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Re: Taxicab Geometry
Hello, It's been 13 years since I learned Taxi. Here is a better distance equation.
D = abs(P1x - p2x) + abs(P1y - p2y)
Or if you had two points (2,1) and (3,4) the distance would be 4. abs(2-3) + abs(1-4). There are four paths from one point to the other.
I just pulled out my "text" book on it. Its inventor is Eugene Krunse. He is (was maybe) a professor at the U of Michigan. (I have his e-mail if you need it).
The purpose of it is really to introduce people to Non-Euclidean Geometry, and was used for me as a warm up to a really hard Sr. Level College Geometry Course.
The circle (or the set of all points equal distance from a single point) turns out to be a square. However the perpendicular bisector (all points on a line perpendicular to another line and equal didtance to two points and the line) turns out really weird. Even weirder if the points on the first line are an odd length away from each other. If memory serves all of the conic shapes are represented.
Oh this brings back memories. Go Alice, Bruno, and Clyde!
-Jim
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