# pi-ratio

Pi Guides the Way

## What Is Pi ?

Pi is the ratio of a circle’s circumference to its diameter. It is also an irrational number, meaning its decimal representation never ends and it never repeats. Pi has been calculated to more than one trillion digits,

## Why March 14?

March 14 marks the yearly celebration of the mathematical constant pi. More than just a number for mathematicians, pi has all sorts of applications in the real world, including on our missions. And as a holiday that encourages more than a little creativity – whether it’s making pi-themed pies or reciting from memory as many of the never-ending decimals of pi as possible (the record is 70,030 digits).

While 3.14 is often a precise enough approximation, hence the celebration occurring on March 14, or 3/14 (when written in standard U.S.  month/day format), the first known celebration occurred in 1988, and in 2009, the U.S. House of Representatives passed a resolution designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi.

## 5 Ways We Use Pi at NASA

Below are some ways scientists and engineers used pi.

## Keeping Spacecraft Chugging Along

Propulsion engineers use pi to determine the volume and surface area of propellant tanks. It’s how they size tanks and determine liquid propellant volume to keep spacecraft going and making new discoveries.

## Getting New Perspectives on Saturn

A technique called pi transfer uses the gravity of Titan’s moon, Titan, to alter the orbit of the Cassini spacecraft so it can obtain different perspectives of the ringed planet.

## Learning the Composition of Asteroids

Using pi and the asteroid’s mass, scientists can calculate the density of an asteroid and learn what it’s made of–ice, iron, rock, etc.

## Measuring Craters

knowing the circumference, diameter and surface area of a crater can tell scientists a lot about the asteroid or meteor that may have carved it out.

## Determining the Size of Exoplanets

Exoplanets are planets that orbit suns other than our own and scientists use pi to search for them. The first step is determining how much the light curve of a planet’s sun dims when a suspected planets passes in front of it.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

William Jones, who first used the symbol π (pi) to represent the ratio of the circumference of a circle to its diameter was the father of William Jones, who first posited the existence of the language that became known as Proto-Indo-European (PIE).

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POI Appreciation week // Day 5: Favourite Quotes   Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating….everything we ever say or do; all of the world’s infinite possibilities rest within this one simple circle.

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My buddy made an amazing Apple Pi for Pi Day!

The ratio of its circumference to its diameter = delicious! And he even made it from scratch! Well… Almost. He didn’t invent the universe first ;)

It’s Pi Day!

Pi Day, the informal holiday beloved by math enthusiasts — and even by the math averse — is here! March 14 marks the yearly celebration of the mathematical constant π (pi).

What is Pi?

Pi (3.1415….) is the ratio of circumference to diameter in a circle. Any time you want to find out the distance around a circle when you have the distance across it, you will need this formula.

Despite its frequent appearance in math and science, you can’t write pi as a simple fraction or calculate it by dividing two integers. For this reason, pi is said to be “irrational.” Pi’s digits extend infinitely and without any pattern, adding to its intrigue and mystery.

How Do We Use Pi at NASA?

Measurements: Pi can be used to make measurements – like perimeter, area and volume.

For example, sometimes we use lasers to explode ice samples and study their composition. In this scenario, we can uses pi to calculate the width of the laser beam, which in turn can be used to calculate the amount of energy, or fluence, that hits the ice sample. A larger fluence equals a bigger explosion in the ice.

Commanding Rovers: Pi is also used every day commanding rovers on the Red Planet. Everything from taking images, turning the wheels, driving around, operating the robotic arm and even talking to Earth!

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

Let me show you. Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it’s all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world’s infinite possibilities rest within this one simple circle. Now what you do with that information; what it’s good for, well that would be up to you.
—  Harold Finch, Person of Interest
pi

pi—the ratio between the circumference and the diameter of a circle.

Calculation of pi:  Archimedes around 250 B.C.E. gave the first recorded algorithm for rigorously calculating the value of the ratio between the circumference and the diameter of a circle, but he didn’t use the letter pi.  Archimedes’ method was tocompute successive upper and lower bounds of the number by drawing successivelycomplex polygons inside and outside a circle.

Computation of pi took a step forward when methods for using infinite series to compute it.  Here for instance is Gottfried Leibniz’ simple infinite series that converges closer and closer to π.

Use of “π” as the symbol for the ratio:  The earliest known use of the Greek letter π to represent the ratio of a circle’s circumference to its diameter was by mathematician William Jones in 1706, but didn’t come into wide use until Euler started using it 1736.

Origin of the Greek Letter pi:  The Greek letter pi (π) was adopted from the letter peh of the Phoenician alphabet.  The earliest examples of the Greek alphabet surprisingly come from Italy.  This came about because of a close trading connection between the Greek island of Euboea and the Phoencians from what is today Lebanon.  The two founded trading centers in the Mediterranean including the western coast of Italy.  It is here that we have the first evidence of the adoption of the Phoenician alphabet for use in writing the Greek language.  The first examples of Greek letters are fragments of Homer’s Iliad and Odessy as if the phonetic alphabet was being used to record and memorize the stories that had previously been orally transmitted by travelling singers.

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(x)

Dots & Lines
Lupe Fiasco

“To make gold from garbage is not the alchemical point of this math, the truth be told it’s the pursuit of gold that turns the goal of men into trash."

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Ryoji Ikeda
π, e, ø
Japan’s leading electronic composer and visual artist Ryoji Ikeda focuses on the essential characteristics of sound itself and that of visuals as light by means of both mathematical precision and aesthetics. Ikeda has gained a reputation as a unique artist working across both visual and sonic media. He elaborately orchestrates sound, visual materials, physical phenomena and mathematical notions into immersive live performances and installations.
Ryoji Ikeda’s exhibition title π, e, ø stands for three important mathematical constants;

π (pi, the ratio of a circle’s circumference to its diameter)
e (the base of the natural logarithm)
ø (phi, golden ratio: a+b/a = a/b), all of which are infinite

## On Pi Day, Let’s Gawk At The Beauty And Controversy Of The Math Constant

Mathematician Carlos Castillo-Chavez says that Pi is so important to math that using its simple, geometric definition denies its greater powers.

“[Pi] brings you into the world of mathematics, which is magic, mysterious and exciting and always full of challenges for everybody,” Castillo-Chavez said.

First calculated 4,000 years ago, Pi represents the ratio of a circle’s circumference to its diameter. You learned it as 3.14, which is why today some take the chance to bask in the brilliance and beauty of the mathematical constant, while others try to tear it down.

Photo credit: Claire O'Neill/NPR

## Happy π Day!

Pi has been known to most cultures since antiquity, with the earliest known calculations dating back to the Great Pyramid at Giza, whose perimeter measures about 1760 cubits and a height of about 280 cubits, giving the ratio 1760/280 ≈ 6.2857 which is approximately equal to 2π ≈ 6.2832. The earliest verifiable use of the lower case Ancient Greek letter π (pi) to symbolize the ratio of the diameter of a circle to its circumference was by the mathematician William Jones in his 1706 work a New Introduction to the Mathematics. In that work, however, Jones says that the ‘truly ingenious Mr. John Machin’ used it before him. There are many ways to derive π (pi), from the rough approximation of 22/7 to the most recent calculations that extend π (pi) to over a trillion digits, calculated over months and years with supercomputers.

To give you an idea of what π looks like, the image above is taken from a single sheet of standard office paper with π printed to the first 4,811 digits, about all that will fit on a single page with the widest margins possible.  Print both sides of the sheet and it will still take you 100 sheets of paper just to print the first million digits.

.

Enjoy π (pi) day, and have a slice of pie!

“Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it’s all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world’s infinite possibilities rest within this one simple circle.” [Person of Interest 2x11 2 PI R]

What are your thoughts on the pi v. tau debate?

(For those unaware of the Pi. vs. Tau debate, read the Tau Manifesto and then the Pi Manifesto).

I’m actually extremely pro-tau, but only under certain conditions. I’ll explain.

Warning: The following is my personal take on these subjects. I’m no authority. This is pretty much late night armchair philosophy and ramblings of a madman. It’s just how I make sense of some of these ideas, and it’s the first time I’m trying to put these into words. Hopefully, they’ll make some sense and I won’t look like a complete nut.

## On the merits of the debate

Mathematics thrives on conventions. Being able to symbolically convey a very precise idea is one of its greatest triumphs and strengths. For that, we have developed a set of (ideally unambiguous) conventional notations. Notation is pretty damn important. Learning this mathematical language takes a lot of effort, and it is a skill we should respect. A lot of important knowledge is being carried by these crazy symbols, knowledge built upon centuries of intense thought and research by some of the smartest people who have ever lived.

The use of the Greek lower-case letter pi (π) to denote a particular irrational number is one of such conventions developed in mathematics. As a convention, it is extremely valuable as it is. There’s little reason to change it. The fact we agreed with π as the ratio of a circle’s circumference to its diameter is of little consequence to any underlying mathematics, it changes nothing, so this isn’t really a point to be argued. The important thing is merely consistency.

In this respect, the tau vs. pi debate is a waste of time in my view. Saying equations are prettier because of a factor of two somewhere is missing is a bit ridiculous and non-mathematical, and entirely misses the point of having a constant defined in the first place. Are we arguing over mathematics or typography/aesthetics?

However, conceptual differences are important. This is where the debate can be fruitful, I think, so dismissing it completely can be (and I believe it is) a bad thing. Oddly nobody else seems to be making this particular point, at least not how I’m going to expose it here.

## Pi

You see, π shows up everywhere in math by itself, no factors of 2 attached at all. It’s a pretty remarkable number on its own. It shows up even when things don’t seem to be related to circles. For instance, the integral of the Gaussian is √π, which is a surprising result (and it’s one of my current math animation projects). The sum of the reciprocal of squares, also known as the Basel problem, is π2/6. No circles in sight here.

But whenever tau (τ = 2π) shows up, people like to talk about circles. They’re missing the point, I think. 2π isn’t the circle constant. It’s the ANGLE constant. The circle just happens to be related to the concept of angles, and not the other way around.

The most mathematically natural way of measuring angles is in units of radians. Everything works out so simply when we use radians that it’s tempting to call it the one true way of doing so.

## “Dimensions” vs. “units”

Now, before I go a little bit more into this argument, I need to clear something up. A lot of people say “radians don’t have units”, but that’s an incorrect use of terms. What these people are trying to say is that radians don’t have a dimension, that is, they are a dimensionless unit. See how we can use both terms together and still make sense? That’s because they have distinct and precise meanings.

A unit is a standard we use to measure other similar things. For instance, you can measure length in several units: meters, feet, the nearest spoon’s length, light-years, (toenail growth rate)·century, (your own name here)’s nipple-to-nipple distance, etc.

What all these units have in common is that they have the same dimension: length, or simply [L]. The other base dimensions in nature are time, [T], and mass, [M]. There are other dimensions that are used, but these are the more basic ones.

One way to understand this is to think of [L], [T] and [M] as the “real” physical quantities, or kinda like how Nature “understands” these quantities. When you read “2 meters”, you should be seeing 2 × (“1 of something we use to define a meter” × [L]).

The “meter” has a certain amount of [L] hidden in it, you see, because we defined it in terms of something else that has a length dimension. The 2 in “2 meters” is just there telling us just how much of that something we are talking about. The 2 is a pure, dimensionless number.

Using these three dimensions, we can build all sorts of quantities. Here’s a few, and some example units:

• Force = [M][L][T]-2 → newton, pound-force
• Energy = [M][L]2[T]-2 → joules, calories, kilotons of TNT
• Frequency = [T]-1 → hertz, radians/seconds

Dimensions can be treated just like variables: you can multiply, divide, take powers and square roots of them, but they don’t “mix” together. You can even add different dimensions, though just like variables, you get nowhere with that: a+b is just a+b. While it makes little physical sense something with dimensions [L]+[M] (think, 1 metre + 1 kg), there’s no reason why you shouldn’t be allowed to have it, if you’re really into that kind of thing. Weirdo.

By the way, this topic is called dimensional analysis, and it’s a very interesting subject.

Radians are an unit defined as the angle enclosed by an arc around a circle that is as long as that circle’s radius. Here’s an animation I created that explains it:

External image

It doesn’t matter what radius you pick (that’s why in the animation the radius is just a generic “r”), the angle is always the same because the arc’s length is also proportional to the radius, so the length of the radius always cancels itself out when you actually end up calculating radians.

But also, notice that the arc-length is a unit with dimension [L], and so is the radius. If you divide one by the other, the [L] dimensions cancel out, just like variables would. We end up with a quantity that’s just a number, a dimensionless quantity. A full turn has about 6.28 radians in it, that is, 1 turn ≈ 6.28 × (“1 of something we call radians” × [no dimension whatsoever]).

So, radians have no dimensions. We can treat them just like any other pure number. This is usually how everyone does it: they say it is a pure number, no meanings attached to it, and call it a day.

This is where my take on the subject takes a weird turn…

## “Dimensions” vs. “Concepts”

But conceptually, these numbers are still measuring something. Two instances of the same number associated with the same dimension can represent two entirely different things, so there’s more to these quantities than dimensions.

For example: “1 hertz” and “1 radian per second”, while dimensionally and numerically identical (both are “1 second-1”), are totally different conceptually. Something happening once every second is completely different than something rotating one radian every second.

In the same way, a torque of 1 newton-meter is numerically and dimensionally equivalent to 1 joule of energy, but the two ideas are very different. That’s why we explicitly write torque with units of “newton-meter” instead of joules. (In fact, it can be argued that the torque would be better expressed in SI units as joules per radian.)

So, here’s where my take on all these things gets weird: I think that beyond dimensions, we also attach “concepts” to numerical quantities and units, and these are also subject to a “conceptual analysis” similar to the dimensional analysis I mentioned up there.

While dimensions have a physical meaning, “concepts” are, well, abstract. (For consistency, I’ll denote concepts in single quotes from now on. E.g.: ‘angle’)

An 'angle’ is such a concept, attached to the unit of a radian: 1 “radian” = 1 × (“something we call radian” × 'angle’), where “something we call radian” is the same as “ratio between length of an arc of a circle and that circle’s radius”, that is, the definition of the radian. So, hidden inside a radian, is the concept of 'angle’ being multiplied by the number, just like a dimension such as [L] would be.

In fact, in terms of concepts, we could say: 'angle’ = 'circular arc’ / 'line segment’, so that we have: 1 radian = (1 × [L] × 'circular arc’) / (1 × [L] × 'line segment’).

In other words, what I’m trying to say here is that even if the dimensions cancel out in the definition of a radian, the concept of 'angle’ shouldn’t really go away with the number we’ve got. The concept 'angle’ is intrinsically in the “radian” unit, and it is not a dimensional quantity.

I love to play with this idea of “conceptual analysis”, and it has given me some weird and accurate insights before.

## Dude, just get to the point

All right, all right, here’s my point. I think we should have two definitions:

• π = 3.14159265…

Notice the difference?

π is just a pure number, like 1, 2.5 or √2. It has no concepts attached to it.

Meanwhile, τ is a number attached to the units of radians, which means τ carries the concept of 'angle’ with it everywhere it is used, always. Seeing τ immediately implies we’re talking about angles.

This is the important conceptual difference I talked about in the beginning. This is where τ really makes a lot of sense and where it would be useful.

## “The Conceptu-tau Manifesto” (groooan)

So, here’s my crazy proposal: let’s adopt tau as THE ANGLE CONSTANT.

Let’s face it, π isn’t going anywhere. It’s already well-established way beyond the scope of circles anyway. It makes no sense to fight it, and it has earned its place.

But whenever we talk about angles and rotations, there’s no question that τ is the proper constant to use, just as surely as the use of radians instead of degrees for angles. A full turn is the important idea, not a half turn.

Here’s the same animation as the one above, except this time using τ for the full turn instead of 2π.

External image

Notice that this time we can just keep using our unit of measure (the red arc of 1 radius in length) all the way around, counting each new whole radius (or radian) that fits, only adding a fractional bit at the end to complete the whole turn (the 0.28.. part). This makes much more sense, since that’s how we awalys used any unit of measurement: we count how many times our unit fits in the whole of the thing we’re measuring, not just in half of the thing.

With π, we are assigning a certain special name for a half-turn, even though it is the full turn the thing we are trying to measure. While this isn’t inherently a bad thing (a rotation of a half turn has a lot of importance in mathematics, hence why π exists), it is an odd special case that’s simply an arbitrary quirk of definitions.

The undeniable fact about all of this is that a full turn is more important than a half turn, so it deserves its own symbol.

However, notice that the foundation of that argument is not the numerical value of the full turn or half turn. That’s totally irrelevant, which is exactly why we’d like to use a symbol in place of these numbers! We don’t care about them! But for some reason, this is what most people seem to focus their attention on.

No. The foundation of that argument is in the word “turn”. It narrows down the single mathematical concept we are addressing in the discussion, and it’s in that context that τ really makes all the sense in the world, since it’s the one that represents a turn.

If you’re not convinced yet, just look at our language. We don’t even have a word (in common use, at least) to describe “half a turn”. We already talk about half a turn in terms of a full turn in our natural language. We all already use the definition π radians = τ/2 radians, but only when we talk about angles and rotation. It’s just how we naturally treat the concept, and it makes perfect sense that way.

If that doesn’t make it deserving of a mathematical notation, I don’t know what does.

## An example of the conceptual use of τ as the angle constant

Now, imagine we live in an alternate reality where τ = 6.28… radians, as I proposed. What could math feel like?

The following is obviously incredibly biased (this is an opinion text, so that’s kind of the point here), but it’s pretty close to the thought process I had when I was trying to make sense of the same ideas.

Euler’s Identity: eτi = 1

You see that mathematical expression for the first time in your life.

You see τ in there. Your brain attaches to it the idea of a “full turn”, as you have been trained to. Your brain is now thinking of things rotating and angles.

You see a representation of a “full turn” multiplied by the imaginary unit, i. You try to make sense of that, and you fail. As you should. But now you’re thinking about the complex plane and what could a “complex full turn” possibly mean.

But your brain doesn’t give up. I hasn’t finished reading the expression yet. So it reads the exponential function. You already know the e0 = 1, that’s one of the key properties of this function. But now, the exponential of a “complex full turn” (whatever that is) is doing something new. What it is? You look at the right of the equals sign.

You see the number 1, the multiplicative identity. This is the same value as e0 that you have already thought of. So, the exponential of a “full complex turn” is doing the same thing as doing nothing.

Your brain makes the connection: the exponential of “a full complex turn” (whatever that is) is bringing you back at the same place as you started. You know something is rotating, and you know this is happening on a complex plane.

Aha! Your brain finally gets it. It’s the only idea that makes sense now: the exponential function is performing a rotation in the complex plane itself.

And if you know trigonometry and think just a little harder, you should deduce that eθi = cos(θ) + i·sin(θ), Euler’s formula.

So, call me crazy or whatever you may, but this actually sounds like a nice convention to have around.

## Final words

To be honest, I feel pretty uncomfortable talking about these things. This notion of concepts attached to numbers may be a bit nutty, and I’m not familiar with this sort of approach to things anywhere. (Though a quick Google Search has brought up Bertrand Russell’s Theory of Descriptions), which sounds kinda alike)

But this is similar to the way my brain works, for better or for worse. This is how I learned to tackle math concepts, and this is the kind of approach I try to convey in all of my animations. I try to carry these 'concepts’ around using things like matching colors and visual styles.

Since so many people are fond of my animations, perhaps this idea has some merits, and I’m not a complete lunatic.

Either way, I don’t think there’s a magic trick to it or anything. It’s just about making sure you are keeping track of what everything represents at all times. This is the key approach to learning mathematics. The more stuff you can connect and correlate, the better and deeper your understanding will be.

And best of all, it’s supposed to make sense, even when it doesn’t. Usually, when it doesn’t make sense, it’s your intuition that’s wrong. It’s an odd lesson to learn, but these are the rules we play by in math.

“But I don’t want to go among mad people,” Alice remarked.

“How do you know I’m mad?” said Alice.

“You must be,” said the Cat, “otherwise you wouldn’t have come here.”

(from Lewis Carroll’s 1865 novel, Alice’s Adventures in Wonderland)

## Happy π Day!

Pi has been known to most cultures since antiquity, with the earliest known calculations dating back to the Great Pyramid at Giza, whose perimeter measures about 1760 cubits and a height of about 280 cubits, giving the ratio 1760/280 ≈ 6.2857 which is approximately equal to 2π ≈ 6.2832. The earliest verifiable use of the lower case Ancient Greek letter π (pi) to symbolize the ratio of the diameter of a circle to its circumference was by the mathematician William Jones in his 1706 work a New Introduction to the Mathematics. In that work, however, Jones says that the ‘truly ingenious Mr. John Machin’ used it before him. There are many ways to derive π (pi), from the rough approximation of 22/7 to the most recent calculations that extend π (pi) to over a trillion digits, calculated over months and years with supercomputers.

To give you an idea of what π looks like, the image above is taken from a single sheet of standard office paper with π printed to the first 4,811 digits, about all that will fit on a single page with the widest margins possible.  Print both sides of the sheet and it will still take you 100 sheets of paper just to print the first million digits.

Apologies to all those not in the Eastern Time zone of the United States-this post should hit your dashboard on 3/14/15 at 9:26 am.

Enjoy π (pi) day, and have a slice of pie!

Get ready to roll out some dough, because it’s Pi Day!

What’s that, you ask? Think back to geometry class. Pi represents the ratio of a circle’s circumference (the distance around the circle) to its diameter (the distance across it). In mathematics, it’s been represented by the Greek letter “π” since the 1700s.

For the math challenged, think of something that’s round. Might I suggest … pie? It’s the perfect example because, in addition to being round, it’s pronounced the same way as pi. And you can even use pies to calculate Pi, more or less.

Now, it’s been a long time since I sat in math class and learned about pi. Here’s what I remember: The value of pi is about 3.14159. (The value of pie, on the other hand, is, of course, deliciousness.) Pi is often shortened further to 3.14, but it actually goes on forever.

Some genius grasped the idea before I did and started Pi Day — which, of course, is celebrated with pie.

Photo credit: Claire O’Neill/NPR

Pi is the ratio of a circle’s diameter to its circumference, in the same way nuclear fission is a way of powering TVs to watch America’s Got Talent: an appallingly simple effect of a reality-defining truth. Pi isn’t a number, it’s a startup constant of spacetime. Take a line in one dimension, rotate it around another, and the resulting ratio of lengths is a precise number. The existence of space has a numerical signature. It’s called a transcendental number, because even attempting to think about how much it means is more mind-expanding than all the drugs.

Calculating pi has become the computer scientist equivalent of tuning muscle cars: we don’t actually need more digits for anything useful, because the basics do everything we actually need it for, but we’ve spent years stacking up air-cooled hardware just because. In 1985 it was calculated to 17 million digits. Srinivasa Ramanujan found the formula used. Around 1910.

It wasn’t the only such formula, but was incredibly useful because it converged exponentially compared to other algorithms, making it ideal for computers. Interesting note: at the time there was no such thing as computers. Srinivasa Ramanujan had pre-empted processors by decades.

## 5 Math Equations That Change the Way You See the World

Happy π Day! Pi has been known to most cultures since antiquity, with the earliest known calculations dating back to the Great Pyramid at Giza, whose perimeter measures about 1760 cubits and a height of about 280 cubits, giving the ratio 1760/280 ≈ 6.2857 which is approximately equal to 2π ≈ 6.2832. The earliest verifiable use of the lower case Ancient Greek letter π (pi) to symbolize the ratio of the diameter of a circle to its circumference was by the mathematician William Jones in his 1706 work a New Introduction to the Mathematics. In that work, however, Jones says that the ‘truly ingenious Mr. John Machin’ used it before him. There are many ways to derive π (pi), from the rough approximation of 22/7 to the most recent calculations that extend π (pi) to over a trillion digits, calculated over months and years with supercomputers.
Apologies to all those not in the Eastern Time zone of the United States-this post should hit your dashboard on 3/14 at 1:59.
Enjoy π (pi) day, and have a slice of pie!

Beautiful photo of Ice in Chicago from the polar vortex!

Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it’s all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world’s infinite possibilities rest within this one simple circle. Now what you do with that information; what it’s good for, well that would be up to you.
—  Person of Interest  - Harold Finch