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.

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