In this post, we will see some of the nice mysteries around the mathematical patterns of the universe. **

Vortex Maths

This a underlying concept that has been contributed by scientist Marko Rodin.

alt text

According to the concept of this maths, everything in the physical world follows a mathematical pattern of numbers – 1, 2, 4, 8, 7 and 5 and this keeps on repeating itself. Consider the following example of calculation, starting with the number 1.

\[\begin{align*} 1 + 1 &= 2 \\ 2 + 2 & = 4 \\ 4 + 4 &= 8 \\ 8 + 8 &=16 = 1 + 6 = 7 \\ 16 + 16 &= 32 = 3 + 2 = 5, \qquad \text{we can also do } 7 + 7 = 14 = 1 + 4 = 5 \\ 32 + 32 &= 64 = 6 + 4 = 10 = 1 + 0 = 1\\ 64 + 64 &= 128 = 1 + 2 + 8 = 11 = 1 + 1 = 2 \end{align*}\]

Now, if we do halving beginning with the number 1, we will get the pattern but in reverse order as shown below:

\[\begin{align*} 1 / 2 &= 0.5 = 0 + 5 = 5 \\ 0.5 / 2 &= 0.25 = 0 + 2 + 5 = 7 \\ 0.25 / 2 &= 0.125 = 0 + 1 + 2 + 5 = 8 \\ 0.125 / 2 & = 0.0625 = 0 + 0 + 6 + 2 + 5 = 13 = 1 + 3 = 4 \\ 0.0625 / 2 &= 0.03125 = 0 + 0 + 3 + 1 + 2 + 5 = 11 = 1 + 1 = 2 \\ 0.03125 / 2 &= 0.015625 = 0 + 0 + 1 + 5 + 6 + 2 + 5 = 19 = 1 + 9 = 10 = 1 + 0 = 1 \end{align*}\]

The numbers 3, 6 and 9 doesn’t belong to the physical world, but are regarded as the driving force that governs the numbers of the physical world. Now, consider the numbers 3 and 6 as shown below:

\[\begin{align*} 3 + 3 &= 6 \\ 6 + 6 &= 12 = 1 + 2 = 3 \\ 12 + 12 &= 24 = 2 + 4 = 6 \\ 24 + 24 &= 48 = 4 + 8 = 12 = 1 + 2 = 3 \end{align*}\]

Similarly, if you do halving as the following:

\[\begin{align*} 3 / 2 &= 1.5 = 1 + 5 = 6 \\ 1.5 / 2 &= 0.75 = 0 + 7 + 5 = 12 + 1 + 2 = 3 \\ 0.75 / 2 &= 0.375 = 0 + 3 + 7 + 5 = 15 + 1 + 5 = 6 \end{align*}\]

This implies if we do doubling or halving of the numbers 3 and 6, it keeps on oscillating back and forth and keeps generating of 3 and 6.

Now, consider the number that can be regarded that doesn’t follow any pattern as can be seen below:

\[\begin{align*} 9 + 9 &= 18 = 1+ 8 = 9 \\ 18 + 18 &= 36 = 3 + 6 = 9 \\ 36 + 36 &= 72 = 7 + 2 = 9 \\ 72 + 72 &= 144 = 1 + 4 + 4 = 9 \end{align*}\]

This implies that the number 9 keeps repeating itself. We can do the similar halving of 9 and it will keep generating 9.

Golden Ratio and Fibonacci Sequence

The Fibonacci sequence is \( 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, \dots \) and so on. Here, each number is the sum of the previous two number.

The golden ratio is the mathematical number which is represented as 1.618.\ Two quantities \( a \) and \( b \) are said to be in golden ratio if

\[ \frac{a}{b} = \frac{a+b}{a} = \phi \]

Going forward in the fibonacci sequence, if we divide any two successive numbers, then the ratio converges to 1.618.

Euler’s Identity

Euler’s Identity is the most beaultiful mathematical equation and is written as:

\( e^{i\pi} + 1 = 0 \)

It involves the 5 mathematical constants, \( e, i, \pi , 1, 0 \), that forms the basis of relationship between real and imginary number in a way that results in nothing. The mathematical constants that are involved in the equation are:

  • \( e \) – the base of natural algorithms, \(log_e \) or \( ln e\). The constant \(e = 2.718281828459 \) and it indicates the idea of exponential growth.

  • \( i \) – represents the imaginary number.

  • \( \pi \) – represents the irrational number that is defined as the ratio of circumference and \( 2 \pi \) of the circle.

  • \( 1\) – multiplicative identitiy and basis of all other numbers.

  • \(0 \) – represents nothingness.

Useful Resources

Vortex Based Mathematics