This page gathers the 757 dictionary entries belonging to the domain “Geometry”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples. Page 5 of 8: from “mediatrix” to “pole”.
- mediatrix noun A bisector, the line that is perpendicular to a line segment and intersects the line segment at its midpoint.
- megagon noun A polygon with one million sides.
- midcircle noun The circle (if one exists) that passes through the midpoint of each side of a given polygon, especially a triangle.
- midsphere noun The sphere which, if it exists, is tangent to every edge of a given polyhedron and with respect to which the polyhedron's vertices are the…
- Minkowski-Bouligand dimension noun A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by…
- mirror symmetry noun A relationship between Calabi-Yau manifolds where two such manifolds look very different geometrically but are nevertheless equivalent when…
- mitre noun A square with one triangular quarter missing from the outside.
- Mittenpunkt noun A triangle center defined as the symmedian point of the triangle formed by the centers of the three excircles.
- Möbius transformation noun A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are…
- Mojette transform noun A discrete and exact version of the Radon transform, using only additions and subtractions, and having applications in medical tomography…
- monogon noun A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.
- monogonal adj Of or pertaining to a monogon.
- monohedrally adv In a monohedral manner; involving only copies of the original tile (allowing for translation, rotation, and reflection).
- monohedron noun A solid figure with a single continuous surface (face) and no edges, such as a torus or spheroid.
- monostatic adj A solid body with a single stable resting point.
- monotile noun A prototile tiling monohedrally; any shape able to completely tile some space on its own (allowing for translation, rotation, and…
- Morley triangle noun Any of a number of triangles described in Morley's trisector theorem, especially the equilateral triangle formed from the points of…
- mucube noun A regular skew apeirohedron with six squares around each vertex, formed by an infinite number of cubic cells (specifically, cubes missing…
- multilobe noun A kind of closed curve.
- muoctahedron noun A regular skew apeirohedron with four hexagons around each vertex, formed by an infinite number of octahedron-like cells (specifically…
- mutetrahedron noun A regular skew apeirohedron with six hexagons around each vertex, formed by an infinite number of truncated tetrahedron-like cells…
- n-gon noun A polygon with n sides, where n represents any integer greater than or equal to three; often used to represent a polygon with an unknown…
- Napoleon point noun Either of a pair of special points associated with a plane triangle. (See Wikipedia for detailed definitions.)
- nef adj Of a line bundle on a complete algebraic variety over a field: such that the degree of its restriction to every algebraic curve in the…
- nephroid noun A plane curve resembling two intersecting ellipses
- nestohedron noun For a building set B, the Minkowski sum of the simplices Δ_S as S ranges over B. (Here Δ_S is the standard simplex of S, i.e., the convex…
- net noun Any set of polygons joined edge to edge that, when folded along the edges between adjoining polygons so that the outer edges touch, form a…
- neusis noun A line segment of prescribed length, fitted between two given curves, part of a line that passes through a given point.
- noble adj Both isohedral and isogonal.
- nodated adj Crossing itself.
- node noun The point at which a curve crosses itself, being a double point of the curve. See crunode and acnode.
- noetherian adj admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;
- non-Euclidean geometry noun Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common…
- nonant noun One ninth of a circle or disc; a sector with an angle of 40°.
- nonic adj Describing a curve the equation of which is nonic.
- nonprimitive noun An object that is not a primitive.
- nonsqueezing adj Being or relating to the theorem in symplectic geometry stating that one cannot embed a sphere into a cylinder via a symplectic map unless…
- normal noun A line or vector that is perpendicular to another line, surface, or plane.
- oblatum noun An oblate spheroid; a figure described by the revolution of an ellipse about its minor axis.
- oblique noun An oblique line.
- oblique reflection noun In Euclidean geometry, an ordinary reflection not requiring that the reflection be performed using perpendiculars.
- obround noun A plane shape consisting of two semicircles connected by parallel lines tangent to their endpoints.
- obtuse adj Larger than one, and smaller than two right angles, equivalently more than 90° and less than 180°.
- occurse noun intersection
- octagon noun A polygon with eight sides and eight angles.
- octahedron noun a polyhedron with eight faces; the regular octahedron has regular triangles as faces and is one of the Platonic solids.
- octant noun The eighth part of a disc; a sector of 45 degrees; half a quadrant.
- oloid noun A three-dimensional curved geometric object, the convex hull of a skeletal frame made by placing two linked congruent circles in…
- omega point noun A well-defined point outside the hyperbolic plane.
- omnitruncation noun An operation applied to a regular polytope in a Wythoff construction that creates a maximum number of facets.
- orbiform noun A plane for which the distance between the points of contact of two nonequal parallel tangents at a circle is the same everywhere.
- orbit noun The subset of elements of a set X to which a given element can be moved by members of a specified group of transformations that act on X.
- ordinate noun The second of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.
- orientation noun The designation of a parametrised curve as "positively" or "negatively" oriented; the analogous description of a surface or hypersurface.
- oriented adj In any of various technical senses, admitting or being equipped with a notion of handedness (i.e. of distinguishing clockwise and…
- orthant noun An n-dimensional generalization of the quadrant (in two-dimensional Cartesian space) and octant (in three-dimensional space).
- orthocenter noun One of the centers (UK:centres) of a triangle, defined as being the intersection of its three altitudes; in an acute triangle, it is inside…
- orthocentric adj Having all three pairs of opposite edges perpendicular.
- orthogon noun A right-angled triangle.
- orthogonal adj Of two objects, at right angles; perpendicular to each other.
- orthonormal adj Of a set of vectors, both orthogonal and normalized.
- orthoptic noun The isoptic whose given angle is a right angle.
- orthotomic adj Cutting at right angles.
- orthotomy noun The property of cutting at right angles.
- orthotope noun The generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.
- osculant noun The point at which two tangent curves touch.
- osculatory adj Relating to, or having the properties of, an osculatrix; capable of osculation.
- osculatrix noun A curve whose contact with a given curve at a given point is of a higher order (or involves the equality of a greater number of successive…
- pair of compasses noun A technical drawing instrument consisting of two hinged legs, one typically equipped with a sharp metal point for anchoring and the other…
- Pappian adj For which Pappus's hexagon theorem is valid.
- parabola noun The conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points…
- paracentric noun A planar curve having the property that, when its plane is placed vertically, a body descending along it, by the force of gravity, will…
- paracomplex adj Hyperbolic complex.
- parallel adj Either not intersecting, or coinciding.
- parallel postulate noun An axiom in Euclidean geometry: given a straight line L and a point p not on L, there exists exactly one straight line parallel to L that…
- parallelepiped noun A solid figure, having six faces, all parallelograms, all opposite faces being similar and parallel.
- parallelogram noun A convex quadrilateral in which each pair of opposite edges are parallel and of equal length.
- parallelohedron noun A polyhedron that can tessellate three-dimensional spaces with face-to-face contacts via translations.
- parameter noun In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the…
- pedal curve noun For a plane curve C and a given fixed point P, the locus of points X such that PX is perpendicular to a tangent to the curve passing…
- pencil noun A family of geometric objects with a common property, such as the set of lines that pass through a given point in a projective plane.
- pentagon noun A polygon with five sides and five angles.
- pentagonal hexecontahedron noun A Catalan solid with 60 irregular pentagonal faces, 150 edges and 92 vertices, being the dual of the snub dodecahedron.
- pentagonal icositetrahedron noun A Catalan solid with 24 irregular pentagonal faces, 60 edges and 38 vertices, being the dual of the snub cube.
- pentomino noun A polyomino consisting of five square units. When packing pentominoes into three-dimensional shapes, the square units commonly are expanded…
- perpendicular adj At or forming a right angle (to something).
- perpendicular bisector noun A line that divides a line segment into two equal parts while also being perpendicular to said line segment.
- perverse noun A chiral opposite of something; a mirror image with opposite handedness.
- perversion noun Ellipsis of tendril perversion.
- petal noun A lobe of a rose (geometric shape).
- plane noun A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane); a bounded portion thereof.
- plane angle noun An angle formed by two intersecting straight lines.
- Platonic solid noun Any of five convex polyhedra with congruent regular polygonal faces, which have a high degree of symmetry and have been studied since…
- plesiohedron noun A special kind of space-filling polyhedron, defined as the Voronoi cell of a symmetric Delone set. Three-dimensional Euclidean space can be…
- Plücker coordinate noun Any of six homogeneous coordinates assigned to a line in projective 3-space, used in geometric algebra and computer graphics.
- point at infinity noun Any point added to a space to achieve projective completion.
- pointlessness noun The quality of not mentioning points.
- polar noun The line joining the points of contact of tangents drawn to meet a curve from a point called the pole of the line.
- polarity noun Ellipsis of trilinear polarity.
- pole noun A fixed point relative to other points or lines.