March 14, 200719 yr I can't get my head around this one "equation." So, I figured out the pattern when it comes to cutting a circle up and finding the resulting pieces. I can't make an equation for it (to my understanding), so I think I need to use a sigma command. Cutting a circle with one line will give you two pieces, for example. Two lines will make four pieces. The maximum number of pieces created from any given cut is what the equation will be all about. received Here, I found this information out by cutting circles. Number of cuts in a circle - Pieces Created (Max) 0 - 1 1 - 2 2 - 4 3 - 7 4 - 11 5 - 16 6 - 22 7 - 29 8 - 37 9 - 46 10 - 56 I think it would looks something like this: X = The Number of Lines you are talking about. The sigma SHOULD give you the Y (max pieces resulting from cut) [(n/2)*(n+1)]+1 ~
March 14, 200719 yr this is going to get locked... the saying here is "these forums arn't for us to do your homework"
March 14, 200719 yr Author Thats ridicules. These forums have way, way to many rules. PLEASE TELL ME AT LEAST A LITTLE INFORMATION IF YOU PLAN TO LOCK ME. ~
March 14, 200719 yr Thats ridicules. These forums have way, way to many rules. PLEASE TELL ME AT LEAST A LITTLE INFORMATION IF YOU PLAN TO LOCK ME. He's right though.. we AREN'T here to do your work for you. ~Defender~ If you love me, send me a PM. 8 - Love me2 - Hate me
March 14, 200719 yr He never asked anyone to. Give him an example of how to make an equation, but don't give him the answer. Pretty easy. Edit: I'm no math expert, but being that you are dividing them, this looks like simple division. X/Y=Z, X being the circle, Y being the number of cuts and Z being the number of peices you end up with...But I think that you're asking for an equation to figure out how many you'd have continuing on with the pattern, and I can't help ya' there. The popularity of any given religion today depends on the victories of the wars they fought in the past. - Me!
March 14, 200719 yr Edit: Nvm read it wrong, i know the pattern but not the equation, sorry :( My Guide to Killing Green Dragon Autoers
March 14, 200719 yr Author I don't really want an exact equation for this pattern. I just need some help, maybe somebody to confirm my sigma I gave, ect... If you look at the data, you can see the difference between the maximum number of pieces is consecutively going up by one. Look.. 0 - 1 1 - 2 Difference = 1 2 - 4 Difference = 2 3 - 7 Difference = 3 4 - 11 5 - 16 6 - 22 7 - 29 8 - 37 9 - 46 10 - 56 See the pattern? I have no experience with equations of this kind. ~
March 14, 200719 yr It's also going up by the number of cuts made in the last one + 1! :P Personally, I'm more interested in how you can cut a circle 4 times and get 11 equal peices. I would have guess 8. :-s The popularity of any given religion today depends on the victories of the wars they fought in the past. - Me!
March 14, 200719 yr Author It's also going up by the number of cuts made in the last one + 1! :P Personally, I'm more interested in how you can cut a circle 4 times and get 11 equal peices. I would have guess 8. :-s Trust me, it CAN be done. I've experimented. It's looking like my sigma is accurate? ~
March 14, 200719 yr Yea, it's accurate according to what you have there. Someone should draw a picture of how you can draw an even number of lines (4) and end up with an odd number of peices, though (11). :P I'm just not seeing how that can be done at the moment... Someone will show me and I'll probably slap my forehead and go "oh..durr" The popularity of any given religion today depends on the victories of the wars they fought in the past. - Me!
March 14, 200719 yr Author Count em' up mate! Four cuts in the right places does = 11 pieces :wink: ~
March 14, 200719 yr Oh, I thought they had to be equal, like, halving the circle. So I'm thinkin' "Okay...Unless this is some weird [wagon] circle, that...Isn't possible..." :lol: The popularity of any given religion today depends on the victories of the wars they fought in the past. - Me!
March 14, 200719 yr Author Heh, now you can see what I have to deal with lol :lol: The equation in relation to cuts - resulting pieces is..a challenge lol I'm finding it a bit stressful. ~
March 15, 200719 yr We did this for extra credit in class. This is what I got, that too I got it checked by my dad, a math proffessor, so hopefully its right. I'll give you a hint. Its in the quadratic equation form.
March 15, 200719 yr I remember an equation , but it's not dividing each time. But just adding another line.
March 15, 200719 yr i believe the answer will be N 1+ (sigma) n n=0 simple as that... 1 plus every number up to the one your "at" theres a simpler way of working that out too i believe... i think 1+(N+1)(N)/2 will give you the answer at any given number of lines (where N is the number of lines) babelfish - level 180 60th placestrongguy - level 173 69th place
March 15, 200719 yr This is what I see: You keep adding both the 2 previous numbers up to get the next number
March 16, 200719 yr This is what I see: You keep adding both the 2 previous numbers up to get the next number i dont think that works...
March 17, 200719 yr Yeah you're right about the equation. You're using sigma cause it's a summation factor, and basically the formula for the given situation is something along the lines of.. 1+ ÃÆâÃâ¹Ã¢â¬Â âââ¬ÃÅ n (with a n on top of the sigma and then x=0 below it)
March 17, 200719 yr Author Yeah you're right about the equation. You're using sigma cause it's a summation factor, and basically the formula for the given situation is something along the lines of.. 1+ ÃÆâÃâ¹Ã¢â¬Â âââ¬ÃÅ n (with a n on top of the sigma and then x=0 below it) That is not correct. I'm talking about a sigma for the number of resulting pieces from a given number of lines, NOT a sigma for "+1." ~
March 17, 200719 yr 0 - 1 1 - 2 2 - 4 3 - 7 4 - 11 5 - 16 6 - 22 7 - 29 8 - 37 9 - 46 10 - 56 Dont know if you noticed, but the answer seems to be the result of the last term plus n, i.e. for the 6th term 22 = 16 + 6 and for the 10th term 56 = 46 + 10 Dont know how you display that as a formula though :x Website Updates & Corrections | Website Discussion
March 17, 200719 yr Author I have written up an eight page report on this. Anyone who wishes to see, it PM me. ~
March 17, 200719 yr Yeah you're right about the equation. You're using sigma cause it's a summation factor, and basically the formula for the given situation is something along the lines of.. 1+ ÃÆâÃâ¹Ã¢â¬Â âââ¬ÃÅ n (with a n on top of the sigma and then x=0 below it) That is not correct. I'm talking about a sigma for the number of resulting pieces from a given number of lines, NOT a sigma for "+1." You need the +1 at the beginning for the number of pieces with 0 lines since summation factor of 0 would give you 0. The sigma part is for anything that's over 0 lines which you'd add to 1 (from 0 lines) to in order to get the total parts in the circle given the number of lines.
March 18, 200719 yr Author Yeah you're right about the equation. You're using sigma cause it's a summation factor, and basically the formula for the given situation is something along the lines of.. 1+ ÃÆâÃâ¹Ã¢â¬Â âââ¬ÃÅ n (with a n on top of the sigma and then x=0 below it) That is not correct. I'm talking about a sigma for the number of resulting pieces from a given number of lines, NOT a sigma for "+1." You need the +1 at the beginning for the number of pieces with 0 lines since summation factor of 0 would give you 0. The sigma part is for anything that's over 0 lines which you'd add to 1 (from 0 lines) to in order to get the total parts in the circle given the number of lines. No matter. The sigma has been found (if you wish to see it, it's on my opening post.) ~
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