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!