3.14 Essential Reads About π for Pi Day
By Jeff Inglis
On March 14, or 3/14, mathematicians and other obscure-holiday aficionados celebrate Pi Day, honoring π, the Greek symbol representing an irrational number that begins with 3.14. Pi, as schoolteachers everywhere repeat, represents the ratio of a circle's circumference to its diameter.
What is Pi Day, and what, really, do we know about π anyway? Here are three-and-bit-more articles to round out your Pi Day festivities.
A Silly Holiday
First off, a reflection on this "holiday" construct. Pi itself is very important, writes mathematics professor Daniel Ullman of George Washington University, but celebrating it is absurd:
The Gregorian calendar, the decimal system, the Greek alphabet, and pies are relatively modern, human-made inventions, chosen arbitrarily among many equivalent choices. Of course a mood-boosting piece of lemon meringue could be just what many math lovers need in the middle of March at the end of a long winter. But there's an element of absurdity to celebrating π by noting its connections with these ephemera, which have themselves no connection to π at all, just as absurd as it would be to celebrate Earth Day by eating foods that start with the letter "E."
And yet, here we are, looking at the calendar and getting goofily giddy about the sequence of numbers it shows us.
There's Never Enough
In fact, as Jon Borwein of the University of Newcastle and David H. Bailey of the University of California, Davis, document, π is having a sustained cultural moment, popping up in literature, film and song:
Sometimes the attention given to pi is annoying. On 14 August 2012, the U.S. Census Office announced the population of the country had passed exactly 314,159,265. Such precision was, of course, completely unwarranted. But sometimes the attention is breathtakingly pleasurable.
Come to think of it, pi can indeed be a source of great pleasure. Apple's always comforting, and cherry packs a tart pop. Chocolate cream, though, might just be where it's at.
Strange Connections
Of course π appears in all kinds of places that relate to circles. But it crops up in other places, too – often where circles are hiding in plain sight. Lorenzo Sadun, a professor of mathematics at the University of Texas at Austin, explores surprising appearances:
Pi also crops up in probability. The function f(x)=e -x², where e=2.71828… is Euler's number, describes the most common probability distribution seen in the real world, governing everything from SAT scores to locations of darts thrown at a target. The area under this curve is exactly the square root of π.
It's enough to make your head spin.
Historical Pi
If you want to engage with π more directly, follow the lead of Georgia State University mathematician Xiaojing Ye, whose guide starts thousands of years ago:
The earliest written approximations of pi are 3.125 in Babylon (1900-1600 B.C.) and 3.1605 in ancient Egypt (1650 B.C.). Both approximations start with 3.1 – pretty close to the actual value, but still relatively far off.
By the end of his article, you'll find a method to calculate π for yourself. You can even try it at home!
An Irrational Bonus
And because π is irrational, we'll irrationally give you even one more, from education professor Gareth Ffowc Roberts at Bangor University in Wales, who highlights the very humble beginnings of the symbol π:
After attending a charity school, William Jones of the parish of Llanfihangel Tre'r Beirdd landed a job as a merchant's accountant and then as a maths teacher on a warship, before publishing A New Compendium of the Whole Art of Navigation, his first book in 1702 on the mathematics of navigation. On his return to Britain he began to teach maths in London, possibly starting by holding classes in coffee shops for a small fee.
Shortly afterward he published "Synopsis palmariorum matheseos," a summary of the current state of the art developments in mathematics which reflected his own particular interests. In it is the first recorded use of the symbol π as the number that gives the ratio of a circle's circumference to its diameter.
What made him realize that this ratio needed a symbol to represent a numeric value? And why did he choose π? It's all Greek to us.
The New Raspberry Pi Zero W Is Your Key to the Hackable Future
EBEN UPTON DIDN’T plan on becoming a computer engineer. It happened out of necessity. The 38-year-old inventor of Raspberry Pi—the credit card-sized computer that costs less than a movie ticket—recalls a day from childhood when he tried to print a homework assignment. The words came out in a jumble, forcing him to learn how tweak the switches on the printer’s circuit board to make the text fill the page. “It was just in accomplishing trivial tasks that we were having to acquire skills,” he says of the experience.
Raspberry Pi offers far more accessibility than the TRS-80, Commodore 64, and early Apple and PC machines his generation worked with. But he hopes the bare bones computer he developed five years ago encourages a younger generation to discover how computers, smartphones and connected devices actually work.
It helps that anyone can program one. If you can follow one of the many online coding tutorials, you can have it performing simple tasks out of the box. You’ll find the Raspberry Pi in industrial machines and hobbyist projects alike. Schools use them in computer science classes. Do-it-yourselfers around the world have installed the diminutive computer in all manner of gadgets that do all manner of things.
The new low-power, low-cost Raspberry Pi Zero W updates the previous Zero computer board released a little more than a year ago. The “W” stands for wireless, because this Pi features built-in Bluetooth and Wi-Fi capabilities. The $10 price reflects Upton’s business model (No VCs or shareholders to answer to!) and guiding principle: there’s value in knowing how things work. As everything grows ever more computerized, he says, the need to understand what lies beneath the software grows more pressing.
“It’s very dangerous to have a world in which people are completely divorced of technical underpinnings of the things around them,” he says. “It’s unsatisfying on an intellectual level that everything should just be like, ‘A wizard did it.'”
Cheap Is the Thing
The Raspberry Pi, like the Arduino, provides an affordable and accessible entry to coding. It also offers innovators, inventors, and entrepreneurs the computing power for a growing number of connected devices. The bargain-basement price opens the internet of things to anyone with an idea and some basic coding skill.
Upton developed the Raspberry Pi five years ago as a teaching tool for undergraduate students in his computer science program at Cambridge University. He soon realized the little circuit board could be so much more. “We slotted into an empty market segment,” he says. “We made the Raspberry Pi and people were like, ‘Hey, that’s the thing I couldn’t describe but always wanted!'”
The computer cost just $25, yet offered surprisingly robust computing power. Tinkerers loved it, because it allowed them to experiment with hacking household devices and drew all kinds of people into developing hardware. “It turns into a disposable thing,” says Will Hart, general manager at the connected device platform Particle. “If you fry it, it’s like, ‘Whatever.'”
Scott Kildall found Linux, the Pi’s operating system, intimidating when started his residency at Autodesk’s Pier 9 workshop in 2014. But he saw tremendous potential for his conceptual art, and so learned the ins and outs of the OS and started exploring the platform. Kildall, now the shop lead for the Pier 9 electronics lab, started posting his Raspberry Pi projects on Instructables.com, the online home for a wide swath of the maker movement. Three years later, the site teems with Raspberry Pi-powered creations.
Granted, you won’t see any of Kildall’s whimsical projects become the next big thing in IoT—his SelfiesBot is a portable robot outfitted with a 2-foot gooseneck arm that takes and posts selfies to Twitter. But the fact that non-scalable absurdist art can be equipped with computational capacities demonstrates the unexpected reach of Upton’s creation.
Upton says tens of thousands of Raspberry Pis have just “disappeared” into products. The computer has become so ubiquitous that companies don’t tout the fact their products use the little computers. But the Raspberry Pi’s larger impact lies with the smaller-scale market. The computer designed to be an educational tool has brought the internet of things era to the masses. Anyone with the money to buy a burrito can bring a product to life.
Did you solve it? Pi Day puzzles that will leave you pie-eyed
Earlier today I set you two puzzles as a pre-party for Pi Day.
1) Pictured below are three identical boxes packed with pies. You can assume that all pies are exactly the same height. Which box contains the most pie?
Solution
A, B and C contain equal amounts of pie.
The tastiest solution is to consider box B as a square box made from four smaller square boxes, and box C as a square box made from 16 smaller square boxes. Pie fills the same percentage of each box, whatever the size of the box. So pie must fill the same percentage of A, B and C. In other words, the amount of pie is the same in each box.
But if you wanted to overcomplicate things, you can also solve with pi. As you remember from school, the area of a circle is pi x (radius)2, or πr2. Let the radius of the smallest pies (in C) be r, which means the radius of the medium pies (in B) is 2r and the radius of the big pi is 4r. Then the area of pie in A is π (4r)2 = 16r2, the area of pie in B is 4 x π (2r)2 = 16r2, and the area of pie in C is 16π (r)2 = 16r2. All the same!
How well did we do? Here are the results, with the results in parentheses of those who attempted the problem on teroes.com . Congrats Guardianistas, you smashed it!
A has the most pie: 23 per cent (21 per cent)
B has the most pie: 2 per cent (3 per cent)
C has the most pie: 10 per cent (18 per cent)
A, B and C have equal amounts: 65 per cent (58 per cent)
2) One hundred computers are connected in a 10x10 network grid, as below. At the start exactly nine of them are infected with a virus. The virus spreads like this: if any computer is directly connected to at least 2 infected neighbours, it will also become infected.
Will the virus infect all 100 computers?
The image shows a possible example of the initial infection. You can try to fill it in to see if ultimately the network will consist of 100 orange dots. But the question is not asking what happens to this example. I want to know what will happen given any initial configuration of infected computers.
Solution
No, the virus will not infect all 100 computers.
The solution is simple to understand, although you would have needed some impressive insight to get there on your own.
They key here is the perimeter of the infection. By perimeter, I mean the length of the boundary of the infection. For the infection to infect all computers, then the final boundary must be 40, since the perimeter of an infected 10x10 square is 10 + 10 + 10 + 10 = 40
Note that the infection can be a single area, or it can be made up of many separate areas. If it is many separate areas, we need to combine the perimeters of all the infected areas.
The perimeter of a single infected computer is 4, as below. So the perimeter of nine infected computers will be maximum 36, which is 4 x 9. (This is the case when no infected computers are adjacent, as in the image above. But the perimeter may be much lower. For example, if the infected computers are all on the same row, the boundary will only be 9 + 9 + 1 + 1 = 20)
The beautiful part of this problem is the fact that the perimeter of the infection never increases as the infection grows. Consider what happens when an uninfected computer is infected by two computers. Two of its sides are absorbed into the infected area, and the other two become part of the perimeter of the infected area. The perimeter loses 2 and gains 2, a net change of 0. We can see this in the mini-grid below. In A, the infected area has a perimeter 8. In B, a new computer is infected, yet the perimeter of the infected area remains 8. Likewise in C, another computer is infected, and the perimeter remains 8.
If an uninfected computer is infected by three computers, three sides are absorbed into the infection, and its fourth side becomes part of the perimeter, a net loss to the perimeter of 2. And if an unifected computer is infected by four computers, the net loss to the perimeter is 4.
So, if the perimeter of nine infected computers is at most 36, and it can never increase, then it can never reach 40, which means the infection cannot spread to all computers. Solved!
You did well on this one two. Here are the results, with Brilliant.org’s results in parentheses again. Top of the class!
Yes, always: 21 per cent (16 per cent)
Depends on the starting position: 30 per cent (44 per cent)
Never: 49 per cent (40 per cent)
The other question was how this puzzle relates to pi. The connection is not obvious, and it is not even mathematical. The Greek letter pi was chosen as the symbol for the circle ratio because it is an abbreviation of periphery, which is basically the same as perimeter. If you were thinking peripherally, about peripheries, you may have got it. (Here’s a great story about the man who invented pi).
I hope you had fun, and see you again in two weeks. Pi Pie!
On March 14, or 3/14, mathematicians and other obscure-holiday aficionados celebrate Pi Day, honoring π, the Greek symbol representing an irrational number that begins with 3.14. Pi, as schoolteachers everywhere repeat, represents the ratio of a circle's circumference to its diameter.
What is Pi Day, and what, really, do we know about π anyway? Here are three-and-bit-more articles to round out your Pi Day festivities.
A Silly Holiday
First off, a reflection on this "holiday" construct. Pi itself is very important, writes mathematics professor Daniel Ullman of George Washington University, but celebrating it is absurd:
The Gregorian calendar, the decimal system, the Greek alphabet, and pies are relatively modern, human-made inventions, chosen arbitrarily among many equivalent choices. Of course a mood-boosting piece of lemon meringue could be just what many math lovers need in the middle of March at the end of a long winter. But there's an element of absurdity to celebrating π by noting its connections with these ephemera, which have themselves no connection to π at all, just as absurd as it would be to celebrate Earth Day by eating foods that start with the letter "E."
And yet, here we are, looking at the calendar and getting goofily giddy about the sequence of numbers it shows us.
There's Never Enough
In fact, as Jon Borwein of the University of Newcastle and David H. Bailey of the University of California, Davis, document, π is having a sustained cultural moment, popping up in literature, film and song:
Sometimes the attention given to pi is annoying. On 14 August 2012, the U.S. Census Office announced the population of the country had passed exactly 314,159,265. Such precision was, of course, completely unwarranted. But sometimes the attention is breathtakingly pleasurable.
Come to think of it, pi can indeed be a source of great pleasure. Apple's always comforting, and cherry packs a tart pop. Chocolate cream, though, might just be where it's at.
Strange Connections
Of course π appears in all kinds of places that relate to circles. But it crops up in other places, too – often where circles are hiding in plain sight. Lorenzo Sadun, a professor of mathematics at the University of Texas at Austin, explores surprising appearances:
Pi also crops up in probability. The function f(x)=e -x², where e=2.71828… is Euler's number, describes the most common probability distribution seen in the real world, governing everything from SAT scores to locations of darts thrown at a target. The area under this curve is exactly the square root of π.
It's enough to make your head spin.
Historical Pi
If you want to engage with π more directly, follow the lead of Georgia State University mathematician Xiaojing Ye, whose guide starts thousands of years ago:
The earliest written approximations of pi are 3.125 in Babylon (1900-1600 B.C.) and 3.1605 in ancient Egypt (1650 B.C.). Both approximations start with 3.1 – pretty close to the actual value, but still relatively far off.
By the end of his article, you'll find a method to calculate π for yourself. You can even try it at home!
An Irrational Bonus
And because π is irrational, we'll irrationally give you even one more, from education professor Gareth Ffowc Roberts at Bangor University in Wales, who highlights the very humble beginnings of the symbol π:
After attending a charity school, William Jones of the parish of Llanfihangel Tre'r Beirdd landed a job as a merchant's accountant and then as a maths teacher on a warship, before publishing A New Compendium of the Whole Art of Navigation, his first book in 1702 on the mathematics of navigation. On his return to Britain he began to teach maths in London, possibly starting by holding classes in coffee shops for a small fee.
Shortly afterward he published "Synopsis palmariorum matheseos," a summary of the current state of the art developments in mathematics which reflected his own particular interests. In it is the first recorded use of the symbol π as the number that gives the ratio of a circle's circumference to its diameter.
What made him realize that this ratio needed a symbol to represent a numeric value? And why did he choose π? It's all Greek to us.
 |
| March 14 is celebrated as Pi Day. (WHITNEY HAYWARD/PORTLAND PRESS HERALD/GETTY IMAGES) |
The New Raspberry Pi Zero W Is Your Key to the Hackable Future
EBEN UPTON DIDN’T plan on becoming a computer engineer. It happened out of necessity. The 38-year-old inventor of Raspberry Pi—the credit card-sized computer that costs less than a movie ticket—recalls a day from childhood when he tried to print a homework assignment. The words came out in a jumble, forcing him to learn how tweak the switches on the printer’s circuit board to make the text fill the page. “It was just in accomplishing trivial tasks that we were having to acquire skills,” he says of the experience.
Raspberry Pi offers far more accessibility than the TRS-80, Commodore 64, and early Apple and PC machines his generation worked with. But he hopes the bare bones computer he developed five years ago encourages a younger generation to discover how computers, smartphones and connected devices actually work.
It helps that anyone can program one. If you can follow one of the many online coding tutorials, you can have it performing simple tasks out of the box. You’ll find the Raspberry Pi in industrial machines and hobbyist projects alike. Schools use them in computer science classes. Do-it-yourselfers around the world have installed the diminutive computer in all manner of gadgets that do all manner of things.
The new low-power, low-cost Raspberry Pi Zero W updates the previous Zero computer board released a little more than a year ago. The “W” stands for wireless, because this Pi features built-in Bluetooth and Wi-Fi capabilities. The $10 price reflects Upton’s business model (No VCs or shareholders to answer to!) and guiding principle: there’s value in knowing how things work. As everything grows ever more computerized, he says, the need to understand what lies beneath the software grows more pressing.
“It’s very dangerous to have a world in which people are completely divorced of technical underpinnings of the things around them,” he says. “It’s unsatisfying on an intellectual level that everything should just be like, ‘A wizard did it.'”
Cheap Is the Thing
The Raspberry Pi, like the Arduino, provides an affordable and accessible entry to coding. It also offers innovators, inventors, and entrepreneurs the computing power for a growing number of connected devices. The bargain-basement price opens the internet of things to anyone with an idea and some basic coding skill.
Upton developed the Raspberry Pi five years ago as a teaching tool for undergraduate students in his computer science program at Cambridge University. He soon realized the little circuit board could be so much more. “We slotted into an empty market segment,” he says. “We made the Raspberry Pi and people were like, ‘Hey, that’s the thing I couldn’t describe but always wanted!'”
The computer cost just $25, yet offered surprisingly robust computing power. Tinkerers loved it, because it allowed them to experiment with hacking household devices and drew all kinds of people into developing hardware. “It turns into a disposable thing,” says Will Hart, general manager at the connected device platform Particle. “If you fry it, it’s like, ‘Whatever.'”
Scott Kildall found Linux, the Pi’s operating system, intimidating when started his residency at Autodesk’s Pier 9 workshop in 2014. But he saw tremendous potential for his conceptual art, and so learned the ins and outs of the OS and started exploring the platform. Kildall, now the shop lead for the Pier 9 electronics lab, started posting his Raspberry Pi projects on Instructables.com, the online home for a wide swath of the maker movement. Three years later, the site teems with Raspberry Pi-powered creations.
Granted, you won’t see any of Kildall’s whimsical projects become the next big thing in IoT—his SelfiesBot is a portable robot outfitted with a 2-foot gooseneck arm that takes and posts selfies to Twitter. But the fact that non-scalable absurdist art can be equipped with computational capacities demonstrates the unexpected reach of Upton’s creation.
Upton says tens of thousands of Raspberry Pis have just “disappeared” into products. The computer has become so ubiquitous that companies don’t tout the fact their products use the little computers. But the Raspberry Pi’s larger impact lies with the smaller-scale market. The computer designed to be an educational tool has brought the internet of things era to the masses. Anyone with the money to buy a burrito can bring a product to life.
Did you solve it? Pi Day puzzles that will leave you pie-eyed
Earlier today I set you two puzzles as a pre-party for Pi Day.
1) Pictured below are three identical boxes packed with pies. You can assume that all pies are exactly the same height. Which box contains the most pie?
 |
| Brilliant |
Solution
A, B and C contain equal amounts of pie.
The tastiest solution is to consider box B as a square box made from four smaller square boxes, and box C as a square box made from 16 smaller square boxes. Pie fills the same percentage of each box, whatever the size of the box. So pie must fill the same percentage of A, B and C. In other words, the amount of pie is the same in each box.
But if you wanted to overcomplicate things, you can also solve with pi. As you remember from school, the area of a circle is pi x (radius)2, or πr2. Let the radius of the smallest pies (in C) be r, which means the radius of the medium pies (in B) is 2r and the radius of the big pi is 4r. Then the area of pie in A is π (4r)2 = 16r2, the area of pie in B is 4 x π (2r)2 = 16r2, and the area of pie in C is 16π (r)2 = 16r2. All the same!
How well did we do? Here are the results, with the results in parentheses of those who attempted the problem on teroes.com . Congrats Guardianistas, you smashed it!
A has the most pie: 23 per cent (21 per cent)
B has the most pie: 2 per cent (3 per cent)
C has the most pie: 10 per cent (18 per cent)
A, B and C have equal amounts: 65 per cent (58 per cent)
2) One hundred computers are connected in a 10x10 network grid, as below. At the start exactly nine of them are infected with a virus. The virus spreads like this: if any computer is directly connected to at least 2 infected neighbours, it will also become infected.
Will the virus infect all 100 computers?
 |
| Brilliant |
The image shows a possible example of the initial infection. You can try to fill it in to see if ultimately the network will consist of 100 orange dots. But the question is not asking what happens to this example. I want to know what will happen given any initial configuration of infected computers.
Solution
No, the virus will not infect all 100 computers.
The solution is simple to understand, although you would have needed some impressive insight to get there on your own.
They key here is the perimeter of the infection. By perimeter, I mean the length of the boundary of the infection. For the infection to infect all computers, then the final boundary must be 40, since the perimeter of an infected 10x10 square is 10 + 10 + 10 + 10 = 40
Note that the infection can be a single area, or it can be made up of many separate areas. If it is many separate areas, we need to combine the perimeters of all the infected areas.
The perimeter of a single infected computer is 4, as below. So the perimeter of nine infected computers will be maximum 36, which is 4 x 9. (This is the case when no infected computers are adjacent, as in the image above. But the perimeter may be much lower. For example, if the infected computers are all on the same row, the boundary will only be 9 + 9 + 1 + 1 = 20)
 |
| Illustration: Alex Bellos |
The beautiful part of this problem is the fact that the perimeter of the infection never increases as the infection grows. Consider what happens when an uninfected computer is infected by two computers. Two of its sides are absorbed into the infected area, and the other two become part of the perimeter of the infected area. The perimeter loses 2 and gains 2, a net change of 0. We can see this in the mini-grid below. In A, the infected area has a perimeter 8. In B, a new computer is infected, yet the perimeter of the infected area remains 8. Likewise in C, another computer is infected, and the perimeter remains 8.
If an uninfected computer is infected by three computers, three sides are absorbed into the infection, and its fourth side becomes part of the perimeter, a net loss to the perimeter of 2. And if an unifected computer is infected by four computers, the net loss to the perimeter is 4.
So, if the perimeter of nine infected computers is at most 36, and it can never increase, then it can never reach 40, which means the infection cannot spread to all computers. Solved!
You did well on this one two. Here are the results, with Brilliant.org’s results in parentheses again. Top of the class!
Yes, always: 21 per cent (16 per cent)
Depends on the starting position: 30 per cent (44 per cent)
Never: 49 per cent (40 per cent)
The other question was how this puzzle relates to pi. The connection is not obvious, and it is not even mathematical. The Greek letter pi was chosen as the symbol for the circle ratio because it is an abbreviation of periphery, which is basically the same as perimeter. If you were thinking peripherally, about peripheries, you may have got it. (Here’s a great story about the man who invented pi).
I hope you had fun, and see you again in two weeks. Pi Pie!
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