Is this geometry question possible to solve?

J

jpicard1

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Oct 12, 2005
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Ok I’ll try to explain this the best I can. I am an artist and have very little math skills.

Start off with 12 circles:
(3) @ 6.5 in
(6) @ 3.5 in
(3) @ 1.5 in

I need to arrange these circles so they create a larger circle and are edge to edge. What I need to figure is the exact diameter of the larger circle. The larger circle's circumference must pass through the center of the smaller circles. The best I could do was add all the diameters and divide by pi (45/3.14= 14.33) but that isn't right. For I'm doing I need the answer to be exact down to the cm.

I know (45/3.14= 14.33) is wrong because using the small circles diameters would just be a approximation, since what appears to be important is the curve created within by the larger circle. If feels like a paradox, the large circle determines the curve within the small circles, but knowing what the curve is exactly is what I need, to find out the diameter of the large circle. Now that I have written this out I'm really confused. Thank you for any help you can provide.
 
Draw the circles.
Construct line segments connecting their centers.
What are the lengths of the line segments so constructed?
What is the figure containing all three segments?
 
Also, notice that the touching (tangent) points of all the circles on the
large circle's circumference are all inside the large circle...

To add to TK's suggestion: join the center of the large circle to the
centers of the other circles; nice buncha triangles, right?
 
Thank you for taking the time to look at my question and give your help.
Just to make sure that I explained the problem correctly, I found a picture of what I am trying to achieve.

http://www.lucypringle.co.uk/photos/1998/uk1998bp.html

So as I wrote earlier, I have given my own numbers for the small circles and need to find the circumference for that circle that is passing through the 12 smaller ones. Does this example change any of your suggestions? Thank you for your help on this.
Jeff
 
Well...."big circle" looks more like an ellipse (but close to a circle)
trying to go through the tangent points of the circles instead of the
centers of the circles.

But it's hard to tell...perhaps I need new glasses...
 
Sorry...the bible quotes turned me off..

Ok happy, no dignity here, here goes: what a buncha crap!
 
Ok don't laugh too hard. My mom is into these crop circle things and I am somewhat of an artist. Im trying to finish a 3d crop circle scultpure thing for her. I have all the pieces I need already made ( the 12 dome/circles and some plywood) all I need to figure out is the exact diameter of the larger circle. I've been out of college for 10 years now and have no idea where to start.
 
happy said:
Don't mind Denis. He is like that sometimes.
Click to expand...
And don't mind happy: he is ALWAYS like that :twisted:

btw, the "dignity" part has nothing to do with you, Mr Picard;
it's a private thing between happy and me...
I'm trying to teach him to be more dignified...

And YES, there are bible quotes: see bottom of last url you provided;
I'm a 110% atheist and simply can't stand these stupidities from the Fible.
 
Sweet, atheism rules! I'm 120% atheist so it looks like I take the gold.
 
Start off with 12 circles:
(3) @ 6.5 in
(6) @ 3.5 in
(3) @ 1.5 in

If those are diameters, then large circle = 7.27328~ radius

If they're radius, then large circle = 7.27328 * 2 radius

What's interesting when arranged as per the diagram in your url's
(6.5-3.5-1.5-3.5-6.5......) is you get 6 equilateral triangles with
sides = radius of large circle, if you join the centers of the 6.5 and 1.5
circles, then join the centers to the center of the large circle.

Right TK?
 
12? Who knows? I got lost in the mysticism. "I could spend hours in the borders of its symbolism." What? I have a Spirograph that will really impress you. It's amazing what can be done in a short time by a couple of guys with ropes and lumber.
 
Don't have any problems with you, Denis. Remember, my only "job" here is to tutor the students. :wink:
 
tkhunny said:
It's amazing what can be done in a short time by a couple of guys with ropes and lumber.
Click to expand...

Anybody in his/her right mind knows that's the way it's done.
Well, makes for good tourist attraction, of course.
Catholic church attendance jumps dramatically every time some
joker sees a religious article shedding tears 8-)
 
happy said:
Denis, you don't believe in creatures from other planets?
Click to expand...
Yes, I believe there is one : you :lol:

Seriously: anybody who believes in that crap is mentally handicapped;
my opinion of course, and I'll respect yours, but if it's not the same as
mine, then it's wrong!
 
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