$$A=\pi r^2$$
The above is perhaps the best known formula and is also rarely understood. Although the formula for the area of ββa circle was already known in Ancient Greece, its justification is not easy at all. So it’s a great topic to enrich the “Why?” series.
βοΈ The area of a circle – formula
As you can see above – a square and a circle of the same area are not “somehow intuitively easy” related. Moreover, it has even been shown that squaring a circle (a procedure performed using a compass and a ruler without a scale) is impossible! And here comes the brilliant idea with a rectangle. Before I tell you what it is, let’s take a look at what the ΟΒ·rΒ² formula really says.
So there are slightly more than 3 squares of the side r in the circle with radius r.
βοΈ The area of a circle – proof by animation
I worked hard on this animation, I hope you like it. Let me know in the comments π
Continue reading “βοΈ Why is the area of a circle ΟΒ·rΒ² (pi r squared)?”
