Bite Sized Science: Pi Day (Why is Pi so beautiful?)

By Kirsty Robathan

Pi (π) was that dreaded number that many students hated, it feels that its beauty was never fully explained and that all it was used for was to remember 3.142 for the equation πr^2. We thank a Welsh mathematician, William Jones for the use of the letter π to express the irrational number 3.14159… in 1706. Quite simply it is the number of times that the diameter of a circle fits around a circles circumference. Part of its illustrious beauty is that it goes on and on, no repeats (unlike Dave the TV channel), and no one will ever know how it ends. It is also transcendental number therefore there is no polynomial with rational coefficients where π is the root. The consequence of this is that it is not constructible.
In the early 1900s many mathematicians strived to figure π to a few thousand decimal places, nowadays computers have allowed for this figure to be calculated to more than a trillion decimal places. Although π only has to be calculated to 39 digits to make a circle the size of the observable universe, accurate to the size of a hydrogen atom.
Π has lead through time to all kinds of weird conspiracy calculations such as websites allowing for you to find out important dates that occur in the π sequence. For example my birthday starts at the 107058 position in π. However its splendour lies in the fact that it is so flexible, it shows up in equations relating to the double helix description of DNA. Also, problems involving harmonic motion (Fourier series), superstrings and even Einstein’s field equation.
One elegance is the geometric relationship of Euler’s formula (e^(iπ))+1=0, which is the relationship between the number of faces(F), edges(E) and vertices(V). When trying to work out why this is the case, think about how many other faces are connected to the points and lines on the first face. For example, the formula can be written as F+V-E, which for a cube where F=6, V=8 and E=2 then the answer is 2 which works for any polyhedral. Try it for a dodecahedron where F= 12, V=20 and E= 30.
The truth is it is a naturally occurring number with irrational and transcendental qualities making it baffling, exciting and downright magnificent.

Now to wait for the ultimate π day on March 14 2015 at 9:26:35. Happy Pi Day!

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0 Responses to Bite Sized Science: Pi Day (Why is Pi so beautiful?)

  1. Happy Pi Day! Thanks for writing this, but I thought I’d better point out that your last paragraph is wrong. Euler’s formula e^{i pi} + 1 = 0 is completely different from Euler’s *other* formula V-E+F = 2 for polyhedra. They are completely unrelated. The first formula comes out of our definition of complex numbers, the exponential function and some trigonometry. The second formula is from topology and graph theory.

    It is also a bit misleading to say that ‘nobody will ever know how it will end’ because pi is transcendental so it will never end!

  2. Kirsty says:

    Sorry, it was meant to be that as it will never end, this would lead to no one knowing how it ends. That should have been more clear. Also, with the formula I should have wrote, ‘another interesting formula by Euler’ rather than ‘which’. Again apologies and noted for next time. Thank you.

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