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Novel by Seichō Matsumoto
Points and Lines (Japanese: 点と線, Hepburn: Ten to Sen), is a novel by Seichō Matsumoto, published in 1958. It was initially serialized, and first translated
Points_and_Lines
Vertices connected in pairs by edges
vertices (also called nodes or points); E, a set of edges (also called directed edges, directed links, directed lines, arrows, or arcs), which are ordered
Graph_(discrete_mathematics)
Geometry with 7 points and 7 lines
possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. These points and lines cannot exist
Fano_plane
Abstract mathematical system of two types of objects and a relation between them
objects and a single relationship between these types of objects. Consider the points and lines of the Euclidean plane as the two types of objects and ignore
Incidence_structure
Existence of a line through two points
which the inflection points of a cubic curve in the complex projective plane form a configuration of nine points and twelve lines (the Hesse configuration)
Sylvester–Gallai_theorem
Compact non-orientable two-dimensional manifold
objects in the projective plane are points and straight lines, and as in Euclidean geometry, every pair of points determines a unique line passing through
Real_projective_plane
Points and lines with equal incidences
consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident
Configuration_(geometry)
Graph representing incident points and lines
collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge
Levi_graph
Axiomatically defined geometrical space
plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Given any line and any point not on
Affine plane (incidence geometry)
Affine_plane_(incidence_geometry)
Card game
card, 7 cards and 7 symbols. In general, a finite projective plane of order n-1 has n points on each line, and n2-n+1 points and lines. The game of Dobble
Dobble
Geometric concept of a 2D space with "points at infinity" adjoined
thirteen points and thirteen lines. We label the points P1, ..., P13 and the lines m1, ..., m13. The incidence relation (which points are on which lines) can
Projective_plane
Geometric configuration of ten points and lines
Desargues configuration is a configuration of ten points and ten lines, with three points per line and three lines per point. It is named after Girard Desargues
Desargues_configuration
Four-sided polygon
and ML intersect at point P that is located on the side AB; the straight lines NL and KM intersect at point Q that is located on the side CD. Points P
Quadrilateral
Japanese detective fiction writer (1909–1992)
best-selling and highest earning author in the 1960s. His most acclaimed detective novels, including Ten to sen (1958; Points and Lines, 1970); Suna no
Seichō_Matsumoto
Concept in projective geometry
formalization of the striking symmetry of the roles played by points and lines in the definitions and theorems of projective planes. There are two approaches
Duality_(projective_geometry)
Geometric structure of 8 points and 8 lines
of eight points and eight lines, with three points on each line and three lines through each point. It is not possible to draw points and lines having this
Möbius–Kantor_configuration
Field of mathematics which studies incidence structures
deals with finite sets of points in the Euclidean plane and what can be said about the number and types of (straight) lines they determine. Some results
Incidence_geometry
Geometric figure made of 4 points connected by 6 lines
on a common line, and of the six lines connecting the six pairs of points. Dually, a complete quadrilateral is a system of four lines, no three of which
Complete_quadrangle
Topics referred to by the same term
primary configuration file for DOS and OS/2 operating systems Configuration (geometry), a finite set of points and lines with certain properties Configuration
Configuration
Type of geometry
configurations of points and lines. That there is indeed some geometric interest in this sparse setting was first established by Desargues and others in their
Projective_geometry
Unique point and line of a conic section
polar line and each line in the plane into its pole. In projective geometry, this affords a one-to-one correspondence between points and lines in the projective
Pole_and_polar
Structure in combinatorial mathematics
rather than two points determining one line (and two lines determining one point), two points determine two lines (respectively, points). A biplane of
Block_design
Geometric system with a finite number of points
true if we exchange points for lines and lines for points. The smallest geometry satisfying all three axioms contains seven points. In this simplest of
Finite_geometry
Type of incidence structure
a set of elements called points, and a set of elements called lines. Each line is a distinct subset of the points. The points in a line are said to be
Linear_space_(geometry)
Flat surface
non-collinear points (points not on a single line). A line and a point not on that line. Two distinct but intersecting lines. Two distinct but parallel lines. The
Euclidean planes in three-dimensional space
Euclidean_planes_in_three-dimensional_space
Concept in geometry
parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were
Point_at_infinity
Method of constructing an image from multiple viewpoints
relates the coordinates of corresponding points or lines in three views, being independent of the scene structure and depending only on the relative motion
Trifocal_tensor
Curve along which a 3-D surface is at equal elevation
individual isolines and their portrayal of slope, pits and peaks. The idea of lines that join points of equal value was rediscovered several times. The oldest
Contour_line
symmetric configuration consisting of 21 points and 21 lines, with four points on each line and four lines through each point. Originally studied by
Grünbaum–Rigby_configuration
Polarization pattern of the daytime sky
direction and the observed pointing at the zenith. Thus, the spherical triangle is defined not only by the three points located at the Sun, zenith, and observed
Rayleigh_sky_model
Property of points all lying on a single line
geometry offers an interpretation of how the points, lines and other object types relate to one another and a notion such as collinearity must be interpreted
Collinearity
Graph divided into two independent sets
points and lines in a configuration. Corresponding to the geometric property of points and lines that every two lines meet in at most one point and every
Bipartite_graph
Irrational system of points and lines
In geometry, the Perles configuration is a system of nine points and nine lines in the Euclidean plane for which every combinatorially equivalent realization
Perles_configuration
Concept in mathematics
calculate a conic section's axis, vertices, tangents and the pole and polar relationship between points and lines of the plane determined by the conic. The technique
Matrix representation of conic sections
Matrix_representation_of_conic_sections
Mathematical model of the physical space
from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects. This is in contrast to analytic
Euclidean_geometry
Geometric configuration of 12 points and 6 lines
configuration of 12 points and 16 lines. Each point of the configuration belongs to four lines, and each line contains three points. Therefore, in the
Reye_configuration
Inscribed circle of a triangle's medial triangle
associated lines, the incenter for the Nagel line relates to the circumcenter for the Euler line. Another analogous pair of points is the Nagel point and the
Spieker_circle
Algorithmic problem on point-line incidence
for a given system of points and lines in the Euclidean plane, whether at least one of the points lies on at least one of the lines. More generally, one
Hopcroft's_problem
Geometry founded on spheres
Lie sphere 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
Lie_sphere_geometry
Line which touches a circle at exactly one point
comparison, secant lines intersect a circle at two points, whereas another line may not intersect a circle at all. This property of tangent lines is preserved
Tangent_lines_to_circles
Bound on the number of incidences between points and lines in the plane
result in the field of Discrete geometry. It asserts that given n points and m lines in the Euclidean plane, the number of incidences (i.e., the number
Szemerédi–Trotter_theorem
Geometric configuration of 9 points and 12 lines
Hesse configuration is a configuration of 9 points and 12 lines with three points per line and four lines through each point. It can be denoted as (94
Hesse_configuration
Smallest 3D projective space
has 15 points, 35 lines, and 15 planes. Each point is contained in 7 lines and 7 planes. Each line is contained in 3 planes and contains 3 points. Each
PG(3,2)
Geometric configuration of 9 points and 9 lines
configuration is a configuration of nine points and nine lines in the Euclidean plane, with three points per line and three lines through each point. This configuration
Pappus_configuration
Geometry problem about finding touching circles
they intersect at zero or two points, they are not tangent. The same holds true for a line and a circle. Two distinct lines cannot be tangent in the plane
Problem_of_Apollonius
Subdivision of the plane by lines
cells of the arrangement, line segments and rays, the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement
Arrangement_of_lines
Concept in geometry
It is possible to define and study a slightly bigger class of objects using only the relationship between points and lines: a polar space is a partial
Polar_space
Euclidean geometry without distance and angles
transformations, which are mappings that preserve alignment of points and parallelism of lines. Affine geometry can be developed in two ways that are essentially
Affine_geometry
Method of drawing geometric objects
constructions using the points, lines and circles that have already been constructed. These are: Creating a line through two points Creating a circle that
Straightedge and compass construction
Straightedge_and_compass_construction
Non-orientable surface with one edge
surfaces of constant curvature. Certain highly symmetric spaces whose points represent lines in the plane have the shape of a Möbius strip. The many applications
Möbius_strip
System of dividing land in the United States
mark exact locations of surveyed points and lines. They are the legally binding markers used for setting property lines and as such are the culminating work
Public_Land_Survey_System
GIS analysis operation on vector data
and create a layer that integrates both the geometry and the attributes of the inputs. Usually, both inputs are polygon layers, but lines and points are
Vector_overlay
coordinates) Extreme points are portions of a region which are further north, south, east, or west than any other. This is a list of extreme points in U.S. states
List of extreme points of U.S. states and territories
List_of_extreme_points_of_U.S._states_and_territories
Isomorphism of projective spaces in geometry
which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies
Homography
Coordinate system used in projective geometry
homogeneous coordinates of points and lines. So plane geometry with points as the fundamental elements and plane geometry with lines as the fundamental elements
Homogeneous_coordinates
Gives a lower bound on the number of lines determined by n points in a projective plane
by Nicolaas Govert de Bruijn and Paul Erdős in 1948, states a lower bound on the number of lines determined by n points in a projective plane. By duality
De Bruijn–Erdős theorem (incidence geometry)
De_Bruijn–Erdős_theorem_(incidence_geometry)
2005 book reformulating plane geometry
coordinates of points that determine a line segment or a pair of crossing lines. Defined in this way, they are rational functions of those coordinates, and can be
Divine Proportions: Rational Trigonometry to Universal Geometry
Divine_Proportions:_Rational_Trigonometry_to_Universal_Geometry
Concept in projective geometry
about points and lines, one could deal with n-dimensional subspaces and m-dimensional subspaces, or even more generally, objects of type 1 and objects
Blocking_set
configuration is a configuration of 15 lines and 15 points, having 3 points on each line and 3 lines through each point, and containing no (non-degenerate) triangles
Cremona–Richmond configuration
Cremona–Richmond_configuration
{\displaystyle n^{2}+n+1} points and n 2 + n + 1 {\displaystyle n^{2}+n+1} lines. The incidence relation between points and lines may equivalently be described
Lam's_problem
Phenomenon in statistics
contrary to intuition, the number of k-point lines expected from random chance in a plane covered with points at a given density, for a given line width
Alignments_of_random_points
Generalised concept of incidence structure of polygons
generalized 2-gon (or a digon) is an incidence structure with at least 2 points and 2 lines where each point is incident to each line. For n ≥ 3 {\displaystyle
Generalized_polygon
Type of construction
states that every straightedge and compass construction can be made with just a compass alone. A set of points or lines is said to be Steiner-constructible
Straightedge-only construction
Straightedge-only_construction
Also included are extreme points in elevation, extreme distances and other points of peculiar geographic interest. Map this section's coordinates using
List of extreme points of the United States
List_of_extreme_points_of_the_United_States
Rounding of an interior or exterior corner
on points and lines of expected high stress. The fillets distribute the stress over a broader area and effectively make the parts more durable and capable
Fillet_(mechanics)
Straight alignments between historic structures and landmarks
straight lines, using "mark points" along the landscape to guide them. He put forward his idea of ley lines in the 1922 book Early British Trackways and then
Ley_line
Common point(s) shared by two lines in Euclidean geometry
skew lines. Satisfaction of this condition is equivalent to the tetrahedron with vertices at two of the points on one line and two of the points on the
Line–line_intersection
Theorem in Euclidean geometry
possible to draw straight lines without a straightedge. However, a line is considered to be determined if two distinct points on that line are given or
Mohr–Mascheroni_theorem
Curve from a cone intersecting a plane
Euclidean plane and the absolute points are two special points on that line called the circular points at infinity. Lines containing two points with real coordinates
Conic_section
often interpreted as representing oriented lines on the plane. The Laguerre transformations map lines to lines, and include in particular all isometries of
Laguerre_transformations
Points with no line through exactly two points
configurations as subsets of the points of a projective space, they may be defined as abstract incidence structures of points and lines, satisfying the properties
Sylvester–Gallai configuration
Sylvester–Gallai_configuration
Collection of mathematical objects
called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables
Set_(mathematics)
Yugoslav American mathematician (1929-2018)
(1987), Tilings and Patterns, New York: W. H. Freeman, ISBN 0-7167-1193-1. Grünbaum, Branko (2009), Configurations of Points and Lines, Graduate Studies
Branko_Grünbaum
Plane curve: conic section
B(V)} of lines at two points U , V {\displaystyle U,V} (all lines containing U {\displaystyle U} and V {\displaystyle V} , respectively) and a projective
Hyperbola
Geometric property of objects being in the same plane
set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the
Coplanarity
Configuration of 3 tetrahedra in projective geometry
tetrahedron. The 12 vertices of the desmic system and the 16 lines formed in this way are the points and lines of a Reye configuration. The three tetrahedra
Desmic_system
Method for specifying point positions
An example of this is the systems of homogeneous coordinates for points and lines in the projective plane. The two systems in a case like this are said
Coordinate_system
Regional train service in the Rhine-Ruhr region of Germany
parallel to Rhine-Ruhr S-Bahn lines on large sections of track and it has some of the character of a fast S-Bahn service and is perceived by passengers accordingly
Wupper-Express
Mathematical set with some added structure
set of points and the set of lines. Moreover, a striking feature of projective planes is the symmetry of the roles played by points and lines. A less
Space_(mathematics)
Straight figure with zero width and depth
it to other lines and points. For example, for any two distinct points, there is a unique line containing them, and any two distinct lines intersect at
Line_(geometry)
Topics referred to by the same term
(flights), regular Soviet (and later Russian) military flights around Japan Tokyo Express, also known as Points and Lines, a murder mystery novel by Seichō
Tokyo Express (disambiguation)
Tokyo_Express_(disambiguation)
Railway points used as safety devices
points are used to derail vehicles which are out of control (known as runaways) on steep slopes. Trap points are used to protect main railway lines from
Catch_points
Plane curve: conic section
B(V)} of lines at two points U , V {\displaystyle U,V} (all lines containing U {\displaystyle U} and V {\displaystyle V} respectively) and a projective
Parabola
Mathematical result
341–355, ISBN 978-3-540-41109-3, MR 1849100. Shult, Ernest (2011), Points and Lines: Characterizing the Classical Geometries, Universitext, Springer-Verlag
Artin–Zorn_theorem
Airline of the United States
Delta Air Lines, Inc. is a major airline in the United States headquartered in Atlanta, Georgia, operating nine hubs, with Hartsfield–Jackson Atlanta
Delta_Air_Lines
Points separated from others by a line
{\displaystyle n} lines in the plane is the curve consisting of the points that lie on one of the lines and have exactly k {\displaystyle k} lines below them
K-set_(geometry)
Mathematical concept
point, whereas without points at infinity, there are no intersection points for parallel lines. So, parallel and non-parallel lines must be studied separately
Infinity
Artistic concept relating to perspective
intersects the x, y, and z axes and therefore lines parallel to these axes intersect, resulting in three different vanishing points. The vanishing point
Vanishing_point
Relation used in geometry
between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the
Parallel_(geometry)
Concept in incidence geometry
L,I} ), where P {\displaystyle P} is the set of points, L {\displaystyle L} is the set of lines and I ⊆ P × L {\displaystyle I\subseteq P\times L} is
Near_polygon
1884 novella by Edwin Abbott Abbott
who are lines, while the women are "lustrous points". These points and lines are unable to see the Square as anything other than a set of points on a line
Flatland
Geometry; how many 3-point lines can n points form
3-point lines attainable by a configuration of a specific number of points in the plane. There are also investigations into how many k-point lines there
Orchard-planting_problem
Abstract geometry without 2-point lines
configurations, configurations of points and lines (in non-Euclidean spaces) with no two-point line. For example, the Fano plane and the Hesse configuration give
Sylvester_matroid
Point from which two similar geometric figures can be scaled to each other
centers. The lines A1A2, B1B2 drawn through corresponding endpoints of those radii, which are homologous points, intersect each other and the line of centers
Homothetic_center
Rules related to the mathematical principles of origami
both of them. Given two distinct points p1 and p2, there is a unique fold that places p1 onto p2. Given two lines l1 and l2, there is a fold that places
Huzita–Hatori_axioms
Problem in coordinate geometry
The distance between two parallel lines in the plane is the minimum distance between any two points. Because the lines are parallel, the perpendicular distance
Distance between two parallel lines
Distance_between_two_parallel_lines
1918 U.S. peace proposals after World War I
The Fourteen Points was a statement of principles for peace that was to be used for peace negotiations in order to end World War I. The principles were
Fourteen_Points
Study of geometries as axiomatic systems
ideas. Typically they include objects and relationships. In geometry, the objects are things like points, lines and planes while a fundamental relationship
Foundations_of_geometry
Type of incidence structure
s + 1 points. There is at most one point on two distinct lines. There is a t (t ≥ 1) such that through every point there are exactly t + 1 lines. There
Generalized_quadrangle
Area of discrete mathematics
made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links, or lines). A distinction is made between undirected
Graph_theory
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POINTS AND-LINES