## Wednesday, May 09, 2018

### Second of N posts on G4G13. Maybe

(Don't forget to vote for SIGACT posistions:here  9th workshop on Flexible network design, May 22-25 at College Park, here.)

My first poston G4G13 is arguably here. To see why its debatable, see that post.

FOXTROT HALF-EMPTY, HALF-FULL PROBLEM, INCLUDING 13 by Thomas Francic Banchoff

In a Foxtrot cartoon (see here) Foxtrot has a glass which looks like it is half-full (or half-empty)
and asks people if its half-full or half empty. But the jokes on them!
The class is slightly angled so its actually 5/12 full (or 7/12 empty)
Given the area of the top and bottom What is the angle?
Generalize to other dimensions.

--------------------------------------
HEX PRIMES by Spandan Bandyopadhyay

Here is an alternative definition of primes that
lends itself to a generalization.

A number x is PRIME if when there is a rectangle with
integer sides and area x, one of the sides is 1.

Lets generalize this!

A number x is TRIPRIME if when there is a triangle with
integer sides of area x, one of the sides is 1.

Rather than use these prefixes we will go with

A number x is n-PRIME if when there is a convex n-gon with
integer sides and area x, one of the sides is 1.

HEXPRIMES are of course 6-primes.

The problem with 5-minute talks (maybe it should have been 6 minutes)
is that the concept is intersting but I didn't get to hear much
about them. And I could not find a paper on line. Note that this
conference has many non-academics for whome PAPERS are not the
basic currency so things are more informal. This is GOOD in that
its more of a free-for-all, but bad for follow up.
ALL of G4G12's are on You-Tube, so when that happens for G4G13,
I can follow up on this.

One thing I did manage to write down- 7 is the first HEX-composite.