Making Spirals

[emitflesti]

In case anybody is interested in visualizing numbers and make your own spirals.

IMHO, here are 2 great sites that I've found where you can make spirals and play with multiple variables.

1)
Here's a link to author, Ryan Somma, which he created and generously added instructions below on how to make your own spirals:
http://ideonexus.com/2014/07/21/number-spiral-mandalas-with-html-canvas/
Comment: What I like about his program is that is shows all the numbers and highlights the Prime Numbers in Red

2)
And here's another one, which is more of an animation:
https://www.khanacademy.org/computer-programming/super-spiral/823021393
Comment: This one has a lot more variables to play with. However it doesn't show any of the numbers in the spiral

 

[Buddy]

In case anybody is interested in visualizing numbers and make your own spirals.

IMHO, here are 2 great sites that I've found where you can make spirals and play with multiple variables.

1)
Here's a link to author, Ryan Somma, which he created and generously added instructions below on how to make your own spirals:
http://ideonexus.com/2014/07/21/number-spiral-mandalas-with-html-canvas/
Comment: What I like about his program is that is shows all the numbers and highlights the Prime Numbers in Red

Interesting. I liked his statement:

It’s wonderful when a program doesn’t give you the answer you designed it to; that means you are about to learn something.

Yes! An adventure begins!

2)
And here's another one, which is more of an animation:
https://www.khanacademy.org/computer-programming/super-spiral/823021393
Comment: This one has a lot more variables to play with. However it doesn't show any of the numbers in the spiral

Mathematics can create gorgeous symmetry, no? Yes!

I especially enjoy spirals in nature based on the Golden ratio or what's also called the Fibonacci sequence:

The famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the Universe.

We've talked about the Fibonacci series and the Golden ratio before, but it's worth a quick review. The Fibonacci sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on forever. Each number is the sum of the two numbers that precede it. It's a simple pattern, but it appears to be a kind of built-in numbering system to the cosmos.

Read this link for 15 "astounding" examples in nature:
_http://io9.gizmodo.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature

Note:
For those who may not know, the Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet.

The Fibonacci Series, a set of numbers that increases rapidly, began as a medieval math joke about how fast rabbits breed. But it's became a source of insight into art, architecture, nature, and efficiency. This mathematical game explains the structures of leaves and lungs, is replicated in paintings and photographs, and pops up as the basis for the pyramids, the Parthenon, and packing efficiency.

Read this page for the origin of the series based on Leonardo Fibonacci's calculations involving rabbits:
_http://io9.gizmodo.com/5768696/the-fibonacci-series-when-math-turns-golden

Thanks for sharing!

 

[emitflesti]

Mathematics can create gorgeous symmetry, no? Yes!

I especially enjoy spirals in nature based on the Golden ratio or what's also called the Fibonacci sequence:

Hi Buddy!
Here's something else I just stumbled upon regarding the Golden Ratio/Phi/Fibonacci sequence in case your interested:
http://www1.lsbu.ac.uk/water/platonic.html

Interestingly the golden ratio also appears in aqueous chemistry as the ratio between atomic and ionic diameters. Thus the diameter of an anion (A-) is twice its atomic diameter divided by φ and the diameter of a cation (A+) is twice its atomic diameter divided by φ2; with the diameter of A- being the golden ratio times the diameter of A+, and simple functions of φ also relating ion-water distances to covalent radii [1091]. The golden ratio has also been associated with the genetic code [1808].

Comment: What I like about this website is their professionalism of having over 2400 references