# Square metric

• Jan 31st 2010, 05:53 PM
spectralsea
Square metric
The square metric defines the distance between two points (x1, y1) and (x2, y2) in R^2 by:

D((x1,y1),(x2,y2)) = max{|x2 - x1|, |y2-y1|} where the function max{a,b} denotes the larger of the two real numbers a and b.

Sketch all points (x,y) in R^2 such that D((0,0),(x,y)) = 1. Measure angles in the usual way. Show by example that R^2 with the square metric does not satisfy the SAS Postulate.

I've already graphed the points that satisfy D((0,0),(x,y))=1. It is the square formed by connecting (1,1), (1,-1), (-1,1), (-1,-1). However, I'm not sure what they mean by using the square metric to show it does not satisfy SAS. Help please!
• Jan 31st 2010, 05:59 PM
Drexel28
Quote:

Originally Posted by spectralsea
The square metric defines the distance between two points (x1, y1) and (x2, y2) in R^2 by:

D((x1,y1),(x2,y2)) = max{|x2 - x1|, |y2-y1|} where the function max{a,b} denotes the larger of the two real numbers a and b.

Sketch all points (x,y) in R^2 such that D((0,0),(x,y)) = 1. Measure angles in the usual way. Show by example that R^2 with the square metric does not satisfy the SAS Postulate.

I've already graphed the points that satisfy D((0,0),(x,y))=1. It is the square formed by connecting (1,1), (1,-1), (-1,1), (-1,-1). However, I'm not sure what they mean by using the square metric to show it does not satisfy SAS. Help please!

Hmm...Side Angle Side? haha
• Jan 31st 2010, 06:01 PM
spectralsea
I know what SAS means. I can't figure out how they want to disprove it by means of this square metric.
• Jan 31st 2010, 06:02 PM
Drexel28
Quote:

Originally Posted by spectralsea
I know what SAS means. I can't figure out how they want to disprove it by means of this square metric.

Well, I don't know what the SAS postulate is. What is it?
• Jan 31st 2010, 06:05 PM
spectralsea
"If triangle ABC and triangle DEF are two triangles such that AB=DE, <ABC=<DEF, and BC=EF, then triangles ABC and DEF are congruent"

*edit* Nevermind, I solved the issue. I was interpreting the wording of the question incorrectly.
• Jul 6th 2012, 09:14 AM
dmarch
Re: Square metric
I am new to this topic. Where can I find more information about square metric, and in particular, how it relates to parabolas, ellipses, hyperbolas and circles