Pi is one of those constants in the mathematical world. And because of that, it often appears in nature, particularly any that involves curves and ​spirals. But it would be too easy to derive pi from those very things - they are ordered, unchanging, predictable.

But what if pi can be derived from a series of improbable, unpredictable actions?

Nothing and everything. Two mathematical concepts that seems intuitive now, but inconceivable before the invention of zero and infinity. Both of these concepts originates from India, both are linked by the philosophical approach of the civilizations of the subcontinent.

In hindsight, it seems that these two concepts, crucial to the modern world, can only arise from a society that appreciates both.

In Part I we tackled the origins of arithmetic, the most basic and fundamental form of mathematics. Now we look at the more abstract world of geometry brought by the Greeks. It's no coincidence that at the same time they formulate mathematical theorems, they also ponder on philosophical paradoxes.

As we shall see, the Greeks idea of mathematics has more to do with attaining perfection than practical solutions.

As explained in a previous article, there is an infinite number of numbers. But what's more important is that there are different types of numbers with unique properties that makes them useful in one kind of mathematics while at the same time makes it seems like they are useless.

In this article, we will be addressing the different types of numbers. For their use on the other hand, we will be needing your help.

What do we mean by exponential growth? How quickly does your bank balance grow? How quickly does a cup of tea cool, or radium decay? What shape is a washing line and what is the link with a single mysterious number?

​Sometimes a solution can be reduced to a single element.