mersenneforum.org 4 not so easy pieces?
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2006-10-04, 04:45   #34
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

40048 Posts
solution

Quote:
 Originally Posted by Wacky That is left as an exercise for the pupil .... :) Actually, it is rather easy. First construct the diameter. Then divide it into 8 equal parts. That gives you all of the centers of the various circular segments.

what about the two different radii? And the proof that it is correct apart from the visual effects?

Hippocrates' solution is far superior than any others given so far.

I'm wondering why there is no comment and why has it not been accepted by the community. Has it been understood at all?

I have a rigorous proof which is elegant and without doubt.

Any takers?

Mally

2006-10-04, 13:52   #35
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

100010000011112 Posts

Quote:
 Originally Posted by mfgoode And the proof that it is correct apart from the visual effects? I'm wondering why there is no comment and why has it not been accepted by the community. Has it been understood at all? I have a rigorous proof which is elegant and without doubt.

As for proving the one that I submitted, I think that it should not be too hard to do. By starting on the left side, assuming that the original circle (disk for the nit picky) has a diameter of 4, calculating the size of the smallest half circle (diameter of 1) on the upper side of the original diameter is easy. Set this as z. Calculate the area of the next half circle (diameter 2) call it y' , subtract z from this and call it y. Repeat for the next (dia. 3) x', subtract y' and get x. Repeat for the original (dia. 4) w', subtract x' to get w.

Add w to z, and y to x. If they are the same, viola.

2006-11-15, 01:07   #36
4 lil pigs mom

Nov 2006

3 Posts
How do you do it with 5 lines?

Quote:
 Originally Posted by R.D. Silverman How does one construct this with ruler and compass? As I said earlier, 5 pieces is easier.
My son has to divide a circle into 16 pieces with only 5 lines and his whole class is stumped but the teachcher won't help! You'd have to know her to understand. Can you help us please?????

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