Happy PI day to everyone! My daughter is a high school math teacher so PI day is always a big day to her!
...hmm OK! That's good to know. That must mean there is a Pi Day 5K race tomorrow...only yesterday did the ice melt on the jogging paths around here. We were under ice about 3 weeks and 2 days in Feb/March and another week in Jan so one month out of the year so far. The 5 k race is 3/14/15 9:26:53 AM which I might make. If it was instead 3.141582653 I'd probably skip it.
If I understand you correctly. 3.14159265359 3 is March - 3rd month of the year 14 is the fourteenth day of the month (tomorrow) 15 is the year 2015 9 is the hour of the day 26 is the minutes 53 is the seconds 59 I forgot to erase but I suppose it could be hundreds of a second.
The goal is "pi = 3.14159265". Saturday in Huntsville is 3.14 easy. The challenge is: 159265 To get "15", we use what the USA calls 'military time': 15 ... leaving "9265" Ah HA! Two, nonsexist periods solve the problem: .9256 * 60 = 51.40 ... 51 minutes .40 * 60 = 24 ... 24 seconds The plan is: Saturday, 3.14, at 15:51:24 - toast 'pi' with an adult beverage There are equally plausible, numerology nonsense that could be applied but this one works for me. So what goes with the adult beverage? Of course, I like: Bob Wilson
By this scheme, e day would be Feb. 7 and perhaps as deserving of its own day. Physics and chemistry offer up others. In a world where people can recite lyrics from many pop songs, it seems sad that they cannot invoke a few (30 might suffice) fundamental numbers. Those that define the physical universe and the chemistry and biology that have 'intruded' it. Pi is a big one, but might we broaden our view? Most compelling about Pi is that it is much more than circular circumference / diameter. It shows up in equations describing many aspects of the physical world. So, good on Pi to have a day. Perhaps you could invoke an environmental hook for Pi to justify it here Bob. None come immediately to my mind. The Golden Ratio (1.618...) is often invoked. So that would mark Jan. 6 on the calendar. We should bear in mind that some of the Golden-Ratio invocations in environmentalia seem a bit squishy What are the 'universal constants' of environmental science? Dang, you got me there. An unknown number of critters interact with an equally unknown number of associates, in mostly unknown ways. Patterns have certainly emerged but they do not rise to the level of universal constants. In this domain, we search for patterns and underlying mechanisms. Exponential and logistic relationships often appear. Pi and other fixed constants do not. Is the a 'fail' for environmental science? Maybe not. Maybe it means that biological interactions are uniquely complex in that small corner of physics and chemistry where they happen.
Ah, so the day is picked as a numerology sort of thing. Dates aside, I've always idly wondered how you derive Pi.
My first thought was that you just measure the circumference and diameter of any circle, and divide one by the other. And in fact a slight variation on that was how Archimedes did it: Archimedes' Method The problem is, it's tricky to accurately measure a curved line. So what Archimedes did was to take a circle and draw two regular polygons touching it as closely as possible, one inside the circle and one outside: It's now easy to measure the perimeter of the polygons and divide each by the diameter of the circle, giving two approximations for pi, one too large and one too small. The actual value of pi must then be between these two values. By adding more and more sides to the polygons their fit to the circle gets better and better, and so the inner and outer numbers get closer and closer, eventually giving a very good approximation for pi.
Thanks for that. Still have this picture of the little boy in Pi, dashing off line after line of numerals across a black board.
Actually, I like Saturday, 3.14, at 15:51:24 better than the time depicted in my OP. It's more accurate....since 9:26:53AM is properly expressed as 09:26:53 ....and I like Pi!
One way: 4 times the sum of the infinite series 1/1-1/3+1/5-1/7+1/9-1/11+1/13 ... . Why does that work?
Here's a word memory for Pi: How I wish I could calculate Pi 3.......1...4....1...5..........9...........2 (courtesy NYTimes crosswords)
Pi is irrational only in the 'mathematical' meaning of that word. But it is still a bit, um, unsettling. It means that while you can, theoretically, exactly measure the length of a straight line segment, you cannot, theoretically, exactly measure the length of a Circle's circumference. If you could, pi would be a rational number. This is not your (or anyone's ) fault, it is just something hanging out there. By extension, I take it to further indicate that the length of any curved line segment cannot be exactly measured. Perhaps one of you wizards could discuss that. While we're at it, all this stuff about pi is true in the classical 3D, x.y.z that we mentally inhabit. I don't know if it is also true in other geometries. I only know that there are a bunch of geometries. I still think that Euler's number e (little e, not E=Energy) deserves a day just as much. It inhabits a vast variety of formulae, perhaps even more than pi does. A shootout seems appropriate. More of a thing for IO9 than PC?
BobW gave us the first 9 digits. Some folks may present many more, hoping you'll be impressed. So how many digits should we commit to memory, given that there are many other things to memorize (song lyrics, etc.). Here is an objective test. If pi is 3 for you, then your error* is about 45,000 parts per million. If that works for you, who am I to say otherwise? Step it up. A common approximation is 22/7, for that you need to remember 3 digits (and where to put the / ). Here the error would be about 400 parts per million. To compare, this error is smaller than remembering 3.14 (about 500 ppm) but 3.141 comes in below 200 ppm. That next "1" pays off. In many fields, 1 ppm error might be seem as adequate. You can get under that using pi = 3.14159. I would not ask anyone to remember more digits than that, unless they have a particular personal reason, and a computer or pocket calculator is somehow not at hand. If you need to work at error levels below 1 ppm, then you really ought to be using calculating machinery of some sort. It that case it is not your problem to remember digits. Only a select, aged few here will remember slide rules with CF DF scales and the like. If there were one at hand, I would assess their accuracy. If somebody here has one, you're at bat. *Author presumes that anyone reading this entire post will know how to set up a spreadsheet to calculate these things. Ye Olde Excel coughs up the first 15 digits of pi. Just learn the first 6, says I, and use your remaining neurons in other ways.
