane
type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is
Conic_section
Perimeter of a 3D object's parallel projection in a given direction
In three-dimensional geometry, the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction.
Girth_(geometry)
Polyhedron with 12 faces
In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with
Dodecahedron
Polyhedra in which all vertices are the same
The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygons and are vertex-transitive,[citation needed] although they
Archimedean_solid
Surface drawn by a moving line passing through a fixed point
Modern Solid Geometry, Graded Course, Books 6-9, D. C. Heath, pp. 400–401 Shutts, George C. (1913), "640. Conical surface", Solid Geometry, Atkinson
Conical_surface
Bottom of a geometric figure
This term is commonly applied in plane geometry to triangles, parallelograms, trapezoids, and in solid geometry to cylinders, cones, pyramids, parallelepipeds
Base_(geometry)
American teacher and textbook author (1835–1906)
arithmetic, an algebra, geometry, trigonometry, or an analytical trigonometry." A 1904 update to his textbook Plane and Solid Geometry was lauded for its discussion
George_A._Wentworth
Convex shape with one stable and one unstable position of equilibrium
the name gömböc, a diminutive form of gömb ("sphere" in Hungarian). In geometry, a body with a single stable resting position is called monostatic, and
Gömböc
Polyhedron with four faces
In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six
Tetrahedron
Shape bounded by non-intersecting line segments
involving simple polygons, polygonalization of point sets, constructive solid geometry formulas for polygons, and visibility graphs of polygons. A simple polygon
Simple_polygon
Convex polyhedron with six faces with four edges each
ISBN 978-0-387-00424-2. MR 1976856. Dupuis, Nathan F. (1893). Elements of Synthetic Solid Geometry. Macmillan. p. 53. Retrieved December 1, 2018. Robertson, S. A. (1983)
Cuboid
Historical development of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry
History_of_geometry
Form of computer-aided engineering
engineering and medical simulations, and are usually built with constructive solid geometry. Shell or boundary – These models represent the surface, i.e., the boundary
3D_modeling
Angle between two planes in space
isohedral has the same value. This includes the 5 Platonic solids, the 13 Catalan solids, the 4 Kepler–Poinsot polyhedra, the 2 convex quasiregular polyhedra
Dihedral_angle
Software for 3D computer-aided design
relationships can be applied directly to the solid features without having to depend on 2D sketch geometry, and common parametric relationships are applied
Solid_Edge
Shape formed from points common to other shapes
In geometry, an intersection between geometric objects (seen as sets of points) is a point, line, or curve common to two or more objects (such as lines
Intersection_(geometry)
in a set of postulates for Euclidean geometry in two (plane geometry), three (solid geometry) or more dimensions. The following are the assumptions of the
Point–line–plane_postulate
Euclidean solid geometry
The sweep Sw of a solid S is defined as the solid created when a motion M is applied to a given solid. The solid S should be considered to be a set of
Solid_sweep
Study of geometry using a coordinate system
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts
Analytic_geometry
Chinese mathematician and writer
Mathematical Art include a proof of the Pythagorean theorem, theorems in solid geometry, an improvement on Archimedes's approximation of π, and a systematic
Liu_Hui
Topics referred to by the same term
Solid trigonometry may refer to: solid geometry, geometry of three-dimensional Euclidean space spherical trigonometry, deals with the trigonometric functions
Solid_trigonometry
Design technique
interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display. 3D objects are largely displayed
3D_projection
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
circle. Book IV discusses classical geometry, which Pappus divides into plane geometry, line geometry, and solid geometry, and includes a discussion of Archimedes'
Ancient_Greek_mathematics
Game engine
level editor, UnrealEd, that had support for real-time constructive solid geometry operations as early as 1996, allowing mappers to change the level layout
Unreal_Engine_1
to write books on mathematics in art. Della Francesca wrote books on solid geometry and the emerging field of perspective, including De Prospectiva Pingendi
List_of_mathematical_artists
Real-time 3D rendering engine for JavaScript
faces to be represented by shell models. Limited use of constructive solid geometry is possible, though only as a transitional method to create the union
Babylon.js
Text-based ray-tracing program
objects support for a number of geometric primitives and constructive solid geometry several kinds of light sources atmospheric effects such as fog and media
POV-Ray
Region between a revolved surface and oblique plane
In solid geometry, an ungula is a region of a solid of revolution, cut off by a plane oblique to its base. A common instance is the spherical wedge. The
Ungula
On dissections between polyhedra
in more modern form, Cavalieri's principle. Similar formulas in plane geometry can be proven with more elementary means. Gauss regretted this defect in
Hilbert's_third_problem
German mathematician (1862–1943)
segments), and congruence of angles. The axioms unify both the plane geometry and solid geometry of Euclid in a single system. Hilbert put forth a list of 23
David_Hilbert
Method of drawing geometric objects
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction –
Straightedge and compass construction
Straightedge_and_compass_construction
Open-source computer-aided design software
computer-aided design (CAD) software that supports basic 2D and 3D constructive solid geometry modeling. It is a constraint-based parametric modeler with simple mechanical
SolveSpace
Solid with four equal triangular faces
Tetrahedron". Alsina, C.; Nelsen, R. B. (2015). A Mathematical Space Odyssey: Solid Geometry in the 21st Century. Mathematical Association of America. ISBN 978-1-61444-216-5
Regular_tetrahedron
Set of polygons to define the surface of a 3D model
operations performed on meshes includes Boolean logic (Constructive solid geometry), smoothing, and simplification. Algorithms also exist for ray tracing
Polygon_mesh
Rocket with a motor that uses solid propellants
burned. More advanced solid rocket motors can be throttled, or extinguished and re-ignited, by control of the nozzle geometry or through the use of vent
Solid-propellant_rocket
Every rigid motion is a screw displacement
parallel to the axis is included in the screw displacement. Euclidean geometry is expressed in the complex plane by points p = x + y i {\displaystyle
Chasles'_theorem_(kinematics)
Geometrical body
shapes of the same constant width? More unsolved problems in mathematics In geometry, a surface of constant width is a convex form whose width, measured by
Surface_of_constant_width
Three-dimensional geometric shape
In geometry, a spherical shell (a ball shell) is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric
Spherical_shell
Mathematical theory
n} spheres of radius r {\displaystyle r} is calculable with elementary geometry. The middle part of the hull is a cylinder with length h = 2 r ⋅ ( n −
Finite_sphere_packing
Common elements of two or more sets
than two classes in his 1908 book Formulario mathematico. Constructive solid geometry, Boolean Intersection is one of the ways of combining 2D/3D shapes Dimensionally
Intersection
Spheres tangent to a plane inside a cone
In geometry, the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane. The intersection of
Dandelin_spheres
Method of using light to measure a 3D object
resulting distortions of the projected pattern reveals the object's solid geometry through triangulation, enabling the creation of a 3D model of the object
Structured_light
Positive real number which when multiplied by itself gives 6
six. In plane geometry, the square root of 6 can be constructed via a sequence of dynamic rectangles, as illustrated here. In solid geometry, the square
Square_root_of_6
Study of the 3D shapes of molecules
quantum chemistry methods to high accuracy. The molecular geometry can be different as a solid, in solution, and as a gas. [citation needed] The position
Molecular_geometry
SOLID GEOMETRY
SOLID GEOMETRY
Surname or Lastname
Spanish and Asturian-Leonese (SolÃs)
Spanish and Asturian-Leonese (SolÃs) : habitational name from SolÃs in Asturies or a similarly named place elsewhere.English : from a medieval personal name bestowed on a child born after the death of a sibling, from Middle English solace ‘comfort’, ‘consolation’. The word also came to have the sense ‘delight’, ‘amusement’, and in some cases the surname may have arisen from a nickname for a playful or entertaining person.
Boy/Male
Hindu, Indian
Solid Redemption
Boy/Male
Tamil
Solid redemption
Girl/Female
Biblical
Nativity, generation.
Girl/Female
Muslim
Strong, Solid
Girl/Female
Indian
Strong, Solid
Boy/Male
Muslim/Islamic
Firm Solid
Boy/Male
Indian
Solid structure
Boy/Male
Arabic, Muslim
Solid
Biblical
nativity; generation;begetter;
Boy/Male
Muslim
Solid structure
Boy/Male
Indian
Firm, Solid
Boy/Male
Indian
Solid
Girl/Female
Arabic, British, Danish, English, Muslim
Solid; Strong
Boy/Male
Indian, Sanskrit
Strong; Solid
Boy/Male
Muslim
Firm, Solid
Boy/Male
Muslim
Solid
Boy/Male
Arabic, Muslim, Parsi
Firm; Solid
Boy/Male
Muslim/Islamic
Solid
Girl/Female
Indian
Firm, Solid, Determined
SOLID GEOMETRY
SOLID GEOMETRY
Girl/Female
Tamil
Flower
Boy/Male
Hindu, Indian
Sweet
Boy/Male
Indian, Punjabi, Sikh
True Love of God
Boy/Male
Chinese, German, Hindu, Indian, Malay, Malaysian
Excellent
Surname or Lastname
English (Devon)
English (Devon) : variant of Morris 1.
Girl/Female
Arabic, Muslim
Heaven; Paradise
Boy/Male
Indian
There have been notable men
Boy/Male
Arabic, French
Baker
Girl/Female
Hindu
Modest
Biblical
quarrel; greatness to him
SOLID GEOMETRY
SOLID GEOMETRY
SOLID GEOMETRY
SOLID GEOMETRY
SOLID GEOMETRY
a.
Firm; compact; strong; stable; unyielding; as, a solid pier; a solid pile; a solid wall.
a.
United; without division; unanimous; as, the delegation is solid for a candidate.
a.
Having all the geometrical dimensions; cubic; as, a solid foot contains 1,728 solid inches.
a.
Impenetrable; resisting or excluding any other material particle or atom from any given portion of space; -- applied to the supposed ultimate particles of matter.
n.
The art of delineating the forms of solid bodies on a plane; a branch of solid geometry which shows the construction of all solids which are regularly defined.
a.
Not hollow; full of matter; as, a solid globe or cone, as distinguished from a hollow one; not spongy; dense; hence, sometimes, heavy.
a.
Applied to a compound word whose parts are closely united and form an unbroken word; -- opposed to hyphened.
a.
Partially solid.
a.
Enduring; solid; firm; substantial.
n.
Solid coal on the side of a gallery; solid ore in a vein.
a.
Sound; not weakly; as, a solid constitution of body.
a.
Of a fleshy, uniform, undivided substance, as a bulb or root; not spongy or hollow within, as a stem.
superl.
Solid; nourishing; as, strong meat.
n.
A substance that is held in a fixed form by cohesion among its particles; a substance not fluid.
a.
Solid; gross; opaque.
a.
Not having the lines separated by leads; not open.
v. i.
To become solid; to harden.
n.
A magnitude which has length, breadth, and thickness; a part of space bounded on all sides.
a.
Fig.: Worthy of credit, trust, or esteem; substantial, as opposed to frivolous or fallacious; weighty; firm; strong; valid; just; genuine.
a.
Having the constituent parts so compact, or so firmly adhering, as to resist the impression or penetration of other bodies; having a fixed form; hard; firm; compact; -- opposed to fluid and liquid or to plastic, like clay, or to incompact, like sand.