I recently (early February, 2006) received an envelope. It had no return address; its postage (and cancellation) was from India.It contained three xeroxed sheets of paper. There was no cover letter, no explanation, just the xeroxes themselves. Two of the sheets were from a pamphlet about squaring the circle, including a section noting that one R. S. J. Reddy had obtained superior results by using an approximation for pi of 3.14644661. The other sheet seemed to provide more information about R. Sarva Jagannadha Reddy and his efforts to show that a geometric approximation for pi is about 3.156844.
Some people might look at this mail and blanch, wondering "Have we been wrong about the value of pi all of this time?" I have more important things on my mind: I wonder, "Why did I receive this mail?"
It's addressed to "Doctor Larry Hosken". I am not a doctor nor a professor nor a what-have-you, doctor-wise. I am not an authority on pi. I admit that on this site, I wrote a simple python script that approximates pi by the Monte Carlo method. However, that script is only accurate to one decimal place. It happily spits out values of 3.11 and 3.16; it does so often. If Shri Reddy and/or his agents seek to impress an authority, they have chosen the wrong person. No one looks to Larry Hosken to find out what digit comes after the "1" in pi.
I guess my question is: has anyone else here received any similar mail recently?
-- (February 8, 2006) on Pi
A quirky article by Mike Keith talks about drawing binary digits of pi on a hexagonal grid and then staring at the result until you can convince yourself you see a picture there.
Towards the end, he points out that in the first 1000 binary digits, zero appears more frequently than one. Around bit 164, it's much more common than you would expect.
-- (May 15, 2005) on Frequency of Each Digit of Pi
Wow, someone sent me some mail about the example. She wrote:
Thank You very much for it! But I would like to please Your help. Could You tell please, what is nesessery to add to this programm for to get Pi colculations in such view 3.******** (i mean in your programm there are 4 numbers after point, but I need 8 numbers).First, the unhelpful literal answer: To specify that you want to view 8 digits of the number, you can use a formatted string. That is, instead of something like
print 4.0 * M / N...you can say something like
print '%0.8f' % (4.0 * M / N)However, when you try this, you will see it is not so useful: our result is an integer divided by 10000. Thus, the last few digits are always zero. This leads to the temptation to use a longer loop to get a more precise answer. But on my wimpy computer, using a longer loop leads to a too-long run time. And raises questions about how good my random number generator is. And when should I switch over to arbitrary-precision numbers? Oh, now my head hurts.
-- (April 15, 2005) on Calculation of Pi Using the Monte Carlo Method
RealPlayer says that the audio file at http://www.eveandersson.com/music/juanune.mp3 is 3:14 long. I'm still trying to guess whether that's a coincidence.
-- (March 8, 2005) on Pi
Looking over the graph of the first 10,000,000 digits, now I think that the question was wrong. Zero isn't the worst lagger. Behold--
0: 999440
1: 999333.Therefore, I would like to amend my answer to "Will some digit lag? Empirical evidence suggests that one must. Therefore, one lags."
-- (March 7, 2004) on Frequency of Each Digit of Pi
Obviously, some digit will lag. Which digit has a reason to lag? None has a reason to lag. Zero is none. Therefore, zero lags.
-- (February 3, 2003) on Frequency of Each Digit of Pi
I wonder if Suresh is looking for something like this.
#!/usr/bin/env python import random import math count_inside = 0 for count in range(0, 10000): d = math.hypot(random.random(), random.random()) if d < 1: count_inside += 1 count += 1 print 4.0 * count_inside / count
-- (December 14, 2002) on Calculation of Pi Using the Monte Carlo Method