We re given a ruler, a compass and square sheets of side length $a$. Using these we need to find the approximate value of π.
I tried to arrange the sheets similar to a graph paper. Then we can draw a circle of know (large) radius and approximately calculate the number of squares overlapping. We can fold the sheet for better approximation.
I want to know your views on this and please share other ways as well.
On
Try this using a toothpick and graph paper. Draw parallel lines on the graph paper that are spaced a distance of 1 1/5 the length of the toothpick. Then put the graph paper on the floor and toss the toothpick onto it from several paces away. Do this a bunch of times keeping track of how many times the toothpick lands across a line (or either of the two edges of the paper parallel to the lines). Divide the total number of tosses by the number of times the toothpick lands on a line and then multiply the result by 5/3.
That is correct.
As long as you can divide your square into many small squares you can get a good approximation.