# Pi Approximation Day and the inner secrets of the number π

Happy Pi Approximation Day!

On 22 July some people celebrate the number$\pi$ and its wonder approximation 22/7 = 3.142 … Although $\pi$ has an infinite number of decimals, as an engineer, this simple approximation is good enough for most applications.

On Pi Approximation Day I celebrate the number $\pi$ and its fantastic approximation 22/7 = 3.142 … Even though $\pi$ has an infinite number of decimals, as an engineer, this simple approximation is good enough for most applications and has been very useful in my professional life.

In this photo, I am smoking sheesha in Egypt and wearing my favourite T-shirt. The number π on the shirt consists of the first 4,493 digits of the number Pi in the shape of the symbol itself. The relationship between $\pi$ and Egypt is not coincidental as many people believe that the design of the Khufu pyramid at Giza shows that Egyptians of the fourth Dynasty knew about $\pi$, long before any other culture. The perimeter of the pyramid divided by its height is approximately 2$\pi$. Whether the designers of the Khufu pyramid knew about $\pi$ is, however, doubtful.

Smoking sheesha in Luxor in my favourite t-shirt.

## The Inner Secrets of π?

The number $\pi$ is an irrational number because it cannot be expressed as a fraction. But being a mathematical constant, it is also one of the most rational tools to understand the universe. Does the number $\latex pi$ hide an inner meaning? In the novel Contact by Carl Sagan, the heroine Ellie discovers a hidden message in the base 11 representation of $\pi$. This is not as miraculous as it sounds as there are an infinite number of decimals, even the complete works of Shakespeare could eventually be found. My birthday appears at the 107,070,083rd decimal digit of  $\pi$.

The idea that an irrational number helps us to understand the universe can be a worrying thought to those people that believe that the world is based on an occult principle. Mathematicians have tried for centuries to square the circle. They sought to find a simple logic to construct $\pi$, but failed. Fully understanding $\pi$ requires dealing with infinity. What does the fact that we cannot grasp $\pi$ in simple terms tell us about the structure of the universe? Is mathematics a human invention, or is it the basic building block of the universe?

Flying back from Egypt, I watched The Oxford Murders. In this movie, the question whether mathematics is the underlying truth of the world is discussed between the two main characters. Martin, a student, played by Elijah Wood, said:

“Things are organised following a model, a scheme, a logical series. Even the tiny snowflake includes a numerical basis in its structure. Therefore, if we manage to discover the secret meaning of numbers, we will know the secret meaning of reality.”

But is Martin correct? Can all philosophical questions and truths be expressed in mathematics? Will we eventually calculate our way out of ethical dilemmas? Can we improve our understanding of Shakespeare by expressing his prose in formal language?

$2b \vee \neg 2b$

I tend to agree with Professor Martin Seldon, played by John Hurt in the same movie, who said:

“Since man is incapable of reconciling mind and matter he turns to confer some sort of entity on ideas because he can not bear the notion that the purely abstract only exists in our brain.”

## Pi and the Horizon of Reason

Pi is an irrational and transcendental number with an infinite array of random digits. Even after calculating billions of digits, there does not seem to be any pattern in the arrangement of the digits. This lack of any design, the absence of logic, illustrates the structure of the universe itself.

Pi is an artificial construct of the human mind, not something that exists in reality. Nature doesn’t care about perimeters and diameters, although it might seem that the ubiquitous nature of $\pi$ in physics seems to suggest differently. This lack of order appears to imply that there is something inherently random in the structure of reality. The existence of irrational numbers shows the great divide between common sense and our scientific description of the world.

## Pi Approximation Day

However, we perceive our environment in discrete terms. Common sense mathematics does not include irrational numbers such as $\pi$. We think in whole numbers and fractions. This thought is reflected in the fact that in ancient cultures, $\pi$ was perceived to be a fraction, such as 22/7. This value is accurate enough for almost all computations.

This is why I celebrate Pi Approximation Day, it recognises the beauty of mathematics but also shows that the infinite precision demanded by mathematical theory is but a construct of our mind.

Peter Prevos

Social scientist and engineer who dabbles in magic tricks.