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ZCubes/Nature is Golden (view source)
Revision as of 14:48, 21 September 2021
, 14:48, 21 September 2021no edit summary
==Video==
==Video==
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{{#ev:youtube|9ZzzN_dpbmI|480|left|Brocards Problem & Brown Numbers}}
{{#ev:youtube|9ZzzN_dpbmI|480|left|Nature is Golden}}
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==Code==
<pre>
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 .....
</pre>
<pre>
2. (1..1000)@["x*137.5","0.05*SQRT(x)"].toframe()
- When observed the above expression in charts, a spiral pattern is observed.
</pre>
<pre>
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
...
</pre>
<pre>
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
</pre>
<pre>
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
360*(1-1/gr[0])<>deg<>rad
Displays the golden angle in radians: 2.3999632297286535rad
</pre>
*[[Z3 | Z3 home]]
*[[Z3 | Z3 home]]
*[[Z^3 Language Documentation]]
*[[Z^3 Language Documentation]]