🚀 go-pugleaf

David G Radcliffe (radcliff@csd4.csd.uwm.edu) wrote:
: Brian Mcdonald (Brian.Mcdonald@p4.f18.n128.z1.fidonet.org) wrote:
: : how many polygons are there that all its sides are longer than any of its 
: : diagonals
: : ?????????????????????????peace and i'm outa here
: 
: There are infinitely many.  Consider the polygon ABCD, with
: A = (-2,0), B = (x,1), C = (0,0), and D = (x,-1).  If x > sqrt(3)
: then all the sides are longer than the diagonals.

Let's make it easy: consider any diamond (let's start with a rhombus).
Draw the diagonals. Take hold of two corners joined by a diagonal.
Pull apart along the infinite line containing the diagonal and you get
a shape whose sides are the longer than the shorter diagonal. The
short diagonal is the shortest side of two (isosceles) triangles.

Now draw a different polygon and its diagonals. Keep one of these
diagonals fixed and pull the other corners until the sides are longer
than the poor old diagonal.

Now how many polygons are there that all its sides are longer than all
its diagonals?
 
--

Henry Choy
choy@cs.usask.ca

What rolls down stairs alone or in pairs            This has been brought to 
Rolls over your neighbor's dog?                     you by the numbers 4
What's great for a snack and fits on your back?     and 9 and the letter P.
It's Log, Log, Log!  -- "The Log Song", from            -- Big Bird
                         Ren & Stimpy

Math is tough!       -- Barbie