# ZCubes/Nature is Golden

## Nature is Golden

The beautiful golden sunflowers are a mathematical marvel. The pattern of seeds in a sunflower follows the Fibonacci series. This video demonstrates how nature uses Fibonacci series, golden ratio and golden angle in sunflower, pinecones etc, and secrets behind our admiration for certain designs, architecture and art. Enjoy watching!

ZCubes is an omnifunctional computing platform. You can create documents, spreadsheets, charts & presentations, draw, paint, graphics & animations, web pages and much more with ZCubes.

Nature is Golden

## Code

```1.FIBONNACI(100)

Output:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181	6765 10946 17711 28657 46368 75025 .....
```
```2. (1..1000)@["x*137.5","0.05*SQRT(x)"].toframe()

- When observed the above expression in charts, a spiral pattern is observed.
```
```3. FIBONNACI(100)
.chunks(2)
.map(r=>r[1]/r[0])
~

- Displays the golden ratio between two consecutive numbers of Fibonnaci series as shown below:

Infinity
2
1.6666666666666667
1.625
1.619047619047619
1.6181818181818182
1.6180555555555556
1.6180371352785146
1.618034447821682
1.618034055727554
1.6180339985218033
1.6180339901755971
1.618033988957902
1.6180339887802426
1.6180339887543225
1.6180339887505408
1.618033988749989
1.6180339887499087
1.618033988749897
1.6180339887498951
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.6180339887498947
1.618033988749895
1.618033988749895
1.618033988749895
1.618033988749895
1.6180339887498947
1.618033988749895
1.618033988749895
1.6180339887498947
1.618033988749895
1.618033988749895
...
```
```4. ROOTS("x^2-x-1")

- Displays the quadratic roots as:
[1/2−1/2∗5(1/2),1/2+1/2∗5(1/2)]

(1+SQRT(5))/2

- Displays golden ratio as 1.618033988749895
```
```5. Golden Angle:

gr=[(1+SQRT(5))/2,(1-SQRT(5))/2]
gr[0]

Displays the golden ratio: 1.618033988749895

360*(1-1/gr[0])

Displays the golden angle: 137.50776405003788