Maths Question
343_guilty_spark
Join Date: 2003-06-18 Member: 17462Members
Join Date: 2003-06-18 Member: 17462Members
Hey, does anyone know the formula to find the area of a circle? If they do could they please tell me and they will go in my Maths coursework credits <!--emo&:)--><img src='http://www.unknownworlds.com/forums/html//emoticons/smile.gif' border='0' style='vertical-align:middle' alt='smile.gif' /><!--endemo-->
Edit: No this isn't cheating, we are allowed to ask around for formulas and such.
Edit: No this isn't cheating, we are allowed to ask around for formulas and such.
Comments
EDIT - BTW, please don't flame 343... it may be basic knowledge but no flaming please <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
Oh and picture to explain it better
Circumference = 2.pi.r
you could work it out in an equation
circumference = 2.pi.r
1000 = 2.pi.r
500 = pi.r
500/pi = r
thus, [area]:
pi.r^2 = pi.(500/pi)^2
and go on from there
or maybe im horribly wrong... i dont know, im too lazy to be thinking maths
Circumference = Pi * Diameter
(Or :
C = 2 Pi R
But that requires an extra number which i'm too lazy to write)
EDIT - Eediot you git you beat me
Edit: No this isn't cheating, we are allowed to ask around for formulas and such. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
what i find odd is:
1) you have to ask for the area of a circle, on a forum... how old are you? and why didnt google help?
2) maths coursework credits?
3) why would it be cheating.. formulas arent cheating, they're HOW you solve things...
4) why did you call it a perimeter, not a circumference... eep <!--emo&:(--><img src='http://www.unknownworlds.com/forums/html//emoticons/sad.gif' border='0' style='vertical-align:middle' alt='sad.gif' /><!--endemo-->
Yeah, that's what I was wondering, too. 343, you may want to get your teacher checked up or something; he doesn't seem to be doing a good job.
circum-thingamabob replaced with perimeter
I remember this.
Is this the "guy has 1000m of fencing and wants to make a pen for his <animals> and wants to figure out what would give him more "bang for his buck" (most area to work with)" thing?
2) We have to mention where we got formulas, ideas or anything else from.
3) Incase some people thought it would be.
4) As i have spent the last 21 days for 6 hours each day writing about the perimeter of triangles, squares, polygons and now its stuck in my perimeter.
Yeah fullauto we aren't given text books <!--emo&:(--><img src='http://www.unknownworlds.com/forums/html//emoticons/sad.gif' border='0' style='vertical-align:middle' alt='sad.gif' /><!--endemo--> But thats English non-royal gramma schools for you, we don't get alot of funding from the goverment.
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->Is this the "guy has 1000m of fencing and wants to make a pen for his <animals> and wants to figure out what would give him more "bang for his buck" (most area to work with)" thing?<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Yes it is <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
Also my teacher is very good, its just our last headmaster wasn't very good and the school took a bad blow in funding.
Jesus H. Christ on a three legged donkey! How do they expect you to learn without textbooks?
Good luck, anyway.
I KNEW IT.
GSCE Mathematics coursework D:
I had to do the exact same thing ~4 years ago <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
You also need to work out an all emcompassing formula that covers any given regular polygon, don't you?
<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Yep <!--emo&:(--><img src='http://www.unknownworlds.com/forums/html//emoticons/sad.gif' border='0' style='vertical-align:middle' alt='sad.gif' /><!--endemo-->
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->How do they expect you to learn without textbooks<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Copying words down of the board in our books then explain how they work i guess.
circum-thingamabob replaced with perimeter<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
I'm not quite sure about this, but I'm going to reckon that pi is more a greek number than a chinese number...
...being pi is actually a greek letter similar to п . It's right up there with rho, sigma, omega... Well, you know what, I've got a greek alphabet right here, so lets use that (obviously, without the symbols - being as: 1. I don't know how to display them, 2. The best I'd have is close cyrillic and modern latin equivalents.
Alpha a
Beta B
Gamma г
Delta [triangle]
Epsilon E
Zeta Z
Eta H
Theta [zero with a horizontal bar]
Kappa K
Lambda /\
Mu M
Nu N (actually, that's a guess, as it's garbled gibberish on this sheet)
Xi [3 horizontal bars]
Omicron O
Pi П
Rho [like an E, but bent]
Sigma P
Tau T
Upsilon Y
Phi [zero with a vertical bar]
Chi [pitchfork]
Omega [horseshoe/sideways C]
And there, the excitement of the greek alphabet - having nothing to do with circumference (which is effectively perimeter, it's just a different word for it - only pertaining to some shapes), circular area or pi in any mathematical way.
Ohh, and <a href='http://www.engineering.usu.edu/mae/faculty/stevef/info/Area.htm' target='_blank'>Behold the power of <s>Cheese</s> Google!</a> [granted half of that stuff you probably wont need, but perimeters and areas of lots of geometric figures are there.
2) We have to mention where we got formulas, ideas or anything else from.
3) Incase some people thought it would be.
4) As i have spent the last 21 days for 6 hours each day writing about the perimeter of triangles, squares, polygons and now its stuck in my perimeter.
Yeah fullauto we aren't given text books <!--emo&:(--><img src='http://www.unknownworlds.com/forums/html//emoticons/sad.gif' border='0' style='vertical-align:middle' alt='sad.gif' /><!--endemo--> But thats English non-royal gramma schools for you, we don't get alot of funding from the goverment.
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->Is this the "guy has 1000m of fencing and wants to make a pen for his <animals> and wants to figure out what would give him more "bang for his buck" (most area to work with)" thing?<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Yes it is <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
Also my teacher is very good, its just our last headmaster wasn't very good and the school took a bad blow in funding. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
I remember this, i did it earlier this year
But i can't remember what I did because i just copied it off someone else <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
It's not that i couldn't do it, i just couldn't be bothered.
i can't remember how it was done though
Circle:
2.pi.r = 1000
pi.r^2 = A
A = 500^2/pi
A ~ 79617
Rectangle:
2l + 2w = 1000
l = 500 - w
A = l.w
A = (500 - w)w
A = 500w - w^2
What math are you going into, because the easiest way to find the greatest possible area is with derivatives.
dA/dw = 500 - 2w
set dA/dw = 0
0 = 500 - 2w
2w = 500
w = 250
l = 250
A = 250.250
A = 62500
Triangle:
s = 1/2.P
A = sqrt(s(s-side1)(s-side2)(s-side3) <--Heron's (sp?) formula
s = 1/2.1000
s = 500
A = sqrt(500(500-side1)(500-side2)(500-side3))
Now, you can try and prove this, or you can use the logic way and argue your intelligence with the teacher (I don't know how the classroom works in GB, but you can argue your point to your teacher in America). The logic way is: you've already proved that "perfect" polygons have the greatest possible area (a square is a "perfect" rectangle, all the sides are the same), so logically a triangle with 3 equal sides would have the greatest possible area for a triangle. If you need more I can give you a better proof.
So side1 = side2 = side3 = 1000/3
A = sqrt(500(500-side1)(500-side1)(500-side1))
A = sqrt(500(166.66_7)^3)
A ~ 48112
Now you need a universal equation for polygons with n sides. Split the polygon into n number of triangles rotated around the center, each with a base of 1000/n meters. The equation for the area of this polygon is
A = n ( Area of one triangle)
To solve this, we're going to need the angles of the triangle. The sum of the "corner" angles of any polygon is 180(n-2). So a square has 180(4-2) = 360 = 90 + 90 + 90 + 90.
Then, to find the angles for any specific triangle you divide that by n, and then to find ONE of those angles you divide it by 2. So now you have 180(n-2)/2n = 90(n-2)/n = one angle of one of the triangles in your theoretical polygon.
A of a triangle = 1/2.b.h. The base of this triangle = 1000/n, but the height = tan(angle (called theta)). 1/2(base)
height = tan(90(n-2)/n)(500/n)
A of theoretical polygon = n * (500/n)^2 * tan(90(n-2)/n)
Now you need to take the derivative of this, I'm sure there's someone on these boards that can help you with that (or just search for it), then you need to show that the derivative never = zero, which means that there is no greatest value for the Area for this equation, but that the greater the "n" the larger the area. This means that as n approaches infinity, A approaches it's maximum value. And as n approaches infinity, the polygon looks more and more like a circle. So basically, the best way for the farmer to make a pen is to make it a circle <!--emo&:)--><img src='http://www.unknownworlds.com/forums/html//emoticons/smile.gif' border='0' style='vertical-align:middle' alt='smile.gif' /><!--endemo--> . I'd prove the rest of it, but I'm leaving in an hour for a week-long trip and I have to pack....have fun! <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
[edit] just to help out whoever helps him, the derivative of tan(x) = (sec(x))^2[/edit]
2) We have to mention where we got formulas, ideas or anything else from.
3) Incase some people thought it would be.
4) As i have spent the last 21 days for 6 hours each day writing about the perimeter of triangles, squares, polygons and now its stuck in my perimeter.
Yeah fullauto we aren't given text books <!--emo&:(--><img src='http://www.unknownworlds.com/forums/html//emoticons/sad.gif' border='0' style='vertical-align:middle' alt='sad.gif' /><!--endemo--> But thats English non-royal gramma schools for you, we don't get alot of funding from the goverment.
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->Is this the "guy has 1000m of fencing and wants to make a pen for his <animals> and wants to figure out what would give him more "bang for his buck" (most area to work with)" thing?<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Yes it is <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
Also my teacher is very good, its just our last headmaster wasn't very good and the school took a bad blow in funding. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
Try the BBC bitesize website, it tends to have every formula you need.
2500 {1/(n^3) * Pi * [sec(Pi(n-2)/2n)]^2 - 1/(n^2) * tan (Pi(n-2)/2n)}
I converted from degrees to radians. n must be an integer, and it must be at least 3. We want to find a value of n that will make this expression 0 or infinity. Immediately we can see that n=0 gives us infinity, but n=0 is not within the domain (since a shape with zero sides doesn't have area). So, we then look at the arguments of tan() and sec(). If either of them ever reach 0 or Pi, then we will have a condition that we are looking for (tan() and sec() being 0 or infinity).
Pi(n-2)/2n, n=3, gives Pi/6. For n=10, you get 2*Pi/5. As n approaches infinity, the argument approaches Pi/2, so we will never get zero or infinity from sec() or tan(). The only thing left is when n approaches infinity, 1/(n^2) and 1/(n^3) both approach zero. Since this makes both terms zero, we know that at n=infinity, the area must be at a minimum or maximum. Show that the area increases when n increases, and that is all that is needed.
Then again, this ignores the fact that you are using fence posts, and n can't be greater than the number of posts that you have.
You have 50 marbles all with the diameter of 1 cm.
What's the total area in cm^2 of the smallest plastic bag that can contain them?
(This is a packaging science question.. not easy by any means.)
I don't know if it'll help with geometry, but it does just about everything else.
whoa I went to a comprehensive and we always had at least a text book D: