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Browse High School Non-Euclidean Geometry

Stars indicate particularly interesting answers or good places to begin browsing.

Introduction to Hyperbolic and Spherical Geometry [06/01/2004]
Why is the sum of the angles in a triangle less than 180 degrees in hyperbolic geometry?

Non-Euclidean Geometry for 9th Graders [12/23/1994]
I would to know if there is non-euclidean geometry that would be appropriate in difficulty for ninth graders to study.

Curvature of Non-Euclidean Space [05/22/2000]
What is the difference between positive and negative curvature in non- Euclidean geometry?

Definitions of Edge and Face in 2D and 3D [10/10/2008]
What is the 'official' definition of 'edge'? Specifically, is an edge restricted to the intersection of two non-coplanar faces or do two- dimensional shapes have edges? I'm also curious about a definition of 'face'. How many faces does a two-dimensional shape have?

Difference Between arsinh and arcsinh Functions [05/13/2004]
Why isn't there a "c" in arsinh, arcosh, and artanh? These are the equivalents of arcsin, arccos and arctan but they are hyperbolic.

Distance Between Points on the Earth [12/11/1997]
The problem is to solve for the distance between two latitude/ longitude points with no parallels, say 24N 70E and 65N and 30W.

Distance Calculation [6/8/1996]
If I have the co-ordinates of two places in Degrees Latitude and Longitude, how do I calculate the distance in nautical miles?

Drawing Triangles [06/18/1997]
Is it possible to draw a triangle with more than 180 degrees?

Euclidean and Riemann Geometry [12/29/2003]
Riemann geometry alters the fifth axiom of Euclidean geometry that parallel lines never meet, saying instead that any two lines must intersect. How did he come up with this and how does it work?

Euclidean/Non-Euclidean Geometry [02/21/2003]
Consider the following geometry called S...

Euclid's Fifth Postulate [6/24/1996]
I am interested in finding some theorems, axioms, or postulates similar to Euclid's Fifth Postulate.

Euler's Formula Applied to a Torus [06/08/2001]
Can you explain why Euler's characteristic is zero for a torus?

Geometry vs. Trigonometry [07/14/1997]
What is the difference between trigonometry and geometry?

Hyperbolic Geometry and the Euclidean Parallel Postulate [01/20/1999]
When is it true that, given a line L and a point P, there is an infinite number of lines passing through P parallel to L?

Is Infinity a Number ... in Inversive Geometry? [01/15/2010]
A reader attempts to demonstrate infinity as concretely measurable in an inversive geometric construction. Doctor Tom explains analyzes the argument, weighing the pros and cons of the axioms of non-Euclidean geometries, and going on to expose an apparent paradox.

Is Pi a Constant in Non-Euclidean Geometry? [06/26/1998]
What if the circle is stretched across a curved surface?

Monogons and Digons - Polygons with Fewer Than 3 Sides [01/24/2006]
What do monogon and digon polygons look like? How can you have a polygon with fewer than three sides?

Non-Euclidean Geometry [10/22/2001]
What is non-Euclidean geometry? What two concepts are different from Euclidean geometry?

Parallel Lines: Euclidean and Non-Euclidean Geometry [4/25/1996]
If two lines are parallel, can they intersect?

Parallel Lines in Projective Space [05/18/1998]
Do parallel lines intersect at infinity? Is this in projective space?

Projective Geometry [01/13/1997]
When seen from a semi-bird's eye view, a fractal terrain looks like a regular trapezoid. When rotated right or left, the four corners seem to move along an ellipse. Find the equation of the ellipse whose center is also that of the trapezoid.

Resource for Euclidean and Non-Euclidean Geometries [9/30/1995]
For my high school project, I would like to get some information on Non-Euclidean geometry.

Riemann, Mayan Math [5/20/1996]
Math projects: A. Riemann - a German mathmatician; B. The Mayan number system and calendar; C. Probability.

The Role of Postulates [03/29/2003]
Who decided what were postulates and what were theorems? Why is it okay that postulates aren't proven?

Spherical Geometry and Triangles [02/09/2004]
Is it possible to have a triangle with two 90 degree angles, where the other two legs from the connected 90 degree angles meet to finish the triangle? Where would you find such a triangle? I thought it might work if the triangle is on a sphere, but then the lines aren't straight.

Spherical vs. Plane Geometry [05/30/1997]
How is spherical geometry different from plane geometry?

Sum of Angles of a Triangle in Non-Euclidean Geometry [08/01/2001]
In a triangle on the surface of a sphere the sum of the angles is not 180 degrees. Is that possible? Why?

Taxicab Geometry [1/11/1996]
I am looking for information online and/or in a college library about taxicab geometry.

A Triangle with Three Right Angles [12/01/1999]
How can you make a triangle with three right angles?

Understanding Non-Euclidean Geometry [05/26/1998]
Can you explain about geometries that are not on the plane? For example, what is a straight line on any surface?

Use of Steradians [7/26/1996]
How are steradians used in real life?

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