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In a role reversal, physics may help find solutions to long-standing mathematical problems.

 


If maths is the language the universe was written in, then pi, written as π, is surely one of its favourite characters. Initially discovered as a mathematical constant of the ratio between the circumference and radius of a circle, we soon realised that the number pops up everywhere when we study the properties of the universe and its constituents. From thermodynamics and electromagnetism to biological sciences and creation of our entire digital ecosystem, the humble pi makes its appearance. The number has gained such a cult following that we even have a day to celebrate it - pi day, celebrated on the 14th of March, because of its resemblance to the first 3 digits

Pi is an irrational number, meaning it cannot be written as the ratio of two real numbers and the digits after the decimal continues to infinity. In order to find the digits of pi after the decimal, mathematicians use what is called a series representation - adding infinitely many digits.

However, using even the most modern series representation, calculating the digits of pi can be an arduous task, and involves summing billions of digits. Pi belongs to a class of numbers called transcendental numbers. These are non-algebraic numbers, meaning they cannot be written in the form of an algebraic equation with rational coefficients.

The Euler-Beta function usually illustrated in theoretical physics provides the backbone for explaining phenomena such as high-energy particle collisions. In high-energy experiments, like the Large Hadron Collider (LHC) in CERN, Switzerland, particles, like protons or electrons, are accelerated to speeds close to the speed of light and then collide. Similar to smashing an object to break it open and reveal its constituents, colliding particles at such high energies allows for the production of virtual particles to be created, thus probing the constituent particles of the Universe. Such experiments can be termed as scattering experiments. Light scattering from objects allows us to see an object. Similarly, particles scattering from high-energy collisions allows us to see the constituents of the particles. The more energy we put into the scattering experiments, higher the resolving power of the experiment, revealing higher- mass virtual particles.



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