The Most Poetic Thing about Mathematics
“Beauty is the first test: there is no permanent place in the world for ugly mathematics”
Mathematics is the language of nature. Every physical phenomenon of the universe can be explained by using mathematics. The notes of music, the economic growth or depreciation of a nation, the beautiful geometry of tiles, the beauty of flowers, the symmetry of snowflakes, the patterns of colors, everything is explainable by using numbers. From the stock market to stellar evolution, everything is mathematics. If you want to express or present any idea, any design, any geometry, any relationship or proportionality, or any logic, you are going to require mathematics.
Take π for example. One of the very first encounters we all had with this astonishingly beautiful symbol was in our schools where we were taught the value of pi being the ratio of the circumference of a circle to its diameter. Sounds pretty simple, right? Well, it is. In fact, you can calculate the value of pi yourself by drawing a perfect circle and its diameter, measuring the circumference (perimeter) of the circle using a thread, and measuring the diameter using a scale. Divide the two and there you have. But guess what? the value of Pi isn’t as simple as it might sound. A number is an irrational number with never-ending digits. It doesn’t have a fixed numerical pattern and as far as finding its value is concerned, there are lots of different ways that we can use it. One of the earliest formulas to calculate the value of Pi was introduced by prolific Indian mathematician Srinivasa Ramanujan in 1910.
Nobody knows how Ramanujan came up with this formula. He always believed that he got visions of his God who used to tell him about the secrets of mathematics in his dreams. Later in 1985, Ramanujan’s formula was used by William Gosper to calculate the value of Pi up to 17 million decimal places. In 1987, mathematicians at the University of Waterloo formulated another formula (similar to the Ramanujan’s) which calculated the value of Pi up to 2 billion decimal places with utmost accuracy. But what is it that makes Pi such a beautiful number in mathematics? Well, the first thing is the association between the simple ratio of circumference to diameter of a circle and the complicated series of numbers in number theory that can lead us to its value up to millions and even billions of decimal places. There are many formulas that have been formulated and proved that can calculate the value of pi with great accuracy. These days certain programs are developed, and the programs run a specific algorithm that can produce the value of pi in surprisingly accurate ways. Here’s a list of a few computers and programs that could calculate the values of Pi. The decimal places are mentioned alongside.
Let us consider another beautiful number, the golden ratio. This seemingly beautiful number, represented by the letter Phi, is one of the most significant numbers in mathematics. Basically, the ratio of two quantities is said to be in the golden ratio when they follow the following relationship,
If we consider a line having two parts: one longer and another shorter then the golden ratio basically represents the equivalence relation between the ratio of the long part to the short part and the whole length of the line to the long part. The value of the golden ratio is 1.618033988749… One of the most fascinating things about this ratio is that it has a huge application in the field of arts and architecture. Interestingly, polymaths like Leonardo DaVinci and sculptor Michelangelo have used the golden ratio in their artworks.
But that isn’t the most amazing thing about it. The most amazing thing about the golden ratio is its association with the Fibonacci sequence. Fibonacci sequence, for those of you who do not know, is a sequence of numbers starting from 1 where the next number is basically the sum of the previous two numbers. When you take two succeeding numbers from the sequence and find their ratio, interestingly the value is very close to the value of the golden ratio. That’s the beauty of mathematics.
To comprehend the fact that this seemingly infinitely long irrational number can have its association with a wide range of eye-pleasing architectural and artistic creations just blows my mind.
“The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.”
— G.H. Hardy
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