Why is Man still obsessed with π
The golden ratio, approximately 1.6, is often used by nature and great artists in their creations, though not universally.
REAL NUMBERS
The first irrational number encountered by man would have be √2, which is the diagonal of a unit square derived using the Pythagoras theorem. This would have been during a time when area calculations were routine every year for collecting taxes or giving rebates as a part of irregular flooding of major rivers like the Nile and Euphrates-Tigris river basin where the Egyptian and Babylonian civilisations thrived.
The first known person who highlighted the irrational behaviour of these number was Hipparchus who had a unusual death.
So, what are Irrational numbers. They are numbers that cannot be expressed in the p/q form and hence cannot be represented on the number line. That means these numbers in their decimal form have to be non-terminating and also non-recurring. And the most important aspect is that three numbers which are key to creation and propagation in Nature are irrational.
Our first number is Pi, the constant that appeared when man tried to find perimeter & area of a circle and also surface area & volume of a sphere. This shape and object was a integral part of Geometry and Mensuration for man. Initially the civilizations approximated this to 2 to 6 decimal places. Slowly starting from approximations of the area of a circle using polygons to circumscribing these circle, we started to make progress. Many mathematicians over millennia have worked on this and even today, with the help of super computers and cloud computing, we have approximated to more than 50 decimal places, without Pi giving its recurrence to us. March 14th, which is equivalent to 3.14 is noted as Pi day.
The second one is the Euler’s number, “e”. Consider that something doubles over a time period. The growth can be calculated as A = P(1+100/100) = P*2. But in nature suppose a plant grows double in size every one year, it does not happen suddenly the day before one year gets over like the system followed by banks earlier. The growth in Nature is doubling at very small instances of time. Hence let’s consider it grows over n-time periods. Then our equation would be A= P [1 + (100/n)/100] n,
A = P [1 + 1/n] n. When n tends to a large number or infinity, we get A = P*e. And sadly the exact e is an irrational number and growth in nature can never be precisely measured. It is approximated to 2.71828…
Finally the Golden ratio, this is a number that is seen in patterns in Nature and probably adapted by great artists like Learnado-da-Vinci and Michelangelo. It is seen in our skeletal system, depicted by Da Vinci in the Vitruvian man. These also seen in the arrangement of flowers in plants and also seeds of the Sunflower. Also from snails to cyclones. Though not everything in Nature follows this ratio.
Now Golden ratio and √2 are solutions of algebraic equations and hence called Algebraic irrational numbers. And Pi and e are not solutions of any algebraic equations and are called Trascendal numbers.