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Any math geek here?

post #1 of 36
2/16/10 at 12:14am
Thread Starter 
Just wonder if any maths expert here could help me with this small problem. Compare the area of the black and white.



Just note that the black is the shape of leaf, not circle.
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post #2 of 36
2/16/10 at 12:17am
What do you mean by compare? Are you looking for a percentage of black vs white or what?
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post #3 of 36
2/16/10 at 12:27am
Do they give you the functions that define the area?
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post #4 of 36
2/16/10 at 12:29am
Thread Starter 
Quote:
Originally Posted by unl3a5h3d View Post
What do you mean by compare? Are you looking for a percentage of black vs white or what?
Yes, percentage of black vs white.

Looks like I've just come up with the solution. Not sure if it's correct though lol.
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post #5 of 36
2/16/10 at 12:34am
What did you come up with?
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post #6 of 36
2/16/10 at 12:44am
Thread Starter 
White = 2/3 total
Black = 1/3 total
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post #7 of 36
2/16/10 at 12:46am
I'd think the lower line is y=x^2 and the upper boundary line is y=x^(1/2)

Thus we could think of the box as a 1by1 box, integrate the difference of the functions from 0 to 1 and get the area of the black portion. 1-area would be area of white portion.

! (I think, im not very good at math..)

thus we'd get the black area as 1/3
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post #8 of 36
2/16/10 at 12:48am
Thread Starter 
^ that's what I did.
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post #9 of 36
2/16/10 at 12:50am
I see how you could estimate it, but I don't see how you could get an exact area without knowing what the functions that define the curves are.

To estimate it, just use the integral of a function that produces a similar looking figure to get the area under the curve. Multiply that by 8 to get the white area.
Then get the area of the whole figure and subtract the above number from it to get the black area.

Disclaimer: It has been 7 years since I took calculus- so don't consider me an expert.
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post #10 of 36
2/16/10 at 12:52am
thats a VERY big assumption :/

it's truly a silly puzzle, in that there really isn't enough information from which to extrapolate any kind of meaningful solution.
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post #11 of 36
2/16/10 at 12:53am
Quote:
Originally Posted by nealric View Post
Then get the area of the whole figure and subtract the above number from it to get the black area.
that is a needless step - you can integrate assuming the boundaries are all 1 then the black's percentage is equal to its area
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post #12 of 36
2/16/10 at 12:54am
Quote:
Originally Posted by nealric View Post
I see how you could estimate it, but I don't see how you could get an exact area without knowing what the functions that define the curves are.

To estimate it, just use the integral of a function that produces a similar looking figure to get the area under the curve. Multiply that by 8 to get the white area.

Then get the area of the whole figure and subtract the above number from it to get the black area.

Disclaimer: It has been 7 years since I took calculus- so don't consider me an expert.
Yeah to find an exact area you would need a specific function. But I got 1/3 and 2/3 as well.
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post #13 of 36
2/16/10 at 12:56am
You can count all the pixels and compare it to the white :P
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post #14 of 36
2/16/10 at 12:59am
Quote:
Originally Posted by shubhangam View Post
I'd think the lower line is y=x^2 and the upper boundary line is y=x^(1/2)

Thus we could think of the box as a 1by1 box, integrate the difference of the functions from 0 to 1 and get the area of the black portion. 1-area would be area of white portion.

! (I think, im not very good at math..)

thus we'd get the black area as 1/3
Yeah you have it right, but with no scale and no functions, not much math going on here. Is it you are supposed to compare the area of black to white for pic 1 vs pic 2? If that's the case they are equal you have and x to y ratio on the left and a 1/4x to 1/4y for each small box, multiplied by 4.

Are there any numbers, any other instructions?

I'd say the majority of people here are in engineering or science-based fields, so asking about math you will get good answers. Asking about math + cables, ehh maybe not so much
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post #15 of 36
2/16/10 at 1:57am
Thread Starter 
Quote:
Originally Posted by El_Doug View Post
thats a VERY big assumption :/

it's truly a silly puzzle, in that there really isn't enough information from which to extrapolate any kind of meaningful solution.
Well, at least we have the exact number (side of the square). The problem is to the percentage, not the exact area, so I think it's fine.
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