1. ## Circlular Conundrum

Jezza Bear was wandering around the forest the other day wondering about a conundrum that wise old Olly Owl from the forest had set him.

Olly had told him the following:

" As we know from school the circumference of a circle is calculated by multiplying the radius of the circle by two and then multiplying the answer by pi. This we cannot argue, or can we? Jezza Bear if you can disprove this age old equation I will give you a very large [choccy bar]"

This is what set Jezza Bear off and he went off with a view to disprove the equation!

Well Jezza Bear thinks he has an answer of sorts. Armed with a straight edge compass which was fixed at 10cm from needle point to pencil point he drew two circles. Amazingly after a bit of calculation he proved that one circle actually had a smaller circumference than the other!!!

How did JB do this and was he right to claim his [choccy bar]?

2. ## Re: Circlular Conundrum

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">He drew one of the circles on a non-flat surface, for example with the needle point at the bottom of a bowl-shaped depression.</span hide>

3. ## Re: Circlular Conundrum

<P ID="edit" class=small>(Edited by Jezza on 28-Jan-06 21:45. Make slight change to attachment)</P>Yes, that is a correct answer. In fact Jezza Bear did this:

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> He drew one circle on a flat piece of paper of paper and the other one on the surface of a sphere. Silly old Jezza Bear had ventured into the realms of non-Euclidan geometry again and forgot to check his proof. Olly the wise old owl drew him a picture which I have attached as a zip file so as not to ruin in it for other puzzlers</span hide>

Olly says you can have the [choccy bar] and [magazine] of your choice

4. ## Re: Circlular Conundrum

But, the TRUE radius of the circle drawn on the sphere, is across the "Cord" of the arc in your sketch.

5. ## Re: Circlular Conundrum

Exactly Dave, so I think Jezza Bear was a bit confused and probably thought he had solved it correctly. He had mixed up his geometry. Silly Jezza Bear.

6. ## Re: Circlular Conundrum

>> Jezza Bear was a bit confused. He had mixed up his geometry.

And you still allow his to wield a chainsaw!!

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