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Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Taxicab Geometry

How will you find the perpendicular bisector points in Taxicab geomety?

Is there any formula?

Please do the needful.

Thanks in advance

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Letter, number, arts and science
of living kinds, both are the eyes.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,418

Re: Taxicab Geometry

Is this of any help?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Taxicab Geometry

I might be wrong, but it seems like Prakash already knows what Taxicab Geometry is, and wants to answer a question that involves it.

I'm nowhere near an expert on this (my knowledge extends only to the amount I learnt skimming over Ganesh's link) but intuitively, I'd guess that the perpendicular bisector of a line in Taxicab Geometry would be the same as a perpendicular bisector in Euclidean ("normal") geometry. I don't see why it would be any different.

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Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Taxicab Geometry

I'd guess that the perpendicular bisector of a line in Taxicab Geometry would be the same as a perpendicular bisector in Euclidean ("normal") geometry. I don't see why it would be any different.

I doubt it. Consider the points (3,4) and (5,0). The origin is Euclidean-equidistant from both points and so lies on the Euclidean perpendicular bisector of the two points. But the origin is not taxicab-equidistant from those two points; therefore it does not bisect the two points in taxicab terms. Hence the taxicab and the Euclidean bisectors don’t coincide.

In general, if T is the taxicab distance and E the Euclidean distance between (x[sub]1[/sub],y[sub]1[/sub]) and (x[sub]2[/sub],y[sub]2[/sub]),

That’s all I’ve managed to discover on my own so far.

Last edited by JaneFairfax (2007-06-11 13:34:15)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Taxicab Geometry

Hey, look what I found.

http://jwilson.coe.uga.edu/EMAT6680Fa06 … /Perp.html

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Taxicab Geometry

Ah well. That's intuition for you.

The diagram on that page isn't quite complete though. It's got two "half-lines" and they should really be connected diagonally for the diagram to be complete.
It was the diagonal part that I thought of initially and so I wrongly assumed that it continued like that.

I'm thinking about it a bit more now, and if I'm right then it does something very odd when the two points are the same distance apart vertically as they are horizontally.
In that case, the perpendicular bisector is a region as opposed to a line.

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Why did the vector cross the road?
It wanted to be normal.

Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Re: Taxicab Geometry

Thanks a lot.

Last edited by Prakash Panneer (2007-06-12 09:27:53)

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Letter, number, arts and science
of living kinds, both are the eyes.