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Browse College Non-Euclidean Geometry

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Area of a Latitude-Longitude Rectangle [07/31/2003]
Given the latitudes and longitudes of four points on the Earth's surface, how do you calculate the surface area enclosed by the four points?

Best-fitting Line to a Number of Points [04/25/2001]
I have a number of points on a plane and want to find a line that best- fits through the points, minimizing the sum of squares of the distances of each point from the line.

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?

Distance from a Point to a Great Circle [05/24/2000]
How can I find the shortest great-circle distance from point C to a great circle connecting two points A and B (specified by their latitude and longitude)?

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?

Finding Area of a Spherical Triangle [07/08/2004]
Assuming the Earth is a sphere, and given three (latitude, longitude) coordinates, what's the easiest way to calculate the area of the spherical triangle formed by those three points?

Finding the Center of Two Points in Latitude/Longitude Form [08/11/2006]
If I have a spherical rectangle defined by the upper left and lower right corners given in latitude/longitude form, how can I find the midpoint between those two points so that I can use the midpoint and each corner to split the original region into four smaller regions?

Hyperbolic Geometry [03/24/2003]
Explain this assumption: Assuming that Euclidean geometry is consistent, had any of the failed attempts to prove Euclid's 5th Postulate from the other axioms succeeded, they would have actually completely destroyed Euclidean geometry as a consistent body of thought.

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?

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.

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

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

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