Mathematics is fun they said. However that is not always the truth; especially you are in an exam and it is ending in 5 minutes with lots of calculus and series to do. Aside from that, we have to admit, mathematics is – as a matter of fact can be fun and is very important to the progress of humankind.
- The golden spiral of Nicki Minaj
On the white carpet of the 2016 VMAs, Nicki Minaj arrived with a sexy navy gown and also managed to rouse up the internet’s interest in the golden spiral with the photo of her below.
The golden spiral, successive points dividing a golden rectangle into squares lie on a logarithmic spiral (Wells 1991, p. 39; Livio 2002, p. 119), is an interesting fact and a pretty pleasing aesthetic to stare at long hours. It’s a common observation in the galaxy and nautilus shells too. The golden spiral also relates to the Fibonacci number sequence, 0, 1, 1, 2, 3, 5, 8, 13, 21… It’s simply a sequence of numbers; in which the next number is found by adding the two numbers before it. Maths is full of fun, eh?
- Cheat code for squares
What’s the square of 1? How about 2? Pretty easy stuff if you passed SPM Maths really. Squaring the numbers up, you’ll get 1, 4, 9, 16, 25, 36… But do you see the pattern? Read between the lines and try to connect the stars in the sky.
The difference between consecutives squares is 3, 5, 7, 9, 11… It’s a nice fact to ponder on in your free time but there are a few explanations to this pattern. There’s a simple medieval method to explain it or the algebraic route or if you want to be Mr Fancy pants, go to the calculus voyage.
Googolplex, a number so large you can’t finish printing the zeros in one page. Fun fact, the number googolplex is written like the world “googol”, as it is ten to the power of ten to the power of hundred. Wait, what?
Basically, it’s a large ass number. Write it out, I dare you. The googolplex is said to be a larger number than the number of atoms in the observable universe. Another nice titbit, the googol was coined after a 9 year old; the nephew of Edward Kasner in 1938, his name is Milton Sirotta. Pretty cool way to be remembered in history.
- How to not fall into the sidewalks
We are fascinated with the optical illusion of 3D paintings, especially ones on the sidewalks. Those where it seems we are about to fall into a painting of chalk, what a way to live life the dangerous way without any actual peril. Now, let yourself be fascinated by the mathematics behind this art.
A system, which plays with perspective to bring an edge to creativity, called anamorphosis. This technique dates back to the Renaissance, where the famous painting The Ambassadors features a distorted skull at the bottom of the painting. We’ll approach this from the geometric angle. These paintings has a parallel lines that seems to stretch out to a common point, and when seen from an angle, it will be brought to life.
Pi is a fundamental constant that I think is the most encountered constants that any person who studied STEM will encounter. It is basically the ratio of the Circumference of a circle to its Diameter. No matter how big the circle is, the ratio will always be the same. Since most things in our world is round or sphere or have curves, the number is very important. So how did we calculate Pi though? Well it turns out that mathematicians have been working on pi since approximately 4000 thousand years and many algorithms have been employed. The simplest way is of course, to just divide the Circumference of a circle to its Diameter, but this method is prone to human error since a circle with Diameter of 1 unit will have a circumference of 3.141592….bla bla bla. We need a way to mathematically calculate pi without using measurements. The most popular algorithm was invented by at around 200 BC by Archimedes who utilizes polygons as his apparatus. Using geometry, he approximates the circumference of a circle with radius of 1 unit as the perimeter of the polygon with its corners on the circumference of the circle. He starts with a hexagon (because if you join the opposite corners you get 6 equilateral triangle). He then double the sides to 12, 24, 48 and stops at 96 – accurately approximates the pi. The pi is an irrational number, the one you will never be able to represent as the ratio between two numbers – it has no repeating pattern in its infinitely long decimal places and if you calculate long enough, you can even find your birthday date inscribed in there!
Exponential number is one of the most intriguing number, placing itself at the same stage as pi. The famous exponential function of e to the power of x is a very pleasing sight when you are doing calculus as its derivative is also e to the power of x. So how do we go about calculating the value of this number? Consider a function, say, f(x) = 1. Remember that we are trying to find a function where the derivative is equal to its original function. But, if the derivative is 1, then the original function should be f(x) = 1 + x. If the derivative is 1 + x, then the original function will be f(x) = 1 + x + 0.5x^2. The next iteration will yield f(x) = 1 + x + 0.5x^2 + (1/6)x^3 and so on, giving us an infinite series. The idea is, the function and the derivative will converge when the series is at infinity. Take a look again at the series, f(x) = 1 + x + 0.5x^2 + (1/6)x^3 … then you should notice that each term holds a pattern, (x^n)/n!. Thus the series is f(x) = 1 + x + 0.5x^2 + (1/6)x^3 …+ (x^n)/n!. Since this is the series that defines e^x, then to get e, set x = 1 then in the end, you will get e = 2.71828… bla bla bla. This problem was first pointed out by Jacob Bernoulli in the 17th century in a problem where if you have a bank giving you 100% interest for an account with 1 unit at the start during different interval in a year; per annum, per month, per week, per day and so on until you go about an instance where the bank is giving you interest at an infinite interval. He of course does not solve it but he knows that the value lies between 2.7 and 3. Euler worked it out later but, it is said that he chose the letter incidentally, not because his name starts with E.