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Geometric concept of a 2D space with "points at infinity" adjoined
complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can be
Projective_plane
cards will then hopefully message back the Project Space Planes team so they could see how far the paper planes had travelled. The point of this exercise
Project_Space_Planes
Completion of the usual space with "points at infinity"
K). The Desarguesian planes (those that are isomorphic with a PG(2, K)) satisfy Desargues's theorem and are projective planes over division rings, but
Projective_space
Several projects have been planned and undertaken to launch paper planes from the stratosphere or higher. The Guinness World Record for the highest altitude
Paper planes launched from space
Paper_planes_launched_from_space
2D surface which extends indefinitely
complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can be
Plane_(mathematics)
Geometric model of the planar projection of the physical universe
geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle
Euclidean_plane
Compact non-orientable two-dimensional manifold
plane and finite projective planes. One common model of the real projective plane is the space of lines in three-dimensional Euclidean space which pass through
Real_projective_plane
Concept in mathematics
mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates
Quaternionic_projective_space
Spacecraft capable of aerodynamic flight in atmosphere
International Space Planes and Hypersonic Systems and Technologies Conference 6–9 July 2015, 2015, "Big Test Looms for British Space Plane Concept". Space.com.
Spaceplane
Mathematical concept
complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label
Complex_projective_space
Geometric system with a finite number of points
constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective planes so constructed are called Galois geometries.
Finite_geometry
Geometry with 7 points and 7 lines
in the Euclidean and real projective planes. Thus, what Gleason called Fano planes do not satisfy Fano's axiom. The Fano plane contains the following numbers
Fano_plane
Circle-like pointset in a geometric plane
differentiability conditions in the real plane. The higher dimensional analog of an oval is an ovoid in a projective space. A generalization of the oval concept
Oval_(projective_plane)
Mathematical space with two coordinates
two-dimensional spaces are often called planes (especially the Euclidean plane), or, more generally, surfaces. These include analogs to physical spaces, like flat
Two-dimensional_space
Subspace of n-space whose dimension is (n-1)
or motions. In a non-orientable space such as elliptic space or projective space, there is no concept of half-planes. In greatest generality, the notion
Hyperplane
Concept in projective geometry
roles played by points and lines in the definitions and theorems of projective planes. There are two approaches to the subject of duality, one through language
Duality_(projective_geometry)
Complex algebraic variety
isomorphic to it. There are exactly 50 fake projective planes. Prasad & Yeung (2006) found four examples of fake projective 4-folds, and showed that no arithmetic
Fake_projective_space
all fake projective planes, by showing that there are twenty-eight classes, each of which contains at least an example of fake projective plane up to isometry
Fake_projective_plane
Projective plane not satisfying Desargues' theorem
the only non-Desarguesian Moufang planes are infinite. Regarding finite non-Desarguesian planes, every projective plane of order at most 8 is Desarguesian
Non-Desarguesian_plane
2007 suborbital spaceplane concept
de l'Air et de l'Espace. The project is the first space tourism entry by a major aerospace contractor. It is a rocket plane with a large wingspan, straight
Airbus Defence and Space Spaceplane
Airbus_Defence_and_Space_Spaceplane
Curve defined as zeros of polynomials
of a plane curve. It is often desirable to consider curves in the projective space. An algebraic curve in the projective plane or plane projective curve
Algebraic_curve
British artist (born 1974)
one of their adverts in Argentina without permission. Veitch led Project Space Planes which was an attempt by amateur scientists to break the flight record
Joel_Veitch
Generalized Euclidean space in mathematics
quantum mechanics, the projective Hilbert space or ray space P ( H ) {\displaystyle \mathbf {P} (H)} of a complex Hilbert space H {\displaystyle H} is
Projective_Hilbert_space
Type of non-Euclidean geometry
demonstrate hyperbolic planes (pictured above) with the first being made by Daina Taimiņa, whose book Crocheting Adventures with Hyperbolic Planes won the 2009
Hyperbolic_geometry
operations of smooth planes are continuous; hence, each smooth plane is a compact topological plane. Smooth planes exist only with point spaces of dimension 2m
Smooth_projective_plane
Smallest 3D projective space
three-dimensional projective space. It can be thought of as an extension of the Fano plane, PG(2, 2). It has 15 points, 35 lines, and 15 planes. Each point
PG(3,2)
Euclidean space without distance and angles
non-collinear points. As well as affine planes over fields (or division rings), there are also many non-Desarguesian planes satisfying these axioms. Cameron
Affine_space
US NASA & DOD hypersonic project in 1986–1993
advanced technology demonstrator project for the National Aero-Space Plane (NASP), part of a United States project to create a single-stage-to-orbit
Rockwell_X-30
Mathematical measure of how much a curve or surface deviates from flatness
from being a plane. If a curve or surface is contained in a larger space, curvature can be defined extrinsically relative to the ambient space. Curvature
Curvature
Theorem in projective geometry
the real projective plane and for any projective space defined arithmetically from a field or division ring; that includes any projective space of dimension
Desargues's_theorem
Projective plane
Cayley plane, lines and points may be defined in a natural way so that it becomes a 2-dimensional projective space, that is, a projective plane. It is
Cayley_plane
2-dimensional complex projective space
{\displaystyle \mathbb {CP} ^{2},} is the two-dimensional complex projective space. It is a complex manifold of complex dimension 2, described by three
Complex_projective_plane
Application of Clifford algebra
Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with
Plane-based_geometric_algebra
Type of geometry
question. Thus, for 3-dimensional spaces, one needs to show that (1*) every point lies in 3 distinct planes, (2*) every two planes intersect in a unique line
Projective_geometry
Self-intersecting compact surface, an immersion of the real projective plane
geometry, Boy's surface is an immersion of the real projective plane in three-dimensional space. It was discovered in 1901 by the German mathematician
Boy's_surface
Upper-half plane model of hyperbolic non-Euclidean geometry
plane. From the hyperboloid model (a representation of the hyperbolic plane on a hyperboloid of two sheets embedded in 3-dimensional Minkowski space,
Poincaré_half-plane_model
Manifold or algebraic variety of dimension n in a space of dimension n+1
A hypersurface in a (Euclidean, affine, or projective) space of dimension two is a plane curve. In a space of dimension three, it is a surface. For example
Hypersurface
Fundamental space of geometry
Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in
Euclidean_space
Algebraic structure in linear algebra
In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled")
Vector_space
Geometric model of the physical space
planes in this 3-space are described by linear equations. A line can be described by a pair of independent linear equations—each representing a plane
Three-dimensional_space
Concept in projective geometry
In projective geometry, a plane at infinity is the hyperplane at infinity of a three dimensional projective space or to any plane contained in the hyperplane
Plane_at_infinity
Axiomatically defined geometrical space
four projective planes of order nine, and seven affine planes of order nine. There is only one affine plane corresponding to the Desarguesian plane of order
Affine plane (incidence geometry)
Affine_plane_(incidence_geometry)
Manned Spacecraft sub-system
body] The Chinese National Manned Space Program was given the designation of Project 921 in 1992. This broad project was divided into three phases: 921-1
China's_spaceplane_program
oval in a projective plane. An ovoid is a special type of a quadratic set. Ovoids play an essential role in constructing examples of Möbius planes and higher
Ovoid_(projective_geometry)
Relation between Lie algebras depicted as a square
spaces in question do not obey the usual axioms of projective planes, hence the quotes on "(putative) projective plane". However, the tangent space at
Freudenthal_magic_square
Field of mathematics which studies incidence structures
from geometric examples, particularly projective planes and affine planes. A projective plane is a linear space in which: Every pair of distinct lines
Incidence_geometry
Two-dimensional geometrical space
an affine plane is a two-dimensional affine space. There are two ways to formally define affine planes, which are equivalent for affine planes over a field
Affine_plane
Projection of a sphere through its center onto a plane
orientations of lines and planes of crystal structures. It is used in structural geology for analyzing the orientations of fault planes. In computer graphics
Gnomonic_projection
Reusable robotic spaceplane used by US military since 2010
project in 1999, before being transferred to the United States Department of Defense in 2004. Until 2019, the program was managed by Air Force Space Command
Boeing_X-37
Geometric object used to describe rotation in any number of dimensions
this article, all planes are planes through the origin, that is they contain the zero vector. Such a plane in n-dimensional space is a two-dimensional
Plane_of_rotation
Type of topological space
In mathematics, real projective space, denoted R P n {\displaystyle \mathbb {RP} ^{n}} or P n ( R ) , {\displaystyle \mathbb {P} _{n}(\mathbb {R}
Real_projective_space
Geometric space with four dimensions
universes or other imagined planes of existence. This usage is derived from the idea that to travel to parallel/alternate universes/planes of existence one must
Four-dimensional_space
Generalized sphere of dimension n (mathematics)
plane. The 2 {\displaystyle 2} -sphere, often simply called a sphere, is the boundary of a 3 {\displaystyle 3} -ball in three-dimensional space
N-sphere
Series of experimental US aircraft and rockets
or classified codenames. This list only includes the designated X-planes. The X-planes concept officially came into being in 1944, as a joint programme
List_of_X-planes
Geometry founded on spheres
geometry is that lines (or planes) should be regarded as circles (or spheres) of infinite radius and that points in the plane (or space) should be regarded as
Lie_sphere_geometry
Non-Euclidean geometry
the points of projective space. A notable property of the projective elliptic geometry is that for even dimensions, such as the plane, the geometry is
Elliptic_geometry
Research and development project of US Air Force
Project Space Track was a research and development project of the US Air Force, to create a tracking system for all artificial satellites of the Earth
Project_Space_Track
has yet to publish anything more about it. Paper planes launched from space "Highest Altitude Paper Plane Launch". GuinnessWorldRecords.com. Archived from
Paper Aircraft Released Into Space
Paper_Aircraft_Released_Into_Space
Affine space over the complex numbers
over the complex affine plane but remain equivalent over the (complex) projective plane. Any complex vector space is an affine space: all one needs to do
Complex_affine_space
Plane tiling corresponding to a polyhedron
In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations
Projective_polyhedron
Space with one dimension
one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded. Examples include the circle on a plane, or a parametric
One-dimensional_space
Locus of the zeros of a polynomial of degree two
complex conjugate intersecting planes). For ε 3 = 0 , {\displaystyle \varepsilon _{3}=0,} one has two intersecting planes (reducible quadric). For ε 4 =
Quadric
Soviet cancelled spaceplane project
until 1978. The actual space plane project was cancelled when the decision was made to instead proceed with the Buran project. The MiG test vehicle itself
Mikoyan-Gurevich_MiG-105
Isomorphism of projective spaces in geometry
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces
Homography
Geometric transformation that preserves lines but not angles nor the origin
subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments
Affine_transformation
American space and aeronautics agency
spaceflight programs, including Project Mercury, Project Gemini, the Apollo program, Skylab, the Space Shuttle, the International Space Station (ISS), and the
NASA
finite projective plane of even order. A k-arc which can not be extended to a larger arc is called a complete arc. In the Desarguesian projective planes, PG(2
Arc_(projective_geometry)
Toy aircraft made of folded paper
on the project. In February 2011, 200 planes were launched from a net underneath a weather balloon 23 miles (37 km) above Germany. The planes were designed
Paper_plane
US-Canada ballistics research project famous for its extremely large gun
above the Kármán line conventionally marking the beginning of outer space. Project HARP originated as the brainchild of Gerald Bull, a renowned but controversial
Project_HARP
Model of the extended complex plane plus a point at infinity
planes together to form the Riemann sphere. The planes are glued in an "inside-out" manner, so that they overlap almost everywhere, with each plane contributing
Riemann_sphere
Topics referred to by the same term
geometry of projective planes Geometry of finite planes, such as the Fano plane Affine geometry of affine planes Geometry of non-Euclidean planes, including
Plane geometry (disambiguation)
Plane_geometry_(disambiguation)
Four-dimensional analogue of the cube
It is possible to project tesseracts into three- and two-dimensional spaces, similarly to projecting a cube into two-dimensional space. The cell-first parallel
Tesseract
Well studied projective geometries over finite fields
translation planes. In these papers, it is shown that a spread of r {\displaystyle r} -dimensional subspaces of the finite projective space P G ( d , q
Spread_(projective_geometry)
Construction in group theory
transforms map planes to planes, so projective linear transforms map lines to lines), but in general not all collineations are projective linear transforms
Projective_linear_group
Mathematical problem
theorem, according to which any mapping of the Euclidean plane (or any higher dimensional space) to itself that preserves unit distances must be an isometry
Hadwiger–Nelson_problem
NASA infrared space telescope
The Nancy Grace Roman Space Telescope (shortened as the Roman Space Telescope, Roman, NGRST, or RST) is a NASA infrared space telescope whose construction
Nancy Grace Roman Space Telescope
Nancy_Grace_Roman_Space_Telescope
Chinese reusable spacecraft
these two projects, in 2020, Chen Hongbo, of China Aerospace Science and Technology Corporation (CASC), the main contractor for China's space agency, said
Chinese reusable experimental spacecraft
Chinese_reusable_experimental_spacecraft
Group of artificial satellites working together as a system
satellites; p is the number of equally spaced planes; and f is the relative spacing between satellites in adjacent planes. The change in true anomaly (in degrees)
Satellite_constellation
Independent aerospace manufacturer and defense contractor
called Commercial Aircraft Corporation for the C919 plane. The project is expected to deliver 4,700 planes to China over the next 20 years. Honeywell manufactures
Honeywell_Aerospace
Skew-symmetric 4 × 4 matrix, which characterizes a straight line in projective space
skew-symmetric 4 × 4 matrix, which characterizes a straight line in projective space. The matrix is defined by 6 Plücker coordinates with 4 degrees of freedom
Plücker_matrix
Study of geometry using a coordinate system
equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions)
Analytic_geometry
1961–1966 US human spaceflight program
program to fly. It was conducted after the first American crewed space program, Project Mercury, while the Apollo program was still in early development
Project_Gemini
United States space program
1958, and was replaced by NASA's Project Mercury. Only two men from the program would actually reach outer space. The first, Joseph A. Walker, did so
Man_in_Space_Soonest
Polynomial characterizing lines in projective 3-space
and v. The 3-space, S, can be reconstructed again from the quadric, Q: the planes contained in Q fall into two equivalence classes, where planes in the same
Klein_quadric
Particular mapping that projects a sphere onto a plane
stereographic projection also lets us visualize planes as points in the disk. For plots involving many planes, plotting their poles produces a less-cluttered
Stereographic_projection
Space of complex matrices with positive definite imaginary part
Poincaré upper half-plane. The space H g {\displaystyle {\mathcal {H}}_{g}} is sometimes called the Siegel upper half-plane. The space H g {\displaystyle
Siegel_upper_half-space
Structural element of a building
dormer is a roofed structure, often containing a window, that projects vertically beyond the plane of a pitched roof. A dormer window (also called dormer) is
Dormer
Initial American crewed spaceflight program (1958–1963)
Project Mercury was the first human spaceflight program of the United States, running from 1958 through 1963. An early highlight of the Space Race, its
Project_Mercury
Family of geometric objects with a common property
a model for pencil beams. A pencil of planes, is the set of planes through a given straight line in three-space, called the axis of the pencil. The pencil
Pencil_(geometry)
Artistic concept relating to perspective
the image plane of a perspective rendering where the two-dimensional perspective projections of parallel lines in three-dimensional space appear to converge
Vanishing_point
Concept in geometry
infinity, the plane at infinity or the hyperplane at infinity, in all cases a projective space of one less dimension. As a projective space over a field
Point_at_infinity
Crystallographic concept
planes is a collection of equally spaced parallel lattice planes that, taken together, intersect all lattice points. Every family of lattice planes can
Lattice_plane
Relation used in geometry
Parallel planes are infinite flat planes in the same three-dimensional space that never meet. In three-dimensional Euclidean space, a line and a plane that
Parallel_(geometry)
Algebraic structure designed for geometry
lines and planes, the versors of this algebra represent all proper Euclidean isometries, which are always screw motions in 3-dimensional space, along with
Geometric_algebra
Geometrical concept
plane. If a surface in a three-dimensional space is defined by a function of two variables, i.e., z = f(x, y), the plane sections by cutting planes that
Cross_section_(geometry)
2025). "Private mission to save NASA space telescope will launch in 2026 on a rocket dropped from a plane". Space.com. Retrieved 14 March 2026. "Swift
List of spaceflight launches in July–September 2026
List_of_spaceflight_launches_in_July–September_2026
Topological space construction
topological space. For example, identifying the points of a sphere that belong to the same diameter produces the projective plane as a quotient space. Let X
Quotient_space_(topology)
Image plane located between an eye point and an object
planes, all on M, and called an 'eject' of the original." "To 'cut' by a fixed plane μ (the picture-plane) a figure, the 'subject' made up of planes β
Picture_plane
Oriented projective geometry is an oriented version of real projective geometry. Whereas the real projective plane describes the set of all unoriented
Oriented_projective_geometry
The concept of a projective space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry
Algebraic geometry of projective spaces
Algebraic_geometry_of_projective_spaces
PROJECT SPACE-PLANES
PROJECT SPACE-PLANES
Boy/Male
Hindu, Indian
Space; Outer Space; Sky
Boy/Male
Hindu
Space
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Limitless Space
Surname or Lastname
English or Scottish
English or Scottish : unexplained.
Boy/Male
Tamil
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Space
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Space; Sky
Girl/Female
Hindu, Indian, Marathi
Space; Sky
Boy/Male
Hindu, Indian
Space; Sky
Boy/Male
Hindu
Space
Boy/Male
Tamil
Antariksh | அஂதரிகà¯à®·
Space
Antariksh | அஂதரிகà¯à®·
Girl/Female
Tamil
Antariksha | அஂதரிகà¯à®·
Space, Sky
Antariksha | அஂதரிகà¯à®·
Girl/Female
Indian, Japanese, Tamil
Space; Star
Boy/Male
Tamil
Prakalp | பà¯à®°à®•à®²à¯à®ªÂ
Project
Prakalp | பà¯à®°à®•à®²à¯à®ªÂ
Boy/Male
Hindu
Space
Boy/Male
Tamil
Antareeksh | அஂதரீகà¯à®·
Space
Antareeksh | அஂதரீகà¯à®·
Surname or Lastname
English
English : from a vernacular short form of the Latin personal name Paschalis (see Pascal, Italian Pasquale).nickname for a mild-mannered and peaceable person, from Middle English pace, pece ‘peace’, ‘concord’, ‘amity’ (via Anglo-Norman French from Latin pax, genitive pacis).Italian : from the medieval personal name Pace, used for both men and women, from the word pace ‘peace’ (see 1).
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Space; Universe
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Girl/Female
Indian, Telugu
Space
Male
English
English surname transferred to forename use, derived from the French personal name Pascal, PACE means "Passover; Easter."
PROJECT SPACE-PLANES
PROJECT SPACE-PLANES
PROJECT SPACE-PLANES
PROJECT SPACE-PLANES
PROJECT SPACE-PLANES
PROJECT SPACE-PLANES
PROJECT SPACE-PLANES
v. i.
To shoot forward; to extend beyond something else; to be prominent; to jut; as, the cornice projects; branches project from the tree.
v. i.
To form a project; to scheme.
n.
To arrange or adjust the spaces in or between; as, to space words, lines, or letters.
n.
A plan proposed; a draft of a proposed measure; a project.
adv.
With a quick pace; quick; fast; speedily.
imp. & p. p.
of Space
v. t.
Scanty; not abundant or plentiful; as, a spare diet.
n.
That which is projected or designed; something intended or devised; a scheme; a design; a plan.
v. t.
To cover or shield from danger or injury; to defend; to guard; to preserve in safety; as, a father protects his children.
v. t.
To season with spice, or as with spice; to mix aromatic or pungent substances with; to flavor; to season; as, to spice wine; to spice one's words with wit.
v. t.
Held in reserve, to be used in an emergency; as, a spare anchor; a spare bed or room.
imp. & p. p.
of Project
v. t.
To dig with a spade; to pare off the sward of, as land, with a spade.
n.
A quantity or portion of extension; distance from one thing to another; an interval between any two or more objects; as, the space between two stars or two hills; the sound was heard for the space of a mile.
v. t.
To cast forward or revolve in the mind; to contrive; to devise; to scheme; as, to project a plan.
n.
An idle scheme; an impracticable design; as, a man given to projects.
n.
The place from which a thing projects, or starts forth.
v. t.
To draw or exhibit, as the form of anything; to delineate; as, to project a sphere, a map, an ellipse, and the like; -- sometimes with on, upon, into, etc.; as, to project a line or point upon a plane. See Projection, 4.
n.
Space.
n.
One who projects a scheme or design; hence, one who forms fanciful or chimerical schemes.