Here's a simple geometric method for obtaining a square root using circles.
1: Start with a circle.
2: Duplicate & divide by the number you want to square
3: Make two intersecting circles which touch the inside of the outer circle and the outside of the inner circle.
4: Where they intersect is the square root.
Very cool stuff
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
Beautiful graphical calculator of circles. I tried many numbers from 1 to 1000,
including a few with halves thrown in. The even and the odd ones are
different the way they intersect. This is really fun to try to memorize!!
igloo myrtilles fourmis
The even and the odd ones are
different the way they intersect.
A perhaps more "proper" version would use a circle in the middle for the odd numbers as well, but I didn't like having half circles on the sides.
Just popping by to update with an equation:
If I didn't write the equation properly or if you can simplify, please do.
circlemaker, that's a beautiful tool. Can you give us a single line of code that turns n into the square root? Can you also show how this can be done on a simple calculator or on paper?
Just replace n with the number you want the square root of.
The equation is much easier if you define (n+1)/2 separately which is the intersecting circle radius:
n = 9; //get square root of this number
ic = (n+1)/2; //intersecting circle radius
sqrt = Math.cos(Math.asin((ic-1)/ic))*ic;