This is a perfect octagon. Solve for the length of the exterior lines (X)
http://corbinrussell.com/staging/oct.jpg
http://corbinrussell.com/staging/oct.jpg
As a perfect octagon, all sides are the same length. Therefore, the vertical side on the right has a length of X, and extending the right and bottom sides will create a new (right) triangle on the bottom right with a hypotenuse of X, and therefore legs of length X/sqrt(2).
The given dimension is equal to the length of one side plus the length of one leg, thus
14 = X + X/sqrt(2).
Solve for X using any manner of your choosing.
Patricio Elicer
Obsessed with Reality
Got same result: X=14sqrt(2)/[1+sqrt(2)]
Paul C. Anagnostopoulos
Nap, interrupted.
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My son is learning the Pythagorean Theorem, so he loved this problem.
~~ Paul
~~ Paul
Ladewig
I lost an avatar bet.
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yep. me, too.
Are we doing your homework or is there some interesting aspect to this problem that would make it more appropriate for the Science forum rather than the Puzzle forum?
Beausoleil
Thinker
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In fact, if you compare that figure with the square redrawn, but with an a x a and a b x b square arranged along a diagonal, and two a x b rectangles each divided into two "ab" triangles, you can prove the theorem geometrically, without recourse to algebra at all.
Is that clear as mud or not?!
I have noted that as a member of JREF, that this forum abounds with math wizards here. Why is that? Are above average intelligent people more prone to being good at math, above that of other subjectmatter? Do people with good logic skills happen to like to post here, because good math logic helps them even with debate logic? (Maybe this should have been a thread of and to itself, eh?)
Patricio Elicer
Obsessed with Reality
Well, maybe the interesting aspect to this problem is that expectedly some people would be misled by intuition into thinking that the vertical sides of the octagon, and thus the unknown X, are 14/2=7.
I have been lurking and posting here at the JREF for about 4 years and I know the kind of food you guys like. I came across a fun problem and knew there would be many here who enjoyed it (including the extended family of the posters here, eh Paul?).
Finally, this is the Science, Mathematics, Medicine, and Technology and thus I figured it you apply.
If this forum is for merely discussing mathmatics and not appllying it and such problems are preferred in the Puzzle's forum, I will post them there in the future.
Finally, this is the Science, Mathematics, Medicine, and Technology and thus I figured it you apply.
If this forum is for merely discussing mathmatics and not appllying it and such problems are preferred in the Puzzle's forum, I will post them there in the future.