Area of a Circle - Wedge/Sector Demonstration
We know that the area of a circle is: A=πr². But this is actually hard to prove.[br][br]So we cut the circle into wedges and place half of the wedges face-up and half face-down. [br]The hanging-out yellow pieces always "fill-up" the empty areas of the rectangle with A=πr²[br][br]As the number of wedges increases, the teal line -> radius and the hanging-out pieces start to fit inside the rectangle.[br]Isn't that cool? Showing this mathematically is called calculus!
What is the total length of the curved parts of the yellow wedges?[br]Why did we label the x-axis with units of π and the y-axis with units of numbers?