# Talk:Analytic geometry

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Field: Geometry

## Comment

This article previously ended with the half-sentence: An example of a line represented in algebra in a cartesian   If you know a little something about analytic geometry, please complete this sentence and put it back.

I removed the line:

Calculus had been originally invented by Madhava of Sangamagrama and his Kerala school in 14th century India, and was later re-introduced by Isaac Newton and Gottfried Wilhelm Leibniz, independently of each other.

Not only is this incorrect, but it has nothing to do with analytic geometry. Grokmoo 20:12, 28 October 2005 (UTC)

The relationship between algebra and geometry is nontrivial. There exist proofs of this relationship based on the theory of geometry and notions of geometric length. What does this mean? Richard Pinch 19:23, 26 October 2006 (UTC)

I've changed it to what I assume it meant. A mildly interesting point for our wonkish bretheren: can this metatheorem that everyone knows be given an accessible reference? Charles Matthews 21:24, 26 October 2006 (UTC)
(Deleting previous comment.) How silly of me. Of course, the metatheorem that Euclidean geometry = analytic geometry is proven somewhere in the course of Tarski's proof that Euclidean geometry is decidable. The key steps are to show that Tarski's axioms are interpretable in the theory of real closed fields and that there exists a decision-procedure for the latter via quantifier elimination. To clarify, Grobner bases provide more efficient algorithms for the second step. An immediate consequence is that elementary geometry is routine. Amcfreely 03:22, 6 January 2007 (UTC)

The line is true but has nothing to do here. — Preceding unsigned comment added by 220.255.2.166 (talk) 00:57, 30 November 2011 (UTC)

## Notation

Why is the notation "A(0,0), B(a,0), C(b,e), D(c,f), and E(d,g)" used in the example? To me this looks like a multiplication or a function. Using "A=(0,0), B=(a,0)", etc. seems much more natural. Twanvl (talk) 22:33, 5 November 2008 (UTC)

## Is there an echo in here?

It seems to me the Algebraic geometry section is largely a direct copy of the history section. Needs fixing. I don't know which parts should rightly belong where, or I would fix it myself. -- Cimon Avaro; on a pogostick. (talk) 05:27, 18 March 2009 (UTC)

## hy

Payal —Preceding unsigned comment added by 116.74.47.238 (talk) 18:06, 24 November 2010 (UTC)

## The centroid of a triangle via analytic geometry

Hello, maybe it could be an example of how some geometry problems are easier to solve with analytic geometry? Also it's a core concept in many areas, I think would be interesting. —Preceding unsigned comment added by 187.107.33.121 (talk) 00:58, 17 February 2011 (UTC)

## Too little info on the modern and advanced meaning

This article has Too little info on the modern and advanced meaning. Maybe this article should be renamed Analytic geometry(classical meaning) and a new article should be created Analytic geometry(modern and advanced meaning) — Preceding unsigned comment added by 220.255.2.141 (talk) 00:56, 30 November 2011 (UTC)

I really can not see an advantage to having words on the tin that don't match what is in the tin. An article entitled "Analytic Geometry" should be about the modern subject of analytic geometry. A separate article entitled "Co-ordinate Geometry" should be about, well how about, co-ordinate geometry. Surely it would be obtuse to have it any other way, especially as this is an encyclopedia with an object of clarifying material. FreeFlow99 (talk) 14:01, 1 December 2013 (UTC)

## Analytic geometry vs Algebraic geometry

There is a lot of implicit mention of algebraic geometric concepts such as algebraic curves. To my knowledge analytic geometry is simply the study of coordinate systems. Perhaps this should be fixed. 67.252.103.23 (talk) 12:10, 11 March 2014 (UTC)