# circle

## Standpoint: A circle is a kind of ellipse

It is important to understand that the «agree» and «disagree» stereotypes do not reflect the opinion of the UML™ Parsing Analysis modeller/author, they reflect the modeller's understanding of whether source sentences of modelled «wrapper» Components agree or disagree with a claim.

## In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section, and all conic sections arise in this way

This diagram is worth some inspection. We will now begin to model two different points of view, namely whether a Circle "is" an Ellipse or a different conic. The point at this stage is NOT to make a decision one way or another, it is rather to represent the different points of view by relating elements from the UML™ Parsing Analysis domain model to new logical contexts and analysis elements representing these different points of view.

## In mathematics, a conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a circular conical surface) with a plane.

Note that this diagram is larger than I would usually recommend; it could be broken up into sub-diagrams. It does however tell quite a complete story, as a sort of UML poster.

## A circle is the locus of points from which the distance to the center is a given value, the radius.

We'll need this shortly to compare Circle with Ellipse (which Apollonius considered to have a different geometrical locus than a Circle).