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| The Pi Day 2010 Google Doodle Image Credit: Google |
Today is the most accurate Pi Day we will have in this century. 3/14/15 and Google chooses to ignore the day. Some people's children! As such, in honor of the day I dragged out the Doodle from 2010 which as far as I know was no great shakes of a day for Pi, so why a Doodle in 2010 but not in 2015 when it is really cool. But what is really cool today is that if you measure time with a 12 hour clock (verses 24 hour clock), you will have two very accurate Pi moments, seconds actually:
3/14/15 9:26:53 AM & PM
It doesn't work with a 24 hour clock because technically the morning is 3 14 15 09 26 53 and the evening would be 3 14 15 21 26 53. Of course we are also dropping the 20 in 2015. We feel justified in do so, simply because we are alive right now and we want to celebrate the day and to hell the inconvenient 2000 years that throws the number out of whack. This alludes to the fact that while we may take pride that we are witness to a once a century event, we should mourn that we missed the really big Pi Day which would have been
March 14, 1592 with Pi seconds at 6:53:58.
That one was pretty big. The next time you will be able to do that is March 14, 15926 (13,911 years from now, alas). But take heart that Pi Day will only have Pi minutes, not Pi seconds:
3/14/15926 5:35
The next digit is 8. The biggest second you can have is 59 (60 if you cheat). So looking at the string of numbers we will not be able to have another Pi second (with a full year like what happened in 1592) until:
March 14, 1,592,653,589,793 2:38:46
That is a whopping 1.59 trillion years into the future. My guess is no one will be around to notice. Anyhow can you see what I mean about mourning the loss of 1592? It was a great year for Pi. I wonder did anyone notice?
EDIT 3/15/15: Taking a second look at this I just realized that there is a slight flaw in my logic. I am accepting single digit hours, but not minutes or seconds. But doing an image search of digital watches, I find that unless in 24 hour format, most watches display h:mm:ss for single digit hours and hh:mm:ss for 10 thru 12. None display single digit minutes or seconds. The single digit minutes and seconds are always preceded by a zero. So going by standard time format my claim still holds true.
EDIT 3/20/15, ERROR CORRECTION On the date 1.59 trillion date, incredibly I somehow missed a digit in the original post and had a date 159 billion years in the future. How exactly I did that when I copied an pasted the number is beyond me. In any event the date has been corrected. It was only 1.433 trillion year error.
Another thing that should be noted is that once you can get the digits of Pi to line up to a second in the 12 hour digital clock format _h:mm:ss format, then the remainder of your Pi moment is simply a decimal fraction that theoretically will go out to an infinite number of digits. So to tell exactly what time our Pi moment occurred we would need a clock with an infinite number of digits. However, in a practical sense, our universe has a limit on how short you can slice time. It is known as Planck Time and represents the time it takes light in a vacuum to travel one Planck length. In some circles it is known as a jiffy. 1 jiffy = 1 Planck Time = 5.39 X 10^-44 second. Hence any digits finer than a jiffy are meaningless. Think of a jiffy being the fastest tick in time allowed in our universe. So our moment has to be a bit slower or it is literally out of this world. So our real Pi moment has to be at least equal to or a bazzilionth of a second longer than longer than 1 plank time. To put that in context, think of having a stop watch that could measure microseconds (millionths of a second). So you could see an event, start the watch, see a second event and stop the watch. So theoretically you could tell how many microseconds the event lasted. The only problem is that the response time of your nervous system probably limits the accuracy to hundreds of a second. So if your event took 0.215,435 seconds, all you can say is that it took about .21 seconds. The 5,435 microseconds would be meaningless accuracy.
EDIT 3/15/15: Taking a second look at this I just realized that there is a slight flaw in my logic. I am accepting single digit hours, but not minutes or seconds. But doing an image search of digital watches, I find that unless in 24 hour format, most watches display h:mm:ss for single digit hours and hh:mm:ss for 10 thru 12. None display single digit minutes or seconds. The single digit minutes and seconds are always preceded by a zero. So going by standard time format my claim still holds true.
EDIT 3/20/15, ERROR CORRECTION On the date 1.59 trillion date, incredibly I somehow missed a digit in the original post and had a date 159 billion years in the future. How exactly I did that when I copied an pasted the number is beyond me. In any event the date has been corrected. It was only 1.433 trillion year error.
Another thing that should be noted is that once you can get the digits of Pi to line up to a second in the 12 hour digital clock format _h:mm:ss format, then the remainder of your Pi moment is simply a decimal fraction that theoretically will go out to an infinite number of digits. So to tell exactly what time our Pi moment occurred we would need a clock with an infinite number of digits. However, in a practical sense, our universe has a limit on how short you can slice time. It is known as Planck Time and represents the time it takes light in a vacuum to travel one Planck length. In some circles it is known as a jiffy. 1 jiffy = 1 Planck Time = 5.39 X 10^-44 second. Hence any digits finer than a jiffy are meaningless. Think of a jiffy being the fastest tick in time allowed in our universe. So our moment has to be a bit slower or it is literally out of this world. So our real Pi moment has to be at least equal to or a bazzilionth of a second longer than longer than 1 plank time. To put that in context, think of having a stop watch that could measure microseconds (millionths of a second). So you could see an event, start the watch, see a second event and stop the watch. So theoretically you could tell how many microseconds the event lasted. The only problem is that the response time of your nervous system probably limits the accuracy to hundreds of a second. So if your event took 0.215,435 seconds, all you can say is that it took about .21 seconds. The 5,435 microseconds would be meaningless accuracy.
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| Image Credit: Wikipedia "Pi pie2" by GJ - Pi_pie2.jpg. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/ File:Pi_pie2.jpg#/media/File:Pi_pie2.jpg |
So what exactly is Pi? It is the ratio of the circumference of a circle to its diameter which always works out to 3.14159.... So roll a toy wheel, 1 inch in diameter, exactly one revolution and the center of that wheel would move 3.14159... inches across the floor. Roll any wheel of any size and it will always roll 3.14159 times the length of the diameter. There is a cute animated graphic of this at Wikipedia. To me, being somewhat of a mathematical nit wit, that seems very odd. But the circumference of any circle is always Pi times the diameter. Very convenient but also very odd.
Pi has another very odd property. You can never quite calculate the exact value of Pi. It is irrational and the decimal value goes forever in a non-repeating sequence.
In my working life, I used Pi probably twice a day in some calculation or other on a slow day. Round things seem to be favored in the industry in which I worked. Here is a trick that I used quite often. I was responsible for a bunch of facilities with miles of pipe. Repairs or modifications required ordering new pipe. Measuring pipe diameters of installed pipe is a bit tricky. If it is small diameter you can use calipers, but as the diameter increases soon the jaws of the caliper no longer reach the sides of the pipe. You can eyeball it but there is a much simple way. Use a flexible tape or just a piece of string to measure the circumference of the pipe and then divide the length by Pi. Voila! Pipe size? Not quite! Pipe sizes in North America below 14 inch pipe are weird. You must consult a nominal pipe size table such as this:
http://en.wikipedia.org/wiki/Nominal_Pipe_Size
For example you measure a pipe and the circumference is, what a coincidence, 3.14 inches. You do the math and that yields a diameter of about 1 inch. Common sense would dictate you have 1 inch pipe. Wrong! Looking at the table at the above site yields that the nominal pipe size of 3/4 inch has an actual outer diameter of 1.05 inches. One inch nominal pipe is actually 1.32 inches in diameter.
All you ever wanted to know about pipe but were afraid to ask.
Have a Happy Pi Day and a Pi moment this evening.
LINKS:
http://en.wikipedia.org/wiki/Pi
http://en.wikipedia.org/wiki/Pi_Day
EDIT 3/20/15: The Internet never fails to delight. Have you ever wondered what is the one millionth digit of Pi after the decimal point? Burning question I know. Well now you can find out at:
ONE MILLION DIGITS OF PI at Pi Day.Org
After holding the page down button for several minutes, I watched 999,999 digits go whizzing by and as a public service, the answer to the question (in case you are ever on Jeopardy), the millionth digit after the decimal point in Pi?
What is 1 Alec.
Here are the first and last lines of Pi taken out to one million decimal places:
3.14159265358979323846264338327950288419716939937510582... lots and lots of digits...
EDIT 3/20/15: The Internet never fails to delight. Have you ever wondered what is the one millionth digit of Pi after the decimal point? Burning question I know. Well now you can find out at:
ONE MILLION DIGITS OF PI at Pi Day.Org
After holding the page down button for several minutes, I watched 999,999 digits go whizzing by and as a public service, the answer to the question (in case you are ever on Jeopardy), the millionth digit after the decimal point in Pi?
What is 1 Alec.
Here are the first and last lines of Pi taken out to one million decimal places:
3.14159265358979323846264338327950288419716939937510582... lots and lots of digits...
346460422090106105779458151 ...and that’s one million digits of Pi after the decimal point!
According to Wikipedia, as of October 2014 Pi has been calculated out to 13,300,000,000,000 decimal places.
i will pass all tis information along to my nephew who is a pipe fitting apprentice.
ReplyDeleteHe probably knows it already, although the circumference measurement I figured out on my own, but I hardly think that it is a rarity.
DeleteI had Pie on Pi Day, does that count in your mathematical world? It was actually quite delicious pecan pie and I didn't have to measure it or ponder it's implications in our world and the way it was created but I still enjoyed it.
ReplyDeleteI do agree with you that it was very non cool that Google didn't doodle this very important Pi Day!
Alicia,
DeleteIn order for me to provide a mathematical validation of your Pi Day celebration of eating pie, I would have to know something about the geometry of the pie that you ate. It is actually quite complex. First your pie must be circular (verses a Mc Donald's or a Hostess pie which are non circular). Looking at only one plane, let's say the upper crust and assume that it is a dimensionless upper crust in depth...a 2 D upper crust, unless you ate the entire upper crust you did not consume PI. Pi is defined as the ratio of the circumference to the diameter. To consume Pi on pie day you have to eat an entire circle. Now you could potentially cheat, for caloric concerns and simply take a series of bites around the circumference of the pie. You may be tempted to believe that you consumed Pi but you did not consume the diameter...ergo you did not consume Pi.
Now I know something about you. 1) You are very social. 2) You are very kind. 3) You watch the carbs. Pie is loaded with carbs, you undoubtedly were with someone, and you would share you pie. Ergo I would be willing to bet three dollars and 14 cents that while you may have consumed some pecan pie, I doubt that you consumed a pecan Pi. So no, most likely you did not have pecan Pi on Pi day even though you did have pecan pie.
Too long, continued below.
Continued from above.
DeleteOther philosophical problems of claiming to eat Pi on Pi day with a wedge shaped piece of pie is that unless your wedge was 1/2 the circle, you did not eat diameter. However this is somewhat ameliorated by the notion that a wedge does have 2 radii. And of course 2r = d. Yet there is something unsatisfying in the consumption of 2 radii when you really want to eat a diameter.
But now let's assume that you made a small 3 or 4 inch personal pie. You consumed the entire thing. Now we must further assume that you made at least two pies because you would want to share. You must consume the entire pie or at least one horizontally cut slices resulting in a circular plane. So if you did eat the entire pie, how many Pi (s) did you eat? One? Well you have the top and bottom crusts, so wouldn't that be 2, but then each crust has a upper and lower surface so we are up to 4. Yet the depth of the pie is bounded by a circle, so thats at least 5 but if your pie pan has slanted sides so that the bottom of the pie is smaller than the top then you see that because a plane has no thickness, your pie is actually an infinite stack of horizontally cut slices, each with a slightly larger diameter and circumference than its predecessor below. So theoretically you consumed an infinite number of Pi (think of the calories). Which begs the question how could one eat an infinite number of Pi (s) in finite time? Ah but there is a solution to that dilemma in a practical sense, in our universe dimensions can only go as small as Planks length. Ergo one can argue that you are not consuming an infinite number of Pi but rather a sum equal to the depth of the pie / Plank's length. Which would still be a pretty big number because Planks length is very small but none the less finite.
So it would seem that the only way to celebrate Pi day is a small pie and consume it entirely yourself. Yet you are consuming it it bites. Ergo you have not consumed Pi.
I was going to suggest a Ritz cracker but they have a serrated edge, not truly a circle, plus a whole Ritz is a bit of mouthful. The solution?
Communion wafers. They have a smooth edge, very thin approaching a plane and indeed you can buy them at religious stores. You need not concern yourself with sacrilege for until they have undergone transubstantiation by a priest, they are merely unleavened bread. They can easily be consumed in one bite. You will have then consumed Pi.
But then I know something else about you. You are very practical and common sense rules your decisions. I can just hear you saying, I am not running out to buy communion wafers to satisfy Sextant's bullshit Pi requirements. As such and especially after reading this reply, I would recommend an aspirin tablet, perhaps two of them. Just make sure they are round tablets and not capsules.
Thanks for stopping by and commenting, Alicia.
I knew it. You are way more intelligent than most of us. My brain is still reeling.... I see you have slacked off in number of annual posts. I recommend throwing out a few casual posts more often just to keep in touch.
DeleteNo I think I am just weird, not intelligent. Who cares about fitting an arcane ratio into a date format.
DeleteAlas I have never been predisposed to casual posts. It seems I have to have something weird to report. The result of a very mundane life.
Thanks for visiting and you kind comment, Fiftyodd.