Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    why does the area of a circle = pi * r^2
    Offline

    2
    ReputationRep:
    (Original post by GayBoy)
    why does the area of a circle = pi * r^2
    using calculus, or not?
    This page explains the non-calculus way i think, although it's not a totally acurate method, it's accepted as being a reasonable demonstration of how the area equation works.
    http://www.ask.co.uk/ix.asp?q=prove+...%2Ehtml&adurl=
    Offline

    11
    ReputationRep:
    A formal proof can be done using integration.

    However, you can think about it more informally...all the formula says is that the area of a circle is proportional to its radius*radius (or diameter*diameter)...since the circle is a symmetrical shape, this should be fairly obvious. A square's area is proportional to length*length as well.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Louise_1988)
    using calculus, or not?
    go for it...i want any type of proof
    Offline

    2
    ReputationRep:
    (Original post by GayBoy)
    go for it...i want any type of proof
    posted above!! (i'm not a pro-maths dude, but my teached did explain this one to us. Somebody who knows more on the subject may be able to explain better!)
    Offline

    0
    ReputationRep:
    imagine you draw a tiny tiny tiny segment of a circle. It's effectively a triangle. A triangle's area is .5(base*height). Now the base is easy, that's just r. But the height? Well if we call the tiny angle dx and it is in radians, then the height of the tiny segment is effecitvely it's arclength, which =rdx. So The triangle area = 0.5r^2dx

    Now we define there to be 2pi radians in a circle (because that allows us to do radius*angle = arclength), so if we integrate our tiny triangles between 0 and 2pi:

    Int(0.5r^2) between = 2pi and 0 =

    (since r is a constant) [0.5r^2x] between 2pi and 0 =

    [0.5r^2 * 2pi] - [0.5r^2 * 0] = 2*0.5pi*r^2 = pi*r^2 as required
 
 
 
Turn on thread page Beta
Updated: August 1, 2004

University open days

  1. Loughborough University
    General Open Day Undergraduate
    Fri, 21 Sep '18
  2. University of Cambridge
    Churchill College Undergraduate
    Fri, 21 Sep '18
  3. Richmond, The American International University in London
    Undergraduate Open Day Undergraduate
    Fri, 21 Sep '18
Poll
Which accompaniment is best?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.