1. ## 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!

2. 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

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

4. 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?

5. "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.

6. ## 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

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# square metric proof

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