Hey! I just noticed that your poem seems to have two mistakes:
verse 5, circles should be a word with 6 letters
verse 6, infinity should be a word with 9 letters
I’m curious to know why some people felt the need to memorize pi out to nine or more digits. Was it required for your line of work or something? (mad scientist, I’m guessing)
Brain cells are a commodity, and I try to resist spending them without a clear ROI. 
Uh … My cat’s name is Pi and he had 18 digits.
Not as good a rhyme as Grimpixie, but still useful:
Now, I have a rhyme assisting
My feeble brain its tasks resisting
You’d have even more precision if you simply take 21.991148575128552666 and divide that by 7. Easy-peasey!
3.1415926 is what the first calculator I owned displayed, so that’s what I know. I didn’t vote because I wasn’t sure whether that counts as 7 or 8.
3.14159. All I know, and all I care to know.
And I’m a math teacher.
I wonder, do electronic calculators actually calculate Pi, or do they simply store it as a hardwired value? Windows Calculator (in Scientific mode) gives Pi to 32 places counting the 3; what floating point precision would that be?
The rhyme I know is:
Sir, I send a rhyme excelling
In sacred truth and rigid spelling
Numerical sprites elucidate
For me the lexicon’s dull weight.
So that’s 21 digits when I have time to write down my little ditty. Offhand? I keep forgetting the second 1 in 3.14159.
We had a ten digit calculator as a kid, and I memorised the number even before what I knew it was for.
3.141592654
When I did get to the point in my education to know what it was for, having memorised it did not help me.
However, I have never forgotten it.
I’m guessing any program to calculate pi takes up more storage than hardwiring it will. Even a program to compute Gregory’s Series will be a few lines of code, and that’s a horrendously slow, inaccurate convergence.
3.14159265358979323846264338327950
This is one digit greater than how many the Windows calculator has, so I guess that was probably my goal to beat and where I learned it from. I didn’t really use any tricks/mnemonics/rhymes; I was just bored at lunch one day in high school.
Nerd child. My parents bought a cool series of Time-Life science books. I still remember the cartoon of the guy on the high speed train approaching light speed showing time dilation. One of the books had pi printed out to at least 100 digits. I went to Pacoima Jr. High, in an extremely impoverished neighborhood in L.A. where they spent millions of dollars building a math center with its own TV studio. In 1970, we had our own PDP-8 mini-computer which someone said they calculated pi to 100 digits. We used it mostly to print out cool looking paper tapes.
Today, it’s a magnet school for the arts, which is fantastic.
I was trying to memorize it to 100 digits, but couldn’t do it. There was zero ROI, although I did mention it at least once, where upon the kid’s MIT going brother knew it to 100 digits.
IIRC in Intel processors the floating point unit does everything in 80-bit scientific notation in base 2 and holds several constants including Pi. There are two bits for the sign of the mantissa and characteristic, and the other bits are divided between mantissa and characteristic. There are 8 registers in a circular stack. If you program with “doubles”, which is the most common practice, you get IEEE 64 bit rounded versions of these, but if you program with “extended precision” values you get all 80. If I find it I will post how many of these bits are in the precision of the value; the rest are used to describe the power of two.
No practical ROI here, but there has been some social ROI in knowing pi to 101 decimal places. It is a great item for ice breakers… especially those where the rest of the group has to guess something about everyone in the group. I had a class in college where the teacher gave each of us a 3x5 card and asked us to put our name on it plus 3 unique things about ourselves. So I wrote down the following: 1) Eagle Scout, 2) Black Belt at age 10, 3) Pi to 100 decimals. The teacher was amazed as well as the rest of the class.
I have that book on my shelf! Life Science Library Mathematics. Chapter Five deals with calculus, and Pi to 206 places spans the top of pages 122 and 123.
Pi =3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214880651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 442881
I remember it to 7, but I can not think of a time where that number of significant figures is warranted.
Hmmm - perhaps circles should be singular and infinity plural…
Now, I will a rhyme construct
By chosen words the young instruct
Cunningly devised endeavour
Con it and remember ever
Widths in circle here you see
Stretched out in strange infinities
Who said poetry had to make sense?
Grim
100 digits. I was bored in high school.
Oops, for some reason I was thinking that we started counting digits after the decimal. So, move one vote from the “2” to the “3” column.
Also, while I don’t doubt that a relatively high percentage of dopers know pi to >3 digits, I also don’t doubt that this poll is relatively unpopular among those of us who stopped at 3.14.