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Topic: Easy: 8 way circle slice (Read 2970 times) |
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cnmne
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I do not see how you can divide a plane into more than seven sections, let alone a circle into eight sections of equal area or equal shape.
I do not think this can be done in two dimensions.
If you give the circle depth then it is the easy cake problem.
If you draw the circle on paper and fold the paper, then it can be done in three folds.
Is there an answer to this problem as stated?
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william wu
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Re: Easy: 8 way circle slice
« Reply #1 on: Jul 30th, 2002, 3:55pm » |
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Yes, there is a solution ... I cut out a circle from a campus cafeteria napkin yesterday and did it 
There are two solutions I know of to the 8-way cake slice problem, and one of these solutions can also solve the 8-way circle slice problem.
Note that the 3D solution you are thinking of for the 8-way cake slice problem does not require you to manipulate the cake in any way aside from simply slicing it.
Rearrange stuff to get more mileage per slice. Good luck!
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Blender
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Re: Easy: 8 way circle slice
« Reply #2 on: Jul 31st, 2002, 1:35pm » |
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Presumably the riddle would have said "Using this knife, slice this piece of round paper into 8 equal sized pieces using 3 straight cuts."
But as far as I know, a circle is 2 dimensional which implies that it's a geometry problem that you should be able to solve on a blackboard with a piece of chalk. If this is the case, your paper napkin solution doesn't work.
I can only figure out how to get 7.
What is the real answer?
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ScottP
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Re: Easy: 8 way circle slice
« Reply #3 on: Jul 31st, 2002, 11:17pm » |
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I'm with cnmne and Blender - looks like the only way to do this if it is down using cuts rather than lines.... and then manipulating the sections in 3D space. Willing to be proved wrong though.
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william wu
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Re: Easy: 8 way circle slice
« Reply #4 on: Jul 31st, 2002, 11:20pm » |
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You guys are absolutely right. The problem statement is misleading. I will rephrase it later so that it is clear you are allowed to do post-cut manipulation in 3d space.
No, I changed my mind. I'm just going to add a footnote to the 8-way cake slice problem: Find 2 solutions.
Thanks guys
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Oski Bear
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Re: Easy: 8 way circle slice
« Reply #5 on: Aug 5th, 2002, 5:47pm » |
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but it's not a 2D circle. it's a CAKE, which has 3 dimensions. so if the cake is in front of you on a table, do this:
1st cut: divide the cake in half
2nd cut: forms a + sign with first cut. the cake is now in quarter slices
3rd cut: slice "horizontally" to divide the cake into 2 circular planes (each being half the height of the original cake). each plane is already divided into four pieces, so now you have eight.
Go Bears
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william wu
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Re: Easy: 8 way circle slice
« Reply #6 on: Aug 5th, 2002, 5:50pm » |
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Hiya Oski. To explain the title of this thread, there used to be a riddle called 8 way circle slice, which asked how to divide a 2D circle into 8 equal pieces using 3 slices. Then I deleted it from the archive, and just modified the cake problem so that it now asks for 2 solutions. The solution that you mentioned would only work for a 3D cake, but not a 2D circle of paper.
Go Bears
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ckb
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Re: Easy: 8 way circle slice
« Reply #7 on: Aug 6th, 2002, 4:52pm » |
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Here's my take on the cake slicing:
1. Slice down the middle (2 pcs)
2. Slice down the middle the other way (4 pcs)
3. Take the quarter pcs and line them up in a row like this:
>>>>
Then slice through all of them.
That gives you 8 equal sized pieces AND each piece is equally frosted (assuming that the cake is frosted on all sides and on the top)
If you slice horizontally through the middle, parallel to the table, then 4 people get no frosting toppings.
ckb
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william wu
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Re: Easy: 8 way circle slice
« Reply #8 on: Aug 6th, 2002, 7:31pm » |
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interesting, i never even thought about the frosting. i guess the transverse plane slice method is suboptimal. you get an A+.
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| « Last Edit: Aug 6th, 2002, 7:31pm by william wu » |
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Kujo
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Re: Easy: 8 way circle slice
« Reply #9 on: Aug 9th, 2002, 7:15am » |
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The problem does not state the cake is frosted. Furthermore, if it was frosted, the frosting is not the cake itself. The pieces of the cake are still equal.
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Luke
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Re: Easy: 8 way circle slice
« Reply #10 on: Feb 8th, 2003, 10:07am » |
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SO what is the answer? I thought of some ways thinking this was a real 3D cake. Can't figure it out if it was just a 2D circle.
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Speaker
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Re: Easy: 8 way circle slice
« Reply #11 on: Feb 10th, 2003, 12:45am » |
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I didn't have a cafeteria napkin, so I just used a post it, and aside from one sticky edge, had no problem.
I just folded the circle up and with one slice created 8 equal pieces. Is that it? It seems pretty easy. I just folded it in half, and then in quarters, and then folded the edges back to make a fan sort of paradigm, and then sliced it down the middle.
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bashar haddad
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Re: Easy: 8 way circle slice
« Reply #12 on: May 26th, 2003, 12:12am » |
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First step: cut down the middle.
Second step: cut down perpenticular to the first cut.
Third step: line up the 4 slices you already cut like this:
<| <| <| <|
and cut down the middle of them all, you get 8 slices all with frosting...= ]
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Grimbal
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Re: Easy: 8 way circle slice
« Reply #13 on: May 18th, 2004, 6:13am » |
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on Aug 6th, 2002, 7:31pm, william wu wrote:| interesting, i never even thought about the frosting. i guess the transverse plane slice method is suboptimal. you get an A+. |
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Just assume there is frosting on the top and the bottom. 
Anyway, with a napkin, you could just fold it 3 times to get a 1/8th of a dîsk and cut it along the median. Unfold and ... voilà! It even works with a cake ... a pancake.
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