To Do and Notice
Add links to the Pi Chain. Each digit 0 through 9 is represented by a color. Select a colored strip of paper that matches the next digit of
pi on the chain, loop it, staple it on, and cross off that digit.
0 = red, 1 = yellow , 2 = white, 3 = green , 4 = blue , 5 = light pink , 6 = purple , 7 = black , 8 = salmon , 9 = hot pink
What’s Going On?
For this activity we are JUST having fun and making something pretty. We’re representing pi using colors rather than digits. However it
is interesting to think about the distribution of the digits of pi. You might want to consider looking into the following “extensions”
EXTENSION 1: Google “The Pi Search Page” and type in YOUR BIRTHDAY to find out where your birthday is within the digits
of pi. This web site will search the first 200 million digits of pi in a fraction of a second. If it finds your sequence, it will tell you at what
position in pi your sequence begins and will display your sequence along with surrounding digits. No result? Try another sequence.
The shorter the sequence, the better the odds of finding it. Pi is an irrational number, which means that its digits never end and that it
doesn’t contain repeating sequences of any length. If Pi-Search didn’t find your sequence of numbers, that’s probably because the
sequence occurs somewhere past the first 200 million digits. Note the qualification “probably”: Mathematicians can’t say with absolute
certainty that pi contains every possible finite number sequence—but they strongly suspect that this is the case.
EXTENSION 2: Strings of digits of pi are sometimes used to generate sequences of random numbers, but are the digits of pi
truly random? To explore this question research what it means for a number to be a “normal number” – a concept introduced in 1909
by mathematician E. Borel. As of 2011, pi has been calculated to 10 trillion decimal places. When mathematicians study any sample of
this huge number, they find that each digit, 0–9, occurs as often as any other, and that the occurrence of any digit seems unrelated to
the preceding digit. This makes pi appear to be statistically random. If this statistical randomness is unending, then pi must contain all
finite sequences of digits, including the birth dates of everyone ever born and yet to be born. It would also contain every winning lottery
number—too bad we don’t know how to identify them.
DIGITS OF PI FOR CHAIN ACTIVITY
Be sure to cross off your digit after you make your link for that digit.
3.1415926535897932384626433
83279502884197169399375105
82097494459230781640628620
89986280348253421170679821
48086513282306647093844609
55058223172535940812848111
74502841027019385211055596
44622948954930381964428810
97566593344612847564823378
67831652712019091456485669
23460348610454326648213393
60726024914127372458700660
63155881748815209209628292
54091715364367892590360011
33053054882046652138414695
19415116094330572703657595
91953092186117381932611793
10511854807446237996274956
7 3 5 1 8 8 5 7 5 2 7 2 4 8 9 1 2 2 7 9 3 8 1 8 3 ETC.!