Chief Delphi - Taxicab Geometry

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- - Taxicab Geometry (http://www.chiefdelphi.com/forums/showthread.php?t=28574)

Re: Taxicab Geometry

Quote:

Originally Posted by Astronouth7303

Ok, Taxicab Geometry is deceptively simple. It's exactly like Euclidean, except distance is defined as the sum of the absolute values of the diferences pf the corrdinates.
OR: d_T = |A_X - B_X| + |A_Y - B_Y| + |A_Z - B_Z| + ...

And you define everyting based on locuses and distance. Circle is easy. A segment = {P | d_T(P, A) + d_T(P, B) = d_T(A, B)}

Confused yet?

Hmm ... you lost me at "Ok" :p

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

Re: Taxicab Geometry

Yes! Really freaky and really cool at the same time.
(sorry I didn't include arguments)

Anyone done this yet?

Quote:

What's this? (A personal favorite)

{P | d_T(P, A) = d_T(P, B)}
Some points to try it with
A, B
(0, 0), (4, 2)
(0, 0), (2, 4)
(0, 0), (3, 3)
(-1, 1), (4, 1)

Re: Taxicab Geometry

Quote:

Originally Posted by Astronouth7303

Yes! Really freaky and really cool at the same time.
(sorry I didn't include arguments)

Anyone done this yet?

I did (0,0)-(3,3) and circle with radius 3.

I wrote a VB program to do it :cool: .

Screen shots are attached. First one is (0,0)-(3,3), second is the "circle" with radius 3.

Re: Taxicab Geometry

Quote:

Originally Posted by gwross

In that case, the "circle" will be a square turned diagonally, right?

Wow! Did you just single-handedly solve the "squring the circle" problem? :D

Anyway, for more information you might check this out.

Re: Taxicab Geometry

Quote:

Originally Posted by SilverStar

I did (0,0)-(3,3) and circle with radius 3.

I wrote a VB program to do it :cool: .

Screen shots are attached. First one is (0,0)-(3,3), second is the "circle" with radius 3.

Can you post it? or is it in the code repos.?

Re: Taxicab Geometry

Oh, I remember doing this in math class. It's not as complicated as some people might think. It's hard to teach through an internet forum.

Re: Taxicab Geometry

I'm not trying to teach taxicab, just introduse an idea and encourage people to think about it. It's sort of fun to screw around with.
But for anyone with Geometer's Sketchpad (Keypress), I made a set of tools for it. (45 kB) Anyone who wants it please e-mail/pm me.

Re: Taxicab Geometry

Quote:

Originally Posted by Astronouth7303

Can you post it? or is it in the code repos.?

Sure, the Visual Basic code and the .EXE files are attached.

A complete ZIP is in the White Papers, also.