[Maths-Education] concentric and congruent circles

[Tandi Clausen-May]

Good morning, Kate!

On Thu, Jan 28, 2010, Kate Mackrell wrote:

...if two circles precisely overlap (i.e. are congruent and concentric), can
we say that two distinct circles exist?  Experience with dynamic geometry
software gives me the automatic answer of "of course..."

So the key issue is whether its position is one of the defining properties
of a circle.   If the circle is defined as a set of points at a uniform
distance from a given point then the question becomes whether the position
of the point is one of its defining properties.  Are all points fixed in
space, or can a point move?  In a dynamic geometry context it can move, of
course.  (And in real life.  The two halves of the pair of scissors on my
desk meet at a point where they are joined together with a rivet and screw.
The rivet and screw are the same rivet and screw if I pick up the scissors
and put them in my bag.)

If a point can't move then nor can any other mathematical object, I think,
without acquiring a new identity.  

Yours,  Tandi