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- Hi, I'm Ron Hipschman, and I'm your host for this portion of our PI Day celebrations. I'm gonna talk a little bit about the number PI, then how to calculate lots of digits of PI, some of the history of PI and how to memorize a good number of digits. So let's get back to our slides here. This is the 34th annual PI Day. It also is coincidentally Einstein's birthday. So happy birthday, Albert. PI Day was founded and invented by Larry Shaw in 1988 at the Exploratorium. And this day is a tribute to him and his life. PI Day has a really nice Wikipedia page. There, you can see our Prince of PI, Larry Shaw. Larry built and placed the original PI shrine on the mezzanine of the Exploratorium back when we were at the Palace of Fine Arts. He placed it in the middle of the round classroom that was made of round cinder blocks, a very appropriate place I think you'll agree. When we moved to pure 15, we dedicated a new PI shrine. It's on the public plaza in front of the museum on the Embarcadero. Be sure to visit it and walk around it 3.14 times in celebration. We celebrate PI Day on March 14th at 1:59. Reduced to its numbers, that would be 3-14 at 1:59. Remove all those extraneous symbols and you get the value of PI, 3.14159. Sometimes we celebrate 2PI Day on June 28th at 3:18 or 6-28 at 3:18. Two times PI is 6.28318. When we're feeling really silly, we celebrate 3PI Day. Three times PI is 9.424778, which would occur on 9-42 or September 42nd, or well, obviously there's no September 42nd so it would really be on October 12th if you carry those extra days from September into October. In Europe, they write the date as day slash month. So they're limited to celebrating PI approximation day on July 22nd or 22/7. You may remember that 22 divided by seven is a good approximation of PI and indeed it is. It's 3.14285, that's good to four hundredths of a percent. One of the most common places where PI shows up is in the famous formula for calculating the circumference of a circle if you know the diameter. The circumference, how far around, is equal to PI times the diameter, how far across, or in shorthand C equals PI times D. By moving things around algebraically, we can see that PI is the ratio of the circumference to the diameter and this is true for every circle no matter its size. For instance, if we start with this lovely cheese pizza and some pepperoni, you'll notice that in this case, seven pepperoni fit across the pizza. Well, if it's seven pepperoni across, you'd also notice that it's 22 pepperoni around. The ratio of the circumference to the diameter here is 22 pepperoni around to seven pepperoni across. Remember that 22/7 is a good approximation for PI. Well, here you see it. And again, it's the same for all circles. PI is irrational. This means a few things. First, it cannot be written as the ratio of two integers like our PI approximation 22/7, that's a ratio of two integers. Next, it has an infinite number of digits. Our approximation, 22/7, does have an infinite number of digits, but it fails a third test that it does not settle into an infinitely repeating pattern of digits. Here, you can see the repeating pattern of our approximation. PI never repeats. You may have heard that PI is also a transcendental number. This is a bit more complicated to explain. So briefly, a transcendental number cannot be calculated with any finite series of algebraic operations. Every transcendental number is also irrational. Well, let's just move on. PI has a long and storied history. Let's take a look at some selected bits. In Egypt around 2,600 BCE, a long time ago, they used our 22/7 approximation of PI and that got them quite far. 700 years later in Babylonia, around 1900 BCE, they were using 25/8 as a reasonable approximation, only a half percent too small. 1300 years later, at the time the Bible was written around 600 BCE, we find a value of PI in the text of Kings chapter seven. And he, Hiram, made a molten sea, 10 cubits, from one rim to the other, it was round all about and a line of 30 cubits did compass it round about and it was a hand breadth thick. 10 cubits diameter, 30 cubits around. That gives us a value of PI equal to three. We're losing some accuracy here, but we're still within about 5%. Archimedes came up with a brilliant geometrical method to calculate PI about 400 years later. He used polygons. He could accurately calculate the area of any polygon because you can break it up into triangles and it's easy to calculate the area of a triangle. Now, Archimedes drew a circle so that it just fits inside this polygon and another similar polygon that just fits inside the circle. Archimedes understood that the area of a circle falls somewhere in between the areas of the bigger and smaller polygons. Remember, the area of a circle is PI times the radius squared. If he could figure out the area, he could figure out the value of PI. Archimedes also determined that the more sides the polygon has, the closer the areas of the two polygons approach the area of the circle. With many, many sides, you can narrow down the value of PI. Archimedes used a 96-sided polygon and calculated the value of PI to be between 3.141 and 3.143, not bad. Moving to China. Zhang Heng in 130 AD calculated that PI was the square root of 10. That's good to a 10th of a percent. He got a postage stamp eventually for his efforts. In India, Madahava of Sangamagrama in 1400 AD calculated PI to 11 digits. Now we're getting some real accuracy. In Persia, present day Iran, Jamshid al-Kashi in 1424 calculated PI to 16 digits. He also got a postage stamp eventually for his efforts. Ludolf van Ceulen, a German-Dutch mathematician, spent most of his life calculating PI to 35 digits using essentially the same method as Archimedes except Ludolf didn't stop with a 96-sided polygon. His had two to the 62 sides or 4.6 quintillion sides. Incidentally, 35 digits of PI is way more than enough to calculate anything anyone can possibly use. More on that later. After his death, the little theme number or PI was engraved on his tombstone in Leiden. The tombstone was unfortunately lost, but later restored in the year 2000. That's what you see here. The first to use the Greek letter PI as a symbol for the number was William Jones in 1706. He took the first letter from the Greek word perimetros meaning perimeter. John Von Neumann in 1949 found 2037 digits with a calculation that took 70 hours of computer time on the new ENIAC computer. The ENIAC or Electronic Numerical Integrator and Computer was the first programmable electronic general purpose digital computer. In 1958, Francois Genuys calculated PI to 10,000 digits in 1.7 hours on an IBM 704 computer, which brings us to the modern era. In the modern era, one million digits were first calculated in 1973. One billion digits in 1989, 1.2 trillion digits in 2002, 2.7 trillion in 2009, 13 trillion in 2014 and 22 trillion in 2016, but we're not done. On PI Day 2019, Emma Haruka Iwao and the PI calculating team at Google used the Google compute engine consisting of 25 Google cloud virtual machines, 170 terabytes of disk storage space, 10 petabytes worth of data reads and 121 days of calculation to compute PI to 31.4 trillion digits, note the significance, 31.4. Lastly, on January 29th, 2020, Timothy Mullican on a computer he built himself calculated PI to 50 trillion digits. His calculation took 303 days at a cost of about $10,000, which was only 5% of Google's $200,000 cost of calculation. Here's Timothy Mulligan's home computer. Maybe a bit more extensive than most of us have at home. Here's a plot of the number of digits calculated through time. Note that the vertical scale is logarithmic, meaning for each vertical square, you multiply the digits by 100. Up until about 1950, the growth of calculated digits grew rather slowly because all that work had to be done by hand. After 1950, the digital computer sped things up tremendously. Well, how much accuracy do we really need? Voyager One is the farthest human made object from Earth and the first spacecraft to reach interstellar space. It's about 14.1 billion miles away moving over 38,000 miles per hour. NASA uses 15 digits of PI to calculate spacecraft positions. 15 digits gives us an accuracy of plus or minus 1.5 inches in Voyager's position. Remember that Jamshid al-Kashi calculated PI to 17 digits in 1424. Here's another example, take the entire universe. We have a pretty good figure for the diameter of the known universe. Let's say that we wanted to calculate the circumference of the universe to an accuracy of plus or minus the diameter of a hydrogen atom. The hydrogen atom is really, really small. A 10000th of a millionth of a meter, a 10th of a nanometer. How many digits of PI would we need to get this accuracy? Using our now familiar formula, we'd need only 39 digits of PI. PI Day has found its way into popular culture. It was first declared national PI Day by an act of Congress in 2009, let's take a listen.

- Council resolution 224, resolution supporting the designation of PI Day and for other purposes.

- On this vote, the yeas are 391, the nays 10. Two thirds being in the affirmative, the rules are suspended, the resolution is agreed to.

- [Ron] Who would vote no on national PI Day? Here, you see the 10 who voted no. Well, this demonstrates that there was political divide back in 2009 as well. By the way, none of those no voters including Mike Pence hold office any longer. That's what you get for voting against PI. Aside from PI Day, PI has found its way into popular culture in Hollywood too. In this episode of Star Trek, an alien has invaded the computer of the enterprise. Spock has a way to keep it busy.

- Ready?

- Implement. Computer, this is a class A compulsory directive. Compute to the last digit the value of PI. As we know, the value of PI is a transcendental figure without resolution. The computer banks will work on this problem to the exclusion of all else until we order it to stop.

- Yes, that should keep that thing busy for awhile.

- [Ron] There was also a rather disturbing movie called PI. A popular activity involving PI is seeing how many digits one can memorize. The current record holder is Rajij Meena who recited 70,000 digits. Nine years before that in 2006, Akira Haraguchi, a retired Japanese engineer, claimed to have recited 100,000 decimal places, but the claim was not verified by the Guinness Book of World Records. What tricks can you use to remember PI? A useful trick called piphilology or pilish is to make up a piece of text where the number of letters in each word help you remember the digits of PI. Here's a sentence that will help you remember PI to a NASA accuracy of 15 digits. Notice the number of characters in each word. How I need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics. This is a form of what's called constrained writing. Mike Keith is a friend of the Exploratorium and a master of constrained writing. He paraphrased Edgar Allen Poe's the Raven to use the first 740 digits of PI. This is also called a piem, but this was just the beginning. Here's Mike Keith in front of his computer with the first 1,000 digits of PI on the screen. Mike also wrote an entire book, Not A Wake, three, one, four, where the words use the first 10,000 digits of PI in all kinds of writing styles. You can get this book online if you want your own copy. Of course, stealing the form of haiku, a pi-ku, has the familiar 5-7-5 syllable form, but it's all about PI. Here is Paul Doherty's entry. A circumference divide by diameter, irrational PI. Here's one from Robert Foss. PI Day's my birthday, can I get free admission? Spent my cash on rent. And one last one from our own Ken Finn. Best pizza value can be found with this number, make mine with mushrooms. And of course, there are limericks. If inside a circle a line hits the center and goes spine to spine and the line's length is D, the circumference will be D times 3.14159. Now you too will be seeing PI everywhere like these M&M's I found. Those aren't complete M's, they're obviously PI's. From the entire staff of the Exploratorium including our executive director, Chris Flink, we'd like to wish you all a happy PI Day.