October: Cyclic Polygons

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

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

IMG_2063

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 work

Joel checking in on our progress

Ellen relates regular polygons to our problem

Ellen relates regular polygons to our problem

CiCi connects arc angles to polygons

CiCi connects arc angles to polygons

A helpful pentagon?

Tom: a helpful pentagon?

Bryce and Nicole: yes their all on a circle - is it the same circle?

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!

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