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Non-Euclidean Geometry

  1. A non-Euclidean geometry is a geometry in which at least one of the axioms from Euclidean geometry fails.
  2. A non-Euclidean geometry is any geometry that contrasts the fundamental ideas of Euclidean geometry, especially with the nature of parallel lines.
  3. Non-Euclidean Geometry is any geometry that is different from Euclidean Geometry.
  4. Non-Euclidean geometry is a system built on not accepting this axiom as true.
  5. Non-Euclidean geometry is a type of geometry that is not based off the "postulates" (assumptions) that normal geometry is based off.


  1. A plane is a flat surface that extends indefinitely in all directions.
  2. A plane is a flat surface made up of points.
  3. A plane is a flat surface.
  4. A plane is a two-dimensional object.
  5. A plane is called a "polynomial" shape because it is defined by a first order polynomial equation.

Differential Geometry

  1. Differential Geometry is a complementary to Algebraic Topology, but I don't plan on going into as deep as I'm planning for Algebraic Topology.
  2. Differential Geometry is a fully refereed research domain included in all aspects of mathematics and its applications.
  3. Differential Geometry is a hard subject.
  4. Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus to study problems in geometry.
  5. Differential geometry is the language of modern physics as well as an area of mathematical delight.

Euclidean Geometry

  1. Euclidean Geometry is the oldest form of geometry, but it is by far not the only accepted form.
  2. Euclidean Geometry is the study of flat space.
  3. Euclidean Geometry was created when Euclid wrote The Elements around 300 BC as a collection of the mathematics known to the Greeks at that time.
  4. Euclidean Geometry was of great practical value to the ancient Greeks as they used it (and we still use it today) to design buildings and survey land.
  5. Euclidean geometry is a First-order Theory .


  1. Geometry - a "deforming" or "bending" of it.
  2. Geometry is a Greek word meaning earth measure.
  3. Geometry is a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids.
  4. GEOMETRY is a FORTRAN90 library which performs geometric calculations in 2, 3 and N dimensional space.
  5. GEOMETRY is a MATLAB library of routines for geometric calculations in 2, 3 and N space.


  1. Theorem: The R of the Law of Sines indeed is the radius of the circumscribing circle.
  2. Theorem: A pair of parallel lines, which interset a circle, bounds equal arcs.
  3. A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions.
  4. Theorem: The altitude to its hypotenuse partitions a right triangle into two similar triangles, similar to the original triangle.
  5. Theorem: The area of a triangle is equal to one-half of the product of the norm of a base and the norm of the corresponding altitude.


  1. Topology is a branch of geometry.
  2. The word "topology" means the study of surfaces.
  3. Topology - The general structure of a network.
  4. Topology is a branch of mathematics, an extension of geometry.
  5. Topology is a branch of mathematics.


  1. Gauss was able to prove the method in 1809 under the assumption of normally distributed errors (see Gauss-Markov theorem; see also Gaussian).
  2. Gauss was also interested in electric and magnetic phenomena and after about 1830 was involved in research in collaboration with Wilhelm Weber.
  3. Gauss was the first to adopt a rigorous approach to the treatment of infinite series, as illustrated by his treatment of the hypergeometric series.
  4. Gauss was extremely careful and rigorous in all his work, insisting on a complete proof of any result before he would publish it.
  5. Gauss was deeply religious and conservative.


  1. Euclid is a Greek mathematician that is best known for his influence on Geometry.
  2. Euclid is known as the father of geometry.
  3. Euclid is probably the most famous figure in geometric history.
  4. Euclid was not the first to write such a work.
  5. Euclid was unable to prove this statement and needing it for his proofs, so he assumed it as true.

Hyperbolic Geometry

  1. A hyperbolic geometry is a non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, and has a constant "sectional curvature" of -1.
  2. Hyperbolic Geometry is a "curved" space, and plays an important role in Einstein's General theory of Relativity.
  3. Hyperbolic Geometry is a "curved" space.
  4. Hyperbolic Geometry is a Hilbert Geometry in which there exist reflections at all straight lines.
  5. Hyperbolic Geometry is a non-Euclidian geometry.

Affine Geometry

  1. Affine geometry is a subset of Euclidean geometry.
  2. Affine geometry is a special case of projective geometry, where the vanishing point [ 7] is located at infinity.


  1. A trigonometry is the study of how the sides and angles of a triangle are related to each other.
  2. The mathematician Bartholemaeus Pitiscus published an influential work on trigonometry in 1595 which may have coined the word "trigonometry".
  3. Trigonometry is a branch of mathematics that solves problems relating to plane and spherical triangles.
  4. Trigonometry is a sine of the times.
  5. Trigonometry is an underlying basis for many mathematics and is used in many fields.

Technical Drawing

  1. Technical drawing is a skill, a vocation, but today it is much replaced by operating Computer-aided design--- software, e.g.
  2. Technical drawing is a basic communication skill used by all technical fields.
  3. Technical Drawing is a core skill for both interior and garden designers.
  4. Technical Drawing is a one semester course which may be repeated for credit (advanced work will be converted in repeat class).
  5. Technical drawing is a universal language and very important in today's technological world.


  1. A Triangle is a figure composed of three points and three lines in the plane.
  2. A triangle is a 3-sided Polygon sometimes (but not very commonly) called the Trigon.
  3. A triangle is a planar self- dual figure.
  4. A triangle is a three-sided polygon.
  5. A triangle is called plane; in distinction, for instance, to a 17-sided heptadecagon.

Geometric Group Theory

  1. Geometric group theory is a new branch of mathematics which advocates a return to geometry when dealing with groups.
  2. Geometric group theory is an expanding area of the theory of more general discrete groups, drawing on geometric models and algebraic techniques.
  3. Geometric group theory is the study of groups as geometric objects.

Finite Geometry

  1. A finite geometry is a geometry with a finite number of points.
  2. A finite geometry is any geometric system that has only a finite number of points.
  3. Finite Geometry is a field of mathematics.
  4. Finite Geometry is a huge field.

Sacred Geometry

  1. A sacred geometry is a feature of most folk mathematics, many forms of theology, and of some theories of philosophy of mathematics.
  2. Sacred Geometry is a PATHWAY TO UNDERSTANDING who we are, where we are from and where we are going.
  3. Sacred Geometry is a branch of metaphysical study dealing with the process of creation.
  4. Sacred Geometry is a scientifically valid spiritual discipline involving the sequential evolution of universal geometric principles.
  5. Sacred Geometry is a set of geometric shapes which in short are used to create the universe.

Algebraic Geometry

  1. Algebraic Geometry is a new emphasis area within the department.
  2. Algebraic Geometry is a subject with historical roots in analytic geometry.
  3. Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry.
  4. Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme.
  5. Algebraic geometry is a central subject in mathematics today.

Analytic Geometry

  1. Analytic geometry is a branch of mathematics that combines algebra and geometry.
  2. Analytic geometry is a branch of mathematics that uses algebraic equations to describe the size and position of geometric figures on a coordinate system.
  3. Analytic geometry is a branch of mathematics which study geometry using cartesian coordinates.
  4. Analytic geometry is a branch of mathematics which uses algebraic equations to describe the size and position of geometric figures on a coordinate system.
  5. Analytic geometry is a great invention of Descartes and Fermat.


  1. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
  2. A circle is a set (locus) of points in a plane that are equidistant from a point.
  3. A circle is a set of points that are equidistant from a fixed point called the center.
  4. A circle is a shape with all points the same distance from the center.
  5. A circle is a special ellipse in which the two foci are coincident.


  1. Circles are conic sections and are defined analytically by certain second-degree equations in cartesian coordinates.
  2. Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone.
  3. Circles are named by their centre, i.e.
  4. Circles are simple closed curve s, dividing the plane into an interior and exterior.
  5. Circles are simple closed curves which divide the plane into an interior and an exterior.


  1. A circumference is the distance around a closed curve.
  2. Circumference is a geometrical locus in a plane, that is a totality of all points, equally removed from its center.
  3. Circumference is a kind of perimeter .
  4. Circumference is a perimeter, but a perimeter is not necessarily a circumference.
  5. Circumference is the distance around a circle.

Convex Geometry

  1. A convex geometry is a closure space which satisfies anti exchange property, and known as dual of antimatroids [3, 10].
  2. A convex geometry is a closure space (X, --) with the anti-exchange property.
  3. A convex geometry is a closure system with the anti-exchange property.
  4. Convex Geometry is the branch of geometry studying convex bodies compact space compact , convex set s in Euclidean space .
  5. Convex geometry is a relatively young mathematical discipline.


  1. Coordinates are further used to model isometries and size transformations and their compositions.
  2. Coordinates are numbers which are used to locate an object.
  3. Coordinates are numbers which describe the location of points in a plane or in space.
  4. Coordinates are used throughout, so that analytic methods are now another tool rather than the subject of a special chapter, late in the book.
  5. Coordinates were specified by the distance from the pole and the angle from the polar axis.

Coordinate System

  1. A coordinate system is a method by which a set of numbers is used to locate the position of a point.
  2. A coordinate system is a method of indicating positions.
  3. A coordinate system is a reference grid used to locate the position of features on a map.
  4. A coordinate system is a system designed to establish positions with respect to given reference points.
  5. Coordinate system is a system of measurement of distance and direction with respect to rigid bodies.


  1. A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex .
  2. A cube is the three-dimensional case of the more general concept of a hypercube, which exists in any dimension.
  3. A cube is the three-dimensional case of the more general concept of a measure polytope.
  4. Cube - One of the platonic solids.
  5. For other meanings of the word "cube", see cube (disambiguation).


  1. A diameter is a chord passing through the center.
  2. A diameter is a straight line through the center and terminating in both directions on the circumference.
  3. A diameter is a straight-line segment that passes through the center of a circle or sphere and whose two end points lie on the circumference of the surface.
  4. A diameter is any line segment connecting two points of a sphere and passing through its centre.
  5. A diameter is the largest chord in a circle.


  1. A duocylinder is a four dimensional object that is an extension of the cylinder to four dimensions.
  2. The Duocylinder is a figure in 4-dimensional space related to the Duoprism s.
  3. The duocylinder is a figure in 4-dimensional space related to the duoprisms.
  4. The duocylinder is a peculiar object that has two perpendicular sides on which it can roll.
  5. The duocylinder is a peculiar object.


  1. A duoprism is a 4- Dimension al figure resulting from the Cartesian product of two polygons in the 2-dimensional Euclidean space.
  2. A duoprism is a 4- dimensional figure resulting from the Cartesian product of two polygons in the 2-dimensional Euclidean space.
  3. A duoprism is a 4- dimensional figure, or polychoron, resulting from the Cartesian product of two polygons in 2-dimensional Euclidean space.
  4. The duoprism is a 4-dimensional polytope, Convex set convex set if both bases are convex.
  5. The duoprism is a 4-dimensional polytope, convex convex if both bases are convex.


  1. Groups are compared using homomorphisms.
  2. Groups are essential abstractions in branches of physics involving symmetry principles, such as relativity, quantum mechanics, and other fields.
  3. Groups are monoids in which every element is invertible.
  4. Groups are very important to describe the symmetry of objects, be they geometrical (like a tetrahedron) or algebraic (like a set of equations).
  5. The groups are invariant in the sense that they do not change if the space is continuously deformed.

Homogeneous Space

  1. A "homogeneous space" is a manifold with enough symmetry that any point looks any other.
  2. A "homogeneous space" is a manifold with enough symmetry that any point looks like any other.
  3. A homogeneous space is a G -space on which G acts transitively.
  4. A homogeneous space is a similar concept.
  5. A homogeneous space is a space with a transitive group action by a Lie group.


  1. Lines are composed of an infinite set of dots in a row.
  2. Lines are also named with lowercase letters or a single loswer case letter.
  3. Lines are either horizontal, vertical, or oblique.
  4. Lines are not parallel.
  5. Lines are now self-polar.

List of Differential Geometry Topics

  1. List of differential geometry topics From Biocrawler, the free encyclopedia.
  2. This is a list of differential geometry topics, by Wikipedia page.
  3. See also curve, list of curves, and list of differential geometry topics.


  1. A matroid is a combinatorial structure whose properties imitate those of linearly independent subsets of a vector space.
  2. A matroid is a gammoid if and only if it is a contraction of a Menger matroid.
  3. A matroid is a mathematical construct, just as a group, a field, or a topology is a construct.
  4. A matroid is a pair.
  5. A matroid is an algebraic construct that is related to the notion of independence.

Minkowski Diagram

  1. A Minkowski diagram is a graph in which time runs along the vertical axis and space along the horizontal axis.
  2. A Minkowski diagram is a representation of Minkowski space in an inertial reference frame.
  3. A Minkowski diagram is a spacetime.
  4. Minkowski diagram is a spacetime diagram without the co- ordinates x and y.
  5. Minkowski diagram is a spacetime diagram without the co- ordinates y and z.


  1. An octant is one of the eight divisions of a Euclidean three-dimensional coordinate system.
  2. An octant is one of 8 parts of the two-dimensional Euclidean coordinate system .
  3. An octant is a navigational instrument used to obtain ---xes.
  4. An octant is one of eight divisions.

Parallel Lines

  1. Parallel Lines are coplanar lines that do not intersect.
  2. Parallel Lines is a seminal New Wave album by the art punk band Blondie, released in September of 1978 (see 1978 in music).
  3. Parallel lines are always a constant distance from each other.
  4. Parallel lines are straight lines that are in the same plane and that in both directions extended infinitely do not meet in either direction.


  1. Points are never split, which explains the requirement of separation by a plane.
  2. Points are closed in X; i.e.
  3. Points are often used to name lines and planes.
  4. Points are only colinear or noncolinear when considered with respect to other points.
  5. Points are represented by points on the sphere.


  1. A polychoron is a four dimensional polytope, where a polytope must be monal, dyadic, and properly connected.
  2. A polychoron is a closed four-dimensional figure with Vertices , Edge s, Faces , and Cells .
  3. A polychoron is a closed four-dimensional figure bounded by cells with the requirements that: # Each face must join exactly two cells.
  4. A polychoron is a closed four-dimensional figure with vertices, edges, faces, and cells.
  5. The use of the term "polychoron" for such figures has been advocated by George Olshevsky[?], and is also supported by Norman W. Johnson[?].


  1. A polyhedron is a 3-dimensional example of the more general polytope in any number of dimensions.
  2. A polyhedron is a geometric shape which in Mathematics is defined by three related meanings.
  3. A polyhedron is a three-dimensional analog of a Polygon .
  4. A polyhedron is a three-dimensional closed surface or solid, bounded by plane figures called polygons.
  5. A polyhedron is a three-dimensional solid whose faces are polygons joined at their edges.


  1. A polytope is a fancy word for a polyhedron in a higher dimensional space.
  2. A polytope is a generalization of the idea of a polygon or polyhedra to any number of spatial dimensions.
  3. A polytope is a multi- faceted solid About This Page This is my (Stephen Schiller's) web site home page.
  4. The term "polytope" was introduced by Hoppe in 1882, and first used in English by Mrs.

Projective Geometry

  1. Projective geometry is a non- metrical form of geometry, notable for its principle of duality.
  2. Projective geometry is a non metrical form of geometry that emerged in the early 19th century.
  3. Projective Geometry is a branch of mathematics that studies some properties about projection.
  4. Projective Geometry - one of the best non-algebraic introductions on the web by Nick Thomas.
  5. Projective geometry is a beautiful subject which has some remarkable applications beyond those in standard textbooks.


  1. A quadric is a 2nd order polynomial while a quartic is 4th order.
  2. A quadric is a quadratic surface.
  3. A quadric is a second order poly.
  4. A quadric is defined in POV-Ray by: quadric { , , , J } where A through J are float expressions.
  5. Quadric is a Fonthead Design font family with 2 styles priced from $12.00.


  1. RADIUS is a common authentication protocol utilized by the 802.1X security standard (often used in wireless networks).
  2. RADIUS is a remote access and dial-in protocol.
  3. RADIUS is also commonly used for accounting purposes.
  4. RADIUS was originally specified in an RFI by Merit Network in 1991 to control dial-in access to NSFnet.
  5. Radius is a fully extensible system.


  1. A reflection is a map that transforms an object into its mirror image.
  2. A reflection is one of the three kinds of transformations of plane figures which move the figures but do not change their shape.
  3. Reflection - The change in direction (or return) of waves striking a surface.
  4. Reflection - The third and fourth Explore these Questions: Obtain a one page handout.
  5. Reflection: A type of transformation that flips points about a line, called the line of reflection.


  1. Rotations are direct isometries, i.e., isometries preserving orientation.
  2. Rotations are direct Isometry, i.e.
  3. Rotations are direct isometries, i.e.
  4. The rotations are being applied about axes with different physical orientations and thus have different physical meaning.
  5. The rotations are of order , and .


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