11 Oct 07
Originally posted by howzzatWell done Howzzat. Your solution is far more elegant than the one provided by the poser.
No..not at all..Here is my proof which is much much shorter than the one given in ranjan's post dated 29 th Sept. Borrowing the notations and symbols in that post, the area of the pentagon ABCDE is:-
w = Ar. of tr.ABC + Ar. of tr. ADE + Ar. of tr. ACD.
= x + x + (AC/SC)*x. =(2 + c)*x where c = AC/SC..............eqn.(1)
[AC/SC is the rati ...[text shortened]... and (2) we get 2+c = 3+1/c; hence c = {sqrt(5) +1}/2
Thus we get the required value of w/x.
11 Oct 07
3 edits
Originally posted by ranjan sinhaGoogling is of no help for finding solutions to puzzles. After seeing this pentagon puzzle here, I found it quite challenging and interesting. I posted this puzzle on a site dedicated to "cutting the Gordian Knot" for the wider mathematical community.
Did you google it up to find this out?
11 Oct 07
2 edits
Originally posted by HolyTNo cheating.. See the post above. I posted this puzzle on that site with a view to expose it to a wider interested audience.
Speaking of cheating, someone here is trying to find the answer by posting it in another forum: http://www.cut-the-knot.org/htdocs/dcforum/DCForumID6/648.shtml