Sunday, March 14, 2010

Happy Pi Day!

CNN has a nice piece noting that today is Pi Day (3/14). Individuals exist that devote extraordinary, and I mean extraordinary, amounts of time and effort into contemplating and working with the number Pi, the ratio of a circle's circumference to its diameter. People have memorized it to thousands of decimal places. Mathematicians have toyed with algorithms to identify patterns (all have failed) or automate its calculation (no luck). The number is irrational (cannot be expressed as a fraction) and transcendental (non-algebraic).

Darren Aronofsy's Pi is an outstanding film about a mathematician on the edge. His search for a magic number puts him in touch with Jewish numerologists seeking ultimate wisdom. It also puts him in the cross hairs of wall street executives.

What cooked my noodle in high school is that if you take e (the base of the natural logarithm) and raise it to the power of i (the square root of – 1) times pi, you get – 1. Start multiplying the exponent by a third number, and you have trigonometry.

Pi to 10,000 digits. Here are the first 1500. If you specify a numerical sequence, for example this year (2010), word is that you can find it somewhere in pi. I put 2010 in red.

3.141592653589793238462643383279502884197169399375105820974944592307816
4062862089986280348253421170679821480865132823066470938446095505822317
2535940812848111745028410270193852110555964462294895493038196442881097
5665933446128475648233786783165271201909145648566923460348610454326648
2133936072602491412737245870066063155881748815209209628292540917153643
6789259036001133053054882046652138414695194151160943305727036575959195
3092186117381932611793105118548074462379962749567351885752724891227938
1830119491298336733624406566430860213949463952247371907021798609437027
7053921717629317675238467481846766940513200056812714526356082778577134
2757789609173637178721468440901224953430146549585371050792279689258923
5420199561121290219608640344181598136297747713099605187072113499999983
7297804995105973173281609631859502445945534690830264252230825334468503
5261931188171010003137838752886587533208381420617177669147303598253490
4287554687311595628638823537875937519577818577805321712268066130019278
7661119590921642019893809525720106548586327886593615338182796823030195
2035301852968995773622599413891249721775283479131515574857242454150695
9508295331168617278558890750983817546374649393192550604009277016711390
0984882401285836160356370766010471018194295559619894676783744944825537
9774726847104047534646208046684259069491293313677028989152104752162056
9660240580381501935112533824300355876402474964732639141992726042699227
9678235478163600934172164121992458631503028618297455570674983850549458
8586926995690927210797509302955321165344987202755960236480665499119881

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10 Comments:

Anonymous Another Anon said...

Does Pi go with the Coffee Party?
(Bad joke.)

3/14/2010 1:07 PM  
Anonymous Thomas said...

Well, Pi would at least be known to some at the Coffee Party. I'm not sure the tea bunch got past sixth grade.

It's interesting that you posted this today, x4mr. I was talking about your blog a couple days ago, and we were curious about your education. What is your PhD in? Other degrees? Are you willing to say? The "reach" of this blog over the years in terms of material is huge. You seem to know a lot about computers, the Internet, math, statistics, science, as well as humanities and politics.

3/14/2010 2:52 PM  
Blogger x4mr said...

Been around the block. The BS was Electrical Engineering (Northwestern). Went ABD PhD, but settled for MS in Mathematics (Arizona), where I discovered my love for teaching. Then did the life thing (house/pool in foothills, wife, van, kiddies, doggies, rat, birds, debt). That lasted awhile. Saw SAIAT was doomed, so transitioned back to school for the PhD in Higher Education.

The formal education is the smaller piece. Most intense was "training" (if you can call it that) for certification to lead a leadership program at Magma Copper. Oh, if you only knew – it almost killed me. Early SAIAT days required formal Sun Microsystems certification in Java Programming and leading Sun programs, as well as CIW certification as a Webmaster. The copper company involved a ton of organization development, in particular Peter Senge of Fifth Discipline fame.

Arizona has (or had - I hear it has been impacted by budget cuts) an excellent Center for the Study of Higher Education with a curriculum deeply rooted in sociology. My dissertation involved institutional theory (e.g. Dimaggio & Powell) emphasizing quantitative methods on massive data sets such as NELS, NPSAS, IPEDS, and others. Both my adviser and I left Arizona at the end of the 2008/2009 academic year.

3/14/2010 4:05 PM  
Anonymous Thomas said...

Thanks.

That sure explains a lot.

3/14/2010 5:35 PM  
Anonymous Observer said...

My birth year of 1970 shows up at decimal places 3917-3921. Weird, huh? But wouldn't any random sequence that goes on forever eventually contain anything?

3/14/2010 7:32 PM  
Blogger Sirocco said...

My old geometry teacher had a little plaque on his desk with pi out to something like 106 places on it. He would say at the start of the semester that we either had to use the symbol to represent pi or, alternatively, we could actually calculate it if we used all 106 places.

So, of course, for one assignment the entire class did the homework using all 106 places of pi for every calculation.

3/15/2010 7:49 AM  
Blogger The Navigator said...

What is interesting is that they are still unable to verify that pi is even a normal number. I can see how the relationship between the magnitudes of pi and the base of the natural logarithm would "cook x4mr's noodle" because there is no real reason (based on my limited knowledge) why e and pi are such that e raised to an exponent of magnitude pi would produce a result of magnitude one. You can show that this has to be true using the series representations of both numbers, but it's still weird.

Reading x4mr's background has resurfaced my anger that this town had an incredible training organization run by someone perfect for such a job, and incompetent, corrupt goons shut the place down because PCC has to be the only training game in town for workplace training. Pathetic.

3/15/2010 9:30 AM  
Blogger TexPatriate said...

Nav,

It's just because you have to use the extra "e" for the very best "pie".

Pi without the e is like an ice cream sundae without nuts. =P

3/15/2010 9:04 PM  
Anonymous Anon said...

Texpat is right, Nav. Pi without e and we don't have a cosmos.

You may not grasp her taunting subtext (x4mr LIKES Texpat).

Pi without e.
Ice cream sundae without nuts.

Think for a second about where a comment from Texpat about an ice cream sundae without nuts puts x4mr.

3/15/2010 9:36 PM  
Anonymous Anonymous said...

Pi is everywhere. The ratio between the actual length of a river and its straight line from source to mouth approaches pi. Probability distributions contain pi. The laws of physics and gravity function according to pi. Da Vinci code fans will recognize that pi is the sacred feminine while e is the masculine.

3/16/2010 7:57 AM  

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