Happy Pi Day! A favorite holiday among geeks, March 14 commemorates one of the most fundamental and strange numbers in mathematics. It's also Albert Einstein's birthday.
This is a great excuse to bake pies, as many iReporters have (send us your pie-report!). But there are also lots of reasons to celebrate this number: Pi appears in the search for other planets, in the way that DNA folds, in science at the world's most powerful particle collider, and in many other fields of science.
Here's a refresher: Pi is the ratio of circumference to diameter of a circle. No matter how big or small the circle is, if you calculate the distance around it, divided by the distance across it, you will get pi, which is approximately 3.14. That's why Pi Day is 3/14!
But the digits of pi actually go on forever in a seemingly random fashion, making it a fun challenge for people who like to memorize and recite long strings of numbers (like this iReporter). By the way, the world record for memorization stands at 67,890 digits, according to the Pi World Ranking List. Here are 10,000 digits to get you started.
To the uninitiated, such enthusiasm over a number may sound ridiculous. But when you think about how many different fields of science incorporate pi, it does seem kind of amazing.
Be forewarned: We're going to have to use a bit of math to explain why. Yes, math formulas may seem scary, but trust us: It's worth the challenge.
The search for new planets
For Sara Seager, professor of planetary science at Massachusetts Institute of Technology, pi is part of everyday work in characterizing and searching for planets outside our solar system, called exoplanets.
Here's her basic formula: The volume of a planet is about 4/3 pi times the radius^{3}.
You need this formula to find the density of a planet, which is mass divided by volume. This number that tells Seager and colleagues whether a planet is mostly gaseous like Jupiter, rocky like Earth, or something in between.
Pi is also involved in calculations regarding an exoplanet's atmosphere, since it can be described spherically, and spheres always involve pi.
"Coincidentally, pi is useful to estimate the number of seconds in a year (on Earth): There are approximately pi times 10 million seconds in a year," Seager says.
And a tiny space telescope that Seager works on called the ExoplanetSat, which is a collaboration between MIT and Draper Laboratory, also incorporates pi in optics equations related to the telescope's mirror.
Astrophysics
Pi helps describe the shape of the universe, says David Spergel, chairman of Princeton University's astrophysical sciences department.
Spergel studies cosmic microwave background radiation, which is basically radiation that's still hanging around from the early universe - it's the afterglow of the Big Bang.
Using a spacecraft called WMAP (Wilkinson Microwave Anisotropy Probe), Spergel and colleagues have been able to get an idea of what the early universe looked like - a "baby picture," as it was called when WMAP's 2003 results were released.
See if you can wrap your head around this:
4pi is the ratio of the surface area of a sphere to the square of its radius, in geometrically flat space.
"Using our measurements of the microwave background, we measure this ratio by determining the angular size of hot and cold spots in the microwave sky. Our measurements show that the large-scale geometry of the universe is accurately described by the Euclidean geometry that we all learned in high school," Spergel says. "This measurement implies that the total energy of the universe is very close to zero."
Why? The positive energy from the universe's expansion (it's been expanding since the Big Bang) is balanced by the negative energy of matter being attracted to itself, via gravity.
The Large Hadron Collider
Pi comes up a lot in what physicists do at the Large Hadron Collider, the $10 billion machine at the European Organization for Nuclear Research (CERN) in Switzerland that smashes protons into protons at unprecedented energies. Scientists are looking for as-yet-undiscovered particles such as the Higgs boson, which popular culture refers to as "the God particle."
Joe Incandela, spokesman for the collider's Compact Muon Solenoid experiment, explains one way that pi shows up at the LHC:
In particle physics, if we can measure particle properties, like masses, very very precisely, we can sometimes find tell-tale evidence of undiscovered new particles. That’s because particles can transform themselves into other particles, and then come back together to make the original particle again. This is called a loop.
When you calculate the contribution of this process to the particle's mass, a factor of something like 1/(16pi^{2}) comes out, along with other factors that depend on the properties of the particles in the loops.
Interestingly, prior to the LHC, some particles could only appear in these loops, and nowhere else, and should come in pairs in order for a special property that they have to be conserved. A very important example of a theory of particles with this kind of behavior is what scientists call supersymmetry, and it helps explain a lot of the holes in our current best understanding of the universe, known as the Standard Model.
Scientists are hoping to see these kinds of particles directly which requires very high-energy particle accelerators like the LHC to make them. They will also continue to try to detect their effects on Standard-Model particles in these loops, which are extremely short-lived and this requires a lot of patience because measurements must be extremely precise.
So, supersymmetry will probably still be out there for us to discover, even though there is no evidence of it in detailed measurements of particle parameters at the LEP and Tevatron accelerators in the past (or at the LHC either, so far, but there's still a lot of room to look for them).
Gravity, energy and mass
Pi appears in Einstein's equation for how energy and mass lead to the curvature of spacetime:
R_ij – (1/2)R g_ij = 8pi*G T_ij.
Wow, what is that? Sean Carroll at California Institute of Technology acknowledges that this is a weird-looking equation, but the important part is that G is Newton's constant of gravitation. "Long story short: in Newton's equation for gravity, the constant is just G; in Einstein's equation, it's 8pi*G," he says.
Why? Carroll explains:
Let's say you know how much mass the Earth has, and you want to figure out what the strength of gravity is at some distance away. Newton's equation tells you what that force is - it's proportional to one divided by the distance squared (the famous "inverse square law"). But let's say you want to do the opposite - you know what the force is, but you want to figure out how much mass is causing it.
You could draw a sphere that completely surrounds the object, and add up the gravitational force at each point on the sphere, to make sure you are correctly capturing what's going on inside. So the answer to one question is related to the answer to the other, by adding up things all over a sphere. And the area of a sphere of radius R is 4pi R^{2}. Voila - pi comes into the expression, because pi relates distances (straight lines) to spheres.
How DNA folds
Pi plays an important role in the way the genome is folded, says Leonid Mirny, associate professor at MIT.
"If you take all DNA of the human genome contained in a single cell and stretch it, the DNA would be a 2-meter-long fiber," he says. How are these two meters of DNA packed inside a cell nucleus, which is only 5 micrometers (that's 5 millionths of a meter) in diameter?
Think about thread around a spool. At the cellular level, there's a core made of special proteins called histones, and they're like the spool. DNA wraps twice around it and then continues to the next spool. Each one of these spools is called a nucleosome, and tens of millions of them pack our DNA, making it look like a string of beads.
How much shorter is this string than the DNA itself? The answer is about 1.5pi (or about 5) times!
Mathematics
Pi is essential for mathematicians whether they care about circles or not, says Jordan Ellenberg, professor of mathematics at the University of Wisconsin. Here's one place where it comes up for Ellenberg:
Choose two random numbers between 1 and 1,000. Then, he could compute whether they have any factors other than 1 in common. "It turns out that the probability of having no common factor is a a little over 60%," he says. "And you can change 1,000 to 10,000, and then to 100,000, etc etc, and amazingly the probability seems to be converging to a fixed value, about 60.79%. More amazingly still, this value is 6/pi^{2}!"
Studying crickets
Crickets use sound to locate mates, and their reaction to fellow crickets' calls are of interest to Gerald Pollack - a biologist at McGill University in Montreal, Quebec. In one of his experiments, crickets walk on a spherical treadmill while a loudspeaker broadcasts a cricket song. How accurately do they walk toward the sound?
"We measure the discrepancy between the direction of the loudspeaker and the direction in which the cricket walks, both of which are measured as angles ranging between zero and 2pi radians," he says.
Magnetism
James Clerk Maxwell Maxwell published famous equations of electromagnetism in the 1860s. They are fundamental to modern electronics and communications.
These equations include an important physical quantity called "the permeability of free space," which has a value of 4pi x 10^{-7} H/m that's units per Henry per meter, where a Henry is a unit used in electronics.
"So we are all using pi every day when we think about magnetic or electric fields, or electromagnetic radiation (light, radio etc)," says Caroline Ross, associate head of the Department of Materials Science and Engineering at MIT.
Engineering
Pi is involved in calculating the surface area and volume of round three-dimensional objects. So, if you're planning to build something involving spheres or arches or some kind of circular geometry, you're going to need pi!
Drug design
Chandrajit Bajaj at the University of Texas, Austin, is researching molecular recognition models for drug design and discovery. She uses simulations of particles in which atoms are often represented as spheres. The formulas for molecular surface area and volume involve pi, and often appear in Bajaj's calculations.
So, there are more than 3.14 reasons that pi is special. Now go eat some pie!
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the error of.1 is 60% the error in 4 is 60% not of a whole number but in the smalles of measurement known to men kind but when multiplied by infinity it's large enough number to show in the shape of abject...cannot used 3.14 in social studies till the accurate number is found...i have no need to measure object here on earth or in the universe or on particle for that matter...so if i have an interest is for social studies reasons...3.14 pi needs more accuracy cause is smaller then paricle its quantum symetry or supersymetry measurement i am trying to achiave here...kindy like psychi prediction kind of a thing...
so the equation should be 3+=4 calculating before 3 then + the calculation of .1 add them all together for the full calculation but the .1 will take the shape of ~3=0infinity and 4 will take the shape of 0 to infinity more thinking need to be done to come up with the right equation here...it seems to me that 3+=4 is larger then 3 as it stand in 3.14 to form the loop of pi...
the universe does not look like an egg the discrepancy of .14 multiply changes the object shape its a large miscalculation and it noticeble by the shape measurement outcome...the arror is smaller then the object measure but large enought to disfigure the object shape on two sides the represented object oposite poles...cause the 4 ends up representing the left side of the object with it errors and the .1 end up representing he right side of the object...but the error is minimal and can only effect the shape when it's a very large object like the inverse's perimeters...infinity is large enought to create the ellusion by the error that the universe is shaped as an egg...
`3=0infinity3.1=3.14 the 4 is larger then .1 in this case cause infinity...this depending on point of reference... if 3 represent a large abject or small object or earth size objects...3 represent all 3 of them accurately .14 is where the discrepancy is...
its like the 4 on pi represent the 3333333333333333333333333 into infinity but its not 4 its less then 4 it's one third of a demantion...represented by 4 a 3+ it's not larger then .1 and its not larger then 5 to make the .1a 2 it's different dimention so it cannat be a 3 so the .1 stays as it is for luck of a better representation of such unite...
see 33333333333 into infinity is one demantion of a whole three parts of 3333333333333 into infinity represent a whole of the universe so 333333333333 into infinity + 33333333333 into infinity + 333333333333 into infinity is one universe...so the first 33333333333 into infinity represent the larger object or in this cause as in pi represent the second demantion 3 the .1 represents the smaller demantions as particle and the 4 = 3+ represent the larger like planets and space demantions...all representing one the whole universe in all it's sizes...this being he most important reason why .14 need to be figure out to be the most accurate which at this time it's not yet but it's workable cause its the closed to perfection we've come to so far in our knowlege of math...so math need to discover how to incorporate the other two demantion of size into math the larger and maller and earth's size object...infinity its not an earth like object its consider large size. particle aren't eath like object they are consider small size 3 in pi represent the earth like object that's why ti works .1 represent the small particle size objects and the 3+ represent infinity large size object...
i still think the inacuracy of pi is with .14 - 3 is correct 3+3+3=9 the problem beggins when .14 attempt to complete the other one missing in the equation to make whole one-1~infinity or 0-1-10-100-1000 and so on...0000000000000 like in computing...when the number is infinity is '0' infinity within zero...so .1 stand for second demantion, and 3+ =4 = "0" infinity so it might be discribed as ~ 0 = infinity's third demantion...right before -0 negative zero not the same as ~0 infinity so one third of ~0 infinity is inacurately represented by the 4 meaning 3+ actually a ~0 infinity value in a third demantion of math... the .14 dismisses about 40% of accuracy in the particle levels or on the large planet levels but isn't noticeble on the measurement of earth shaped objects the discrepancy isn't noticeble...how to create a more accurate pi??? with this knowledge???