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:
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!