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        riddles >> medium >> japanese temple geometry 1
        
(Message started by: klbarrus on Jul 27^th, 2002, 10:44pm)

Title: japanese temple geometry 1
Post by klbarrus on Jul 27^th, 2002, 10:44pm

1) r1, the radius of the small circle, c1

dropping a line segment from the center of c1, and using right triangles:

(a+r1)^2 = (a-r1)^2 + (a/2)^2

This solves out to r1 = a/16

2) l, the side of the inscribed square

drawing a line from the upper left corner of the inscribed square to the bottom right corner of the big square:

a^2 = l^2 + (l+z)^2 (z = length of small segment)
we also know a = l + 2Z, so

l^2 + 2lz + 4z^2 = l^2 + l^2 + 2lz + z^2
l^2 - 2lz - 3z^2 = 0

factors to (l-3z)(l+z)= 0, or z = l/3
sub back in, a = l + 2l/3 or a = 5l/3 or

l = 3a/5

3) r2, the radius of the big circle c2

dropping a line segment from center of c2 and using right triangles

(a-r2)^2 = (r2+l)^2 + (a/2)^2

which if I subbed in correct and reduced, comes out to

r2 = 39a/320

Title: Re: japanese temple geometry 1
Post by Razor_Gaunt on Aug 2^nd, 2002, 3:40pm

Maybe I am not seeing something, if so, sorry.
1: I think you are right in the answer but the EQ should be (A+R1)^2 = (A/2)^2 + (A-R1)^2.

2: I just don't see the right triangle you are making with l+z, A and l.

3: Stuck on B.

Let me know where I went wrong.

Title: Re: japanese temple geometry 1
Post by Razor_Gaunt on Aug 2^nd, 2002, 4:16pm

Ok, I see where I went wrong with 2, DOH!

Title: Re: japanese temple geometry 1
Post by klbarrus on Aug 3^rd, 2002, 12:49am

Yes, I think I typed in the equation for part 1 wrong, sorry about that! I'll see if I can edit it ...

Title: Re: japanese temple geometry 1
Post by jeffab on Aug 21^st, 2002, 10:12am

Uhh, I am not sure how you can get the circles, but here is what I got for i.
assuming that "trig" is not verboten.

r1 := small circle radius
r2 := large circle radius
a := r3 = given large square side and radius of large circle arc segments.
i := small square side
Theta = angle (from horizontal) from large square corner to small square corner (long way)

given that i intersects the large arcs at the same point, you can use

sin(Theta) = cos(PI - Theta) Therefore Theta = Pi/4
i = a sin(PI/4)

I haven't had the time to figure out either of the circles, but I am not sure that the answer above for the small circle is correct. I think similar techniques to the above can be used to find
both circles.

Title: Re: japanese temple geometry 1
Post by Yournamehere on Aug 21^st, 2002, 12:04pm

on 08/21/02 at 10:12:06, jeffab wrote:

given that i intersects the large arcs at the same point, you can use

sin(Theta) = cos(PI - Theta) Therefore Theta = Pi/4

This is not correct. You're saying Theta is 45 degrees, yet the triangle formed by Theta (from corner of large square, to intersection of circle and small square, to bottom corner of small square) is clearly not isoceles. If Theta were 45 degrees, both of the shorter sides must be equal in length.

Where does this cos(PI-Theta) come from?

Title: Re: japanese temple geometry 1
Post by jeffab on Aug 21^st, 2002, 12:52pm

sorry make that Pi/2 - theta (90 degrees minus theta)...
This is what I get for calculating subnet masks simultaneously... Both this answer and the
masks were screwed up...

sin (theta) *a = i = cos(90 - theta) * a..
and that makes it an identity.... my bad...still working..
I think part of the trick is to stack this on top of a mirror image under it to see
the full half circle :)

Title: Re: japanese temple geometry 1
Post by Immanuel_Bonfils on Aug 26^th, 2010, 10:47am

How comes those posts form 2002 in here?

Title: Re: japanese temple geometry 1
Post by towr on Aug 26^th, 2010, 11:00am

Probably someone posted spam, and it got deleted. That would still leave the thread on the first page.

Title: Re: japanese temple geometry 1
Post by ThudanBlunder on Aug 26^th, 2010, 11:27am

on 08/26/10 at 11:00:57, towr wrote:

Probably someone posted spam, and it got deleted.

Spam
Moved
Quietly
?

Title: Re: japanese temple geometry 1
Post by SMQ on Aug 26^th, 2010, 3:06pm

No, not I; could also have been mis-posted and self-deleted--we may never know, but we can of course continue to clutter up the thread with idle speculation. ;)

--SMQ

Title: Re: japanese temple geometry 1
Post by ThudanBlunder on Aug 27^th, 2010, 8:03pm

on 08/26/10 at 15:06:58, SMQ wrote:

...but we can of course continue to clutter up the thread... ;)

--SMQ
--SMQ
_--SMQ

Of course. ;D