57 replies to this topic

[imaseoulman]

So, I asked this question as part of a puzzle challenge on a different forum, and nobody had a clue. This requires creative thinking and it took me about forty minutes of straight thinking while staring at the circle to come up with the answer. I'm wondering, though, if the population here, being better at math and engineering can come up with the answer. The question stems from a real life situation, trying to find the ideal OD of a barrel material in a certain set-up. So here's the question copied from the other forum:

Alright, here comes one that you all may not like. It is a math puzzle. It requires nothing more than the ability to think originally and use deduction, but it's not easy. Simple? Yes. Easy? No.

The question is one that I came across in the real word:
Take a circle and divide into fourths (draw two lines that are perpendicular to each other and run through the focus of the circle). Now, inside one of the fourths, draw a circle with three tangent points: one, tangent to the circle itself, and the other two tangent to the lines that divide the circle into fourths. Finally, define the radius of the smaller circle in terms of the larger circle. You may not use calculus. Here is a drawing to help out a bit:

So essentially, define the radius of the green circle in terms of the red circle.

If you don't have the mathematical background to understand that last sentence, then answer this question:
If the radius of the red circle were 1, then what would be the radius of the green circle?

I will accept an answer to either question as they both are essentially the same thing and require the same work. Again, this takes very little actual math and while it can be solved with calculus, I won't accept the answer if it is derived by calculus. You must show how you got the answer. For those of you with math teachers, feel free to ask them for help...see what they come up with. Good luck.

P.S. Rossco, this one's for you. It's about as opposite as you get from those word play puzzles.

Just as a heads up, this took me a good forty-five minutes of staring at the circle and thinking before I arrived at the answer.

[rokor]

Is the answer 0.3333... ? I don't think I'm right but maybe...

[bobafan]

nope
*thinks more*

Edited by bobafan, 02 February 2009 - 09:27 PM.

[rokor]

nope
*thinks more*

Quoted right before you edited.

EDIT:Nevermind from before...

Edited by rokor, 02 February 2009 - 09:30 PM.

[Demo tay26]

I have no idea on how to solve this, but if the radius of the big circle is 1, would the radius of the smaller one be 1/3? This is just a quick calculation, tho.

EDIT: Holy crap, how do you post so fast? (P.S. I didn't see rokor's answer, and I don't know if I'm right.)

Edited by Demo tay26, 02 February 2009 - 09:52 PM.

[Split]

Christ. I got it eventually. Props to those who did. I've been slipping.

Edited by Splitlip, 02 February 2009 - 11:11 PM.

[iMod1]

Gah I'm too tired!
-iMod

Edited by iMod1, 02 February 2009 - 10:43 PM.

[Echnalaid]

I'm gonna guess the smaller circle's radius is .25. This is just from sight.

[Rogue Warrior]

I got something similar to Enchelaid. The radius is half of the circle, so half of the larger circle is 1. So that means that 1 is the diameter of the green circle which is a .5 radius.

Edited by Rogue Warrior, 02 February 2009 - 09:43 PM.

[Uncle Hammer]

Isn't it just a 1/4th of the red circle?

[nerfer34]

I got something similar to Enchelaid. The radius is half of the circle, so half of the larger circle is 1. So that means that 1 is the diameter of the green circle which is a .5 radius.

Yaaaa...it's a bit more complicated than that.

[durka durka]

Isn't it just a 1/4th of the red circle?

The green circle is inside 1/4 of the red circle.

[Echnalaid]

I got something similar to Enchelaid. The radius is half of the circle, so half of the larger circle is 1. So that means that 1 is the diameter of the green circle which is a .5 radius.

You did that by sight, or did you actually think?

Off Topic- Goddamn! No one ever gets my name right!

[rokor]

I got it now from skillz. It's aprx. 4.9926.

While finding the answer I realized that I learned how to solve these sort of things in grade 8.

Edited by rokor, 02 February 2009 - 09:52 PM.

[rokor]

You would do this by- C/pie/2 xpie. I think anyways, right now I'm confused.

Edited by rokor, 02 February 2009 - 09:56 PM.

[imaseoulman]

Rokor, I don't know where that answer came from (how you arrived at it) but it's incorrect.

So far nobody has gotten. Splitlip may have, but I'm waiting for him to clarify as he solved it differently than I did.

No, it's not a simple fraction like 1/3 or 1/4 or 1/2.

edit: I just checked Splitlip's solution and it is incorrect. You guys are thinking much better and more quickly than the other group, though.

Edited by imaseoulman, 02 February 2009 - 10:00 PM.

[nerfman600]

I know it has to be less than .50.

[imaseoulman]

I know it has to be less than .50.

You would be correct. Feel like playing twenty questions.

[Echnalaid]

I know it has to be less than .50.

You would be correct. Feel like playing twenty questions.

Well, in that case, is it greater than .4?

[imaseoulman]

Yes, but not by much.

[rokor]

Well is my formula correct?haha.

I would go all into this untill I get the answer but I am very tired, so I'll just stop here...

Edited by rokor, 02 February 2009 - 10:12 PM.

[nerfman600]

.43?

[imaseoulman]

I've carried the decimal out to over 30 places, and it doesn't repeat. This also doesn't involve pi. You don't even need to know about pi to solve this. That's a little bit of a clue.

[rokor]

My last guess is 4.09763548125374826282623787216. Yes?

[nerfer34]

I think the answer might be .414213562. (If that's right then.... I don't even know what I'll do)