Re: Radius of Arcs

"linux" <w@xxxxxxxxxx> writes:


"Robert Israel" <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> a écrit dans le
message de news: rbisrael.20090626182125$022d@xxxxxxxxxxxxxxxxxxxx
"linux" <w@xxxxxxxxxx> writes:


"Robert Israel" <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> a écrit dans le
message de news: rbisrael.20090604165210$6ea2@xxxxxxxxxxxxxxxxxxxx
AI <vcpandya@xxxxxxxxx> writes:

Unit circle (with radius r=1) is divided by 3 equal arc in to the 7
parts of equal area, as shown in the picture:
http://s524.photobucket.com/albums/cc321/Krejakovic/7krug.jpg

Find radius of arcs.

Nice problem.

Suppose the arcs have radius r and centres (in the complex plane) at
c, wc and w^2 c where w = -1/2 + i sqrt(3)/2.

Why are three centres of arcs the summits of an equilateral triangle?
Thanks.

Symmetry.
thanks but i do not understand always why.

It's natural to look for a symmetric solution, and I found one. I don't know
if there are non-symmetric solutions.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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