Hello all! I'm taking a look at Meserve's "Fundamental Concepts of Geometry" for an introduction to the world of geometry. Section(adsbygoogle = window.adsbygoogle || []).push({}); 1-7, A geometry of number triplescompletely confunded me. It introduced homogeneous points, and in my opinion it either a) did a horrible job, or b) did a horrible job explaining the significance of of these things. Furthermore after reading section 1-7 at least 5 times andstillnot really understanding what the point of these strange points are, they have not been mentioned in the subsequent sections yet.

Mathworld's page on the topic here didn't help me out, either.

In short I'm curious what the heck these points are all about. The pages seem to say that for a given triplet [tex](x_{1}, x_{2}, x_{3})[/tex] any other point which is amultipleof it, for example [tex](kx_{1}, kx_{2}, kx_{3})[/tex], is actually the same point. Furthermore it says that there is no triplet (0,0,0), and that usually [tex]k = 1/x_{3}[/tex]. This looks like smashing a 3D coordinate system in (x,y,z) into a plane at (x,y,1)...

Why? What for? What's the point of starting with an (x,y,z) and "smashing" to z=1? How do you start with the triplet? What does this triplet mean?

Any help is very much appreciated, I feel like I'm close but still far enough away that I'm completely confounded about homogeneous points' purpose or use.

Thanks!

-sev

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# Homogeneous points & coordinates

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