This morning, Joel Patterson led us in exploring the question:

Given a polygon, is it cyclic (all vertices land on a circle), or not?

Early related conjectures:

- all regular polygons are cyclic
- all squares are cyclic
- all triangles are cyclic
- some quadrilaterals are non-cyclic
- all cyclic polygons are convex

A question arose about interior angle relationships and cyclic-ness (cyclicality?), and we were off and running:

Joel checking in on our progress

Ellen relates regular polygons to our problem

CiCi connects arc angles to polygons

Tom: a helpful pentagon?

Nicole and Bryce: yes, the points are all on *a* circle – is it the *same* circle?

Prior to the session, Joel had offered the following “Top Ten” list of possible titles for the session:

10. A roundtable on polygons

9. Wheel In The Sky Keeps On Turning–actually it’s not in sky just one some paper on the table.

8. Fitting square pegs in round holes

7. A roundabout conversation on polygons

6. DISCover something about polygons

5. R.E.M.’s first album, track 6

4. A circular discussion of polygons

3. A roundabout look touching on polygons

2. Joel rolls out an exploration of polygons of all types

And the number 1 title for next week’s session is…

Turning the MTC into an MTP (Math Teachers’ Polygon!)

For those of you who haven’t joined us for a session, please do come by – all the sessions are independent, and we love having new folks join in!