of buoyancy in hydrostatics? How he celebrated his work on π is not recorded.
Given that π is defined as the ratio of its circumference to its diameter, what
does it have to do with the area of a circle? It is a deduction that the area of a
circle of radius r is πr^2 , though this is probably better known than the
circumference/diameter definition of π. The fact that π does double duty for area
and circumference is remarkable.
How can this be shown? The circle can be split up into a number of narrow
equal triangles with base length b whose height is approximately the radius r.
These form a polygon inside the circle which approximates the area of the circle.
Let’s take 1000 triangles for a start. The whole process is an exercise in
approximations. We can join together each adjacent pair of these triangles to
form a rectangle (approximately) with area b × r so that the total area of the
polygon will be 500 × b × r. As 500 × b is about half the circumference it has
length πr, the area of the polygon is πr × r = πr 2. The more triangles we take
the closer will be the approximation and in the limit we conclude the area of the