April 10th, 2018, 01:41 PM  #1 
Global Moderator Joined: May 2007 Posts: 6,511 Thanks: 585  area of circle
Can the area of a circle $\pi R^2$ be derived from the definition circumference=$2\pi R$, without calculus?

April 10th, 2018, 04:55 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,163 Thanks: 867 
Imagine cutting the disk into n, a large integer, "slices of pie" then put them back together alternating "point down" with "point up" so you get something like a rectangle (Except that the sides slant and the top and bottom are "rippled". But the larger n is the smaller those differences are.) The height of the rectangle is the radius, r. The top and bottom together make up the circumference, $2\pi r$, so each is $\pi r$. The area of that "rectangle" is $r(\pi r)= \pi r^2$. In the limit, as n goes to 0 we get the area of the disk, $\pi r^2$. 
April 10th, 2018, 05:03 PM  #3 
Senior Member Joined: Aug 2012 Posts: 1,888 Thanks: 525  

Tags 
area, circle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
circle area  mathman  Geometry  14  April 10th, 2018 11:50 PM 
Area of circle  ma78s  Trigonometry  1  March 21st, 2017 12:55 AM 
Finding the area of a circle inside a square only given the area of the square  skimanner  Math  12  July 8th, 2016 07:55 AM 
Area enclosed by a semicircle and a quarter circle  yeoky  Algebra  4  May 3rd, 2014 01:06 AM 
Area of square with convex parts  area of circle  gus  Algebra  1  April 17th, 2011 04:25 PM 