XKCD

XKCD is one of my favorite comics, and one that I occasionally share with the kids.  

Warning: this comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).  

Anyway, themes on pi are occasionally featured in its panels.   Here are a few:

Pi vs. Tau
e to the pi Minus pi - fav!
e to the pi times i - language
Pi Equals

Too Much Pi

I came across this article earlier this week:

How Many Decimals of Pi Do We Really Need?

It's some interesting stuff.   On the way to church, I talked with the kids a little about this article, and posed the following question (based loosely on the article):

Voyager 1, being about 12.5 billion miles away, is the most distant man made object from earth.   If it were in orbit around the earth at this distance, how many places of pi would you have to use to calculate the circumference of that orbit to within 1 inch?

I meant for the question to be rhetorical, to illicit guesses and discussion, but to my amazement, the kids jumped on it.   My wife, the math PhD, gave them a very quick primer on significant digits with some examples:

diameter (inches)	estimated pi	estimated circumference (inches)	actual circumference (inches)	error (inches)
100	3	300	314.1592...	14.1592,,,
100	3.1	310	314.1592...	4.1592...
100	3.14	314	314.1592...	0.1592...

They quickly realized they needed as many decimal places as there were digits in the diameter.   The rest of their solution went something like the following:

• We need the diameter in inches!  
• What is 12.5 billion miles in inches?
• No, *25* not 12.5 - we need the diameter, not radius! dork.
• I don't know, but I think there around 5,000 feet in a mile.
• That means there are about 60,000 inches in a mile.
• How did you get that?  5*12 is 60, then times a 1,000.  duh!
• So what's 25 billion times 60,000?
• Well 6 times 25 is 150...
• So how many zeroes do we add?
• A billion has 9 zeroes.   60,000 has 4.  We add 13!
• So it's around 150 with 13 zeroes.  That's 16 digits.
• Is the answer 16?

They got the correct answer.   I was amazed and full of pride.  They had worked together, used approximation techniques, and came up with the solution.

Anyway, turns out, NASA uses 3.141592653589793, or pi to 15 places for high precision orbital calculations.  I would hazard a guess this was chosen around the fact that a 64-bit double precision floating point number in IEEE 754 format (the most common format used in computing) is only accurate to 15.95 decimal digits and not because they needed to calculate the circumference of the orbit of Voyager 1.

Mathematicians Jörg Arndt and Christoph Haenel have suggested that for most "cosmological" scale calculations that 39 digits are all that's needed because that’s what's needed to calculate the circumference of the observable universe to within one atom’s diameter.

As of October 2014, the record for calculating the most digits of pi is 13,300,000,000,000.   That's a pretty big pie.

Pi Day

Every family has their own little quirky traditions, and ours is no exception.   One of those is celebrating Pi Day.    My wife makes a big pot pie for dinner, and for dessert, I make my famous Pi Cookies:


We're just wild and crazy that way.

This year's Pi Day, like last year's, has some uniqueness.   3/14/15 gives you pi to the first 4 decimal places, 3.1415..., while 3/14/16 gives you pi to a better approximation, since 3.14159... rounds to 3.1416.

Introductions

My family talks about math - a lot.  My wife, the math phD and school teacher, and me, the engineer, love sharing our passion for math with our four kids - 14, 12, 11, and 3.  We have fun solving everything from brain teasers to home work problems to poking fun at "bad math" used in the news.  I'm hoping to capture some of that passion here in this blog

Our first born, J, likes to be the first to answer any problem, and will often blurt out an answer just to be first, even if his answer doesn't make sense.   With enough prodding and coaxing, he generally finds his way to right answer.

Number two, B, is just as competitive, but she is also fiercely prideful, adamantly refusing any help or hints.   She may not get to the answer as quickly as she would like, but you can count on her being right.

And then there's M.   He's our little math prodigy.   Often he can intuitively jump to the answer, and give a very reasonable informal "proof" of why he's right, much to the chagrin of his siblings.  Still, his overconfidence tends to be his undoing as he rarely takes the time to double check his work.

Our youngest, G, in typical 3 year old fashion, thinks she's the center of the universe.   Sometimes she gets frustrated at all the talk about numbers because, as she puts it, she "doesn't get a chance to talk".  I think she enjoys it as much as the rest of us though.   She was practicing counting to 100 the other day, and would stop and giggle when ever she got to a double number like 44 or 77 claiming they were funny.

Anyway, that's us.  Hopefully you can share in some of our fun.