Euclidean and non-euclidean geometries?
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I'm going to focus on the usual non-euclidean geometry due to Lobachevsky. In that geometry, there are infinitely many lines parallel to a given line and through a given point. Squares (i.e. figures with 4 equal sides and 4 equal angles) don't have right angles. There is a pentagon with all right angles. The area of a triangle can be determined by the sum of the angles in the triangle (it is proportional to the difference of 180 degrees and the sum of the angles). There is a 'natural' unit of distance obtained from angles between parallel lines and perpendicular lines.
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Differential geometry/manifolds, Optimization word problems in 3D, topology proofs.
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go to www.google.com and type in \n\nriemann spaces  3 4 dimensions\n\nit will bring up alot of information for you to look at
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Think what you are looking for is Euclidian Space:\n\nAround 300 BC, the Greek mathematician Euclid laid down the rules of what has now come to be called "Euclidean geometry", which is the study of the relationships between angles and distances in space. Euclid first developed "plane geometry" which dealt with the geometry of two-dimensional objects on a flat surface. He then went on to develop "solid geometry" which analyzed the geometry of three-dimensional objects. All of the axioms of Euclid have been encoded into an abstract mathematical space known as a two- or three-dimensional Euclidean Space. These mathematical spaces may be extended to apply to any dimensionality, and such a space is called an n-dimensional Euclidean space or an n-space. This article is concerned with such mathematical spaces.\n\nIn order to develop these higher dimensional Euclidean spaces, the properties of the familiar Euclidean spaces must be very carefully expressed and then extended to an arbitrary dimension. Although the resulting mathematics is rather abstract, it nevertheless captures the essential nature of the Euclidean spaces we are all familiar with.\n\nAn essential property of a Euclidean space is its flatness. Other spaces exist that are not Euclidean. For example, the surface of a sphere is not a Euclidean space, nor is the four-dimensional spacetime described by the theory of relativity when gravity is present.
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Xcuse me dude, plz be clear abt wt u wanna ask abt the PRINCILES OF GEOMETeRY
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The Geometry of Perspective Drawing on the Computer\nhttp://www.math.utah.edu/~treiberg/Perspect/Perspect.htm
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hyperbolic\n\nare u not doing your own homework?\n\n\n\n\ntriangle drawn on a sphere always have total angles of more than 180 and they approach 180 as the triangle gets smaller. This type of geometry is called Elliptic Geometry.\n\nAnother type of geometry where all angles add up to less than 180, with 180 being the limiting case, is called hyperbolic geometry.\n\nThe geometry we r familiar with, geomatry of the flat is called Euclidean geometry.
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Hi there,\n\nTry looking for "Klein space" (without the 's). You get for instance this page : http://www.mccallie.org/myates/The%20Shape%20of%20Space/Student%20Projects/group10.htm
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Most introductory books on differential geometry discuss this. Looks at 'From Calculus to Cohomology' and 'Introduction to Smooth Manifolds' as references.
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length, width, depth. Time and space
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The geometry of the universe is non-euclidian. if you carry on going in a straight line you will eventually come back to your starting point.
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Generally, non-euclidean geometries are geometries that use a different fourth postulate, that, in Euclidean geometry, says that corresponding angles of a transversed parrallel lines are equal.  This basically means that parrallel lines never meet.  There are two other possible postulates.  One is that parrallel lines do meet, i.e. that space is like a globe where longitudinal lines meet at the poles.  The other is that other lines, besides parallel lines don't meet. In this situation space is shaped like a saddle, and lines get farther and farther apart.  Those are the two I know.  There are three other Euclidean postulates (e.g. you can draw exactly one circle through a point in the center and one on the rim) that someone might be able to change, but I am not aware that anyone has done that.
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There are in infinate number of 2d shapes, but here are diagrams of some of them --> http://www.mathleague.com/help/geometry/polygons.htm
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im a geo student, but i havent done proofs for a long time sorry. ok\n2. false, because squares are parallelograms with 4 congruent sides and 4 right angles, while kites have 2 pairs of congruent sides and only 1 pair of congruent angles that are NOT right angles\n3. false, because a rhombus is a parallelogram with 4 congruent sides, while a kite is any thing BUT a parallelogram. enuff said\n4. false, because kites are quadrilaterals with only two pairs of congruent sides, while the quadrilateral mentioned has 3 congruent sides\n5. false, for example- do trapezoids have 4 congruent sides, and 4 right angles, and is a parallelogram (characteristic of squares)? i think NOT\n6. read above- trapezoids are not parallelograms.
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I know u r not doing your own assignment but i cannot help it, i must answer your question.\n\nPositive curvature, elliptic\nnegative, hyperbolic
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The most popular atomic geometries are Linear, Trigonal Planar, Octahedral and Tetrahedra.\n\nI've added a link to a visualization program, though I couldn't get the plug-in to work.
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Here's a nice site:\n\nhttp://www.mathematische-basteleien.de/tangrams.htm