Geometry in nature #2: Golden Ratio, Fibonacci and spirals by kalemandra

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nature · @kalemandra · Jul 22 '17 (edited)

$20.66

Geometry in nature #2: Golden Ratio, Fibonacci and spirals

###  Mathematics and geometry is a universal language with which we can describe nature phenomena. Plants and animals are built  from the regular patterns of nature. If not so, it would be chaos, and many living creatures would be unviable.  The geometry is encoded in the genes.  DNA chains project a kind of hologram, into which the living creature grows in. If the DNA is damaged (for example by radiation), the geometry will be distorted. Just think about four-leaves clover, which is abnormal.
***
![_8126890a.jpg](https://steemitimages.com/DQmTpbrfWhx2yMvT8bdCf4Fr8rKjn6WUqmtMVTEB8KQ73jg/_8126890a.jpg)
(Spiralized flower by @kalemandra)
***
*I made a selection of my original photos, which are good examples  to geometry.  The second series is about Golden Ratio, Fibonacci and spirals.*
* What is Golden Ratio?
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure  illustrates the geometric relationship. <center>https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Golden_ratio_line.svg/220px-Golden_ratio_line.svg.png</center>
(Info and image source: https://en.wikipedia.org/wiki/Golden_ratio)
***
* What is Fibonacci-series?
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
<center>https://upload.wikimedia.org/wikipedia/commons/thumb/d/db/34%2A21-FibonacciBlocks.png/300px-34%2A21-FibonacciBlocks.png</center>
<center>https://upload.wikimedia.org/wikipedia/commons/thumb/2/2e/FibonacciSpiral.svg/220px-FibonacciSpiral.svg.png</center>
(Info and image source: https://en.wikipedia.org/wiki/Fibonacci_number)
***
* There is a special relationship between the Golden Ratio and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it). Note that the ratio of the two adjacent Fibonacci numbers approximates the Golden Ratio!
<center>![math.JPG](https://steemitimages.com/DQmXYP9NuQK4jZaWBeKxYrp2bNrdN62EQT65xRife7aH55L/math.JPG)</center>
(Source: https://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html)


***
<center>![_3186296.JPG](https://steemitimages.com/DQmX3a22Lmup1YpDYykyBixoL9Mg2m7oNJhJ4A3weNvk4nd/_3186296.JPG)</center>

<center>![_6159302.JPG](https://steemitimages.com/DQmdYp6QqTKYM23QF8tWzpptzpjgKpLkSewYzSjYXtZQLRL/_6159302.JPG)</center>

<center>![1-_4177825.JPG](https://steemitimages.com/DQmePsZYVT9bvshm5cqNW1ub1kcS4Kx5PdPesncRLvxnQdV/1-_4177825.JPG)</center>

<center>![1-_6128960.JPG](https://steemitimages.com/DQmS1f76jUuGvATRMHd36KHFXAENM9kFW3DCs1NbRc5VdjM/1-_6128960.JPG)</center>

<center>![1-_6128978.JPG](https://steemitimages.com/DQmPb5zeiFBhjSoojsdCcL2CJMirNZYpteiENWmTjF6zHFT/1-_6128978.JPG)</center>

<center>![20160113_142711.jpg](https://steemitimages.com/DQmVpW7nyvqok4Mb9sbKnNzi4tqucKjDeBq6mJm76sPHyLP/20160113_142711.jpg)</center>

<center>![20160412_182019.jpg](https://steemitimages.com/DQmUuD4pJ2i5JENfYKqURc6zoJTdxJ4a51SYvwgfRjp2Bst/20160412_182019.jpg)</center>

<center>![20160604_200004.jpg](https://steemitimages.com/DQmPRWwBPjvhPtsqbvJ25GWnZh8rKWeyZQDnAgqaKgBi9UR/20160604_200004.jpg)</center>

<center>![20160810_095756.jpg](https://steemitimages.com/DQmbUXheWgrV5gTW4vkCMbVCXbREc8q9jajggnqm7fs4MHq/20160810_095756.jpg)</center>

![_3105380.JPG](https://steemitimages.com/DQmNMw2RcgHTUHNFgFVPibTEgvcXwD7HNf8omq1Z28BSc3g/_3105380.JPG)

![_3105382.JPG](https://steemitimages.com/DQmQVk4Hi4uW9aSXZ1gh8SbompwDiJjBFYFNTdRqaW2d5pd/_3105382.JPG)

***

# <center>Áldás!♥♥♥Blessings!♥♥♥Namaste!♥♥♥Aloha!</center>
https://steemitimages.com/0x0/https://i.supload.com/B1diLaPLl.jpg

👍 v4vapid, hanshotfirst, matt-a, booster, speda, kalemandra, lichtblick, creatr, inphiknit, flurgx, bleujay, livingfree, marius19, olegst, hiroyamagishi, genics, lexcited, the-sassy-owl, futurefood, samstonehill, maestroali, ekaterinka, pipurilla, steemiteducation, cheftony, shaunmza, becausehelives, pennsif, olegw, pandamama, ocrdu, birjudanak, mehdibca, eyeofthestorm, anneke, holoz0r, alexkoshy, deleni, hawaiianstyle, minnaloushe, taowithbow, tanyaschutte, cipriang, szokerobert, stolen-id, costopher, firesteem, jaredcwillis, tensaix2j, yoogyart, curationbot, dp3ns7, curationguild, edgar.allen.poet, usaherald, calinconst, luke-skywalker

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@anneke · Jul 22 '17

Amazing - how wonderful is God's creation

👍 stefanus

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@kalemandra · Jul 22 '17

God is everywhere, in everything, and we are in God also.
"As above, so bellow..."

👍 anneke, stefanus

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@birjudanak · Jul 22 '17 (edited)

$0.15

Wonderful photography of all flowers as all flowers look so beautiful. From photos its look you taken with very high resolution camera because its look like in front of us. I just little week in geometry. I like the 6th flower from bottom image and its look so pinky  and beautiful. Hope you have a wonderful day. Namaste

👍 kalemandra

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@kalemandra · Jul 22 '17

Thanks for your kind words! These photos were taken with my Samsung mobile phone, which has a really good camera. These are about 1-year-old pictures.
Namaste! @kalemandra

👍 birjudanak

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@birjudanak · Jul 22 '17

Wow then its really good photography with mobile. Hats off you to you and your work. Best of luck for ahead friend.

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@booster · Jul 22 '17

<p>This post has received a 0.99 % upvote from @booster thanks to: @kalemandra.</p>

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@cipriang · Jul 22 '17 (edited)

$0.16

Beautiful post indeed. I have been fascinated with the Golden Ratio and Fibonacci sequence for  a long time. 

If I may, I'd like to share a beautiful video of this very topic, which goes into great details about both. I recommend anyone to watch it if interested in this two topics. Here: Inner Worlds, Outer Worlds - The Spiral 

(https://www.youtube.com/watch?v=ZIMoxXO0XvM).

**Thank you** for the beautiful post @kalemandra. Upvoted and followed. Looking forward to see more posts from you. :)

👍 kalemandra

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@kalemandra · Jul 22 '17

Thank you for this inspirational video! I'll watch it soon, if I have time.
Have a wonderful day! Greetings: @kalemandra

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@creatr · Jul 22 '17 (edited)

$0.10

Hi, @kalemandra,

Your photos are beautiful and they magnificently illustrate a very instructive and delightful article. Thanks for such a clear and engaging presentation!

😄😇😄
<a href="https://rebrand.ly/3d97" target="_blank">
  <img src="https://steemitimages.com/DQmWvzuqZ51DoiSjXXf8bukb7JeeVV1eAJJhGBkDiYc8ajj/creatr_ap.gif" alt="@creatr" style="border:0;">
</a>

Re-Steemed.

👍 kalemandra

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@kalemandra · Jul 22 '17

Thank you, I appreciate your comment and resteem.

👍 creatr

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@deleni · Jul 22 '17

I really like your work!
Another interesting post and good photos!

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@elsabailey6 · Jul 22 '17

Thanks for sharing it with us. :)

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@kalemandra · Jul 22 '17

Thanks, too!

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@eyeofthestorm · Jul 22 '17

Beautiful photos!  God is indeed a supreme artist and mathematician!  Thanks for a fascinating post

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@kalemandra · Jul 22 '17

Thank you too! :)))

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@flurgx · Jul 22 '17

Yes, and we humans are of the same beauty and perfection, unfortunately our mind doesn't get it and is always seeking to ridicule and destroy the beauty in creation.. Time to wake up from this dream that we are somewhat less or are here to destroy us or our planet...

👍 flurgx

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@kalemandra · Jul 22 '17

Destruction is much easier and fast than building up a structure. Yes, we are responsible for our Mother Earth, our biosphere, our Home.

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@lichtblick · Jul 22 '17

I am a great fractal fan :-) Resteemed :-)

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@olegst · Jul 22 '17

Fractals in nature is great!

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@olegw · Jul 22 '17

$0.12

You inspire with your post and initiatives, Thank you- i made something for colorchallenge maybe it can be useful.
![collorchalange0.png](https://steemitimages.com/DQmW4Y61qayoDWCVkXWuXksfuYJgwy2SKF61PrCbk51LUxh/collorchalange0.png)

👍 kalemandra, olegw

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@kalemandra · Jul 22 '17

This is great! Thanks for sharing!

properties (22)

@pandamama · Jul 22 '17

Beautiful photo's.  Mathematics is amazing in nature, in music.

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@kalemandra · Jul 22 '17

Thank you! Yes, music is also good example for math. Many mathematicians are good at music as well.

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@pandamama · Jul 24 '17

Yes, that is so true @kalemandra

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@phanhoang · Jul 22 '17

This is so awesome!! And It are really beautiful ðŸ˜ @kalemandra

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@kalemandra · Jul 22 '17

Thank you! :)

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@rtdcs · Jul 22 '17

Breautiful post. Fibonacci is used also in technical analysis!

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@steemiteducation · Jul 22 '17

https://imgoat.com/uploads/4173cb38f0/29566.jpg

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@stefanus · Jul 22 '17

Awesome post! It's amazing to see math in nature and not just on paper.

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@kalemandra · Jul 22 '17

Thoug math is an abstract language, it has strong relationship with nature and art.

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