Weekend commentary: Circle gets the square
In figuring the area of a circle, there is instead one radius. Just multiplying the radius by itself would not compute it accurately. Why? Because if you have a square and, for instance, each side is 2”, you can “square” it to get the area.
What is Pi?
The polygons, as Archimedes mapped them, gave the upper and lower bounds for the area of a circle, and he approximated that pi is between 3 1/7 and 3 10 ... radius squared times pi, or. So in trying to find the area of a circle with a radius of 3 ...
Squaring the Circle: New Light on Old Riddle
The Hungarian mathematician, Miklos Laczkovich of Eotvos Lorand University in Budapest, proved theoretically that the circle must be cut into 10#50 pieces ... is impossible because the area of a circle, pi times the radius squared, involves pi, and ...
Take It to the Limit
That’s not really true, but it works … as long as you take it to the limit and imagine infinitely many pieces, each infinitesimally small. That’s the crucial idea behind all of calculus. Here’s one way to use it to find the area of a circle.
What Is Squeezing?
What does “squeezing” mean ... Since the point representing our system is always on this circle, we only really need two numbers to characterize it: the radius of the circle (the “amplitude” of the oscillation), and the angle that an arrow ...