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What is a straight line? I need a geometric definition of it. The equation of a straight line is known to me.I am saying about a straight line of 2D plane.

What is a circle? I need a geometric definition of it. The equation of a circle is known to me.

I know there is an algebraic side and a geometric side in 2D geometry. I needed geometric explanation.And, I thought points make a straight line.Is it fine to think like that?

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To go along with amWhy's nice response, you can also read Line (geometry) for a historical perspective. Regards – Amzoti Jan 25 '13 at 18:20
    
"The locus of points satisfying an 'equation of a straight line'" is a perfectly good definition of "straight line". – Hurkyl Jan 25 '13 at 19:11
    
I needed geometric explanation.And, I thought points make a straight line.Is it fine to think like that? – ReekMaths Jan 26 '13 at 20:11
up vote 4 down vote accepted

A straight line is the path of shortest distance between two points, though "line" and "point" are typically considered to be "primitives," axiomatically.

A circle is the set of all points equidistant from a given point (the given point being the center of the resultant circle).

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Those are not equations, they are Euclidean geometric definitions. – amWhy Jan 25 '13 at 17:56
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@ReekMaths: There's not a single equation in the above answer... – Henry T. Horton Jan 25 '13 at 17:57
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This answer is valid only when the space is endowed with a (Riemannian) metric. – Andrea Mori Jan 25 '13 at 18:06
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@Andrea I am answering in the context of Euclidean Geometry (as indicated by the given tag). It's as valid as is Euclidean Geometry. I'm not advocating its merits, only constraining myself within that context. – amWhy Jan 25 '13 at 18:08
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Within the framework of Euclidean geometry, a circle is by definition what amWhy said, and as far as I know, straight lines are primitive notions like points are (in classical Euclidean geometry, that is... of course it can be redone with metrics and such). – rschwieb Jan 25 '13 at 18:22

straight line locus of a point without changing any direction is a straight line.

circle: locus of a point forming closed curve and maintain equal distance from a fixed point(the center)

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The definition of line is not ok, mathematically speaking. The definition of circle is poorly phrased. Overall, it's just a confusing mixture of physical definition and basic geometrical properties. – G. Sassatelli Jul 4 '15 at 8:17
    
The concept of "direction" is not clear from the point of a grumpy Greek geometer with a straightedge and a compass, so this is not a good definition of a line. – Joonas Ilmavirta Jul 4 '15 at 8:21

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