Pi is 4 (again)

I’ve been busy this week. On Monday I gave my new Auto-Tune talk to the School of Maths (I spent the previous Saturday reading the patent for Auto-Tune. Very interesting.) And yesterday I was in London to give a talk on Teaching Analysis. The meeting was also interesting but poorly attended as just about every project is running conferences and workshops. During my talk I showed my Pi is 4 video as an example of something I am using in my lectures. You can see it here. Anyhow, Vi Hart has a video on the subject which is worth...

Pi is 4 video

I mentioned the “proof” of π=4 in a previous post. In time for Pi Day on Monday, I’ve created a new video setting out the problem. For those not inclined to view videos here is the problem: Take a circle of diameter 1. Its circumference is π since its radius is 1/2 and a circumference is 2π times radius. Now put a square round it. The length of the perimeter of the square is 4 since each side has length equal to the diameter of the circle. Now fold in the corners like so. Since there was no stretching or shrinking, the length of this new curve is also 4. Do the process again, i.e., fold in all the corners. The length of this curve is still 4 since no stretching or shrinking was involved. Do it again. The length is again 4. We can take the limit of this process. The limit is a circle. Since the jagged curve gets closer and closer to the circle and always has length 4 we can see that the perimeter of the circle has length 4. But the perimeter length is also equal to π. Therefore, π is 4. Where is the...