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vonpietro
02-17-2015, 02:48 AM
https://www.youtube.com/watch?v=kkGeOWYOFoA#t=207

nice - the connection between the math and the nautilus shell -just amazing. So, the nautilus is basically constructed of the golden ratio in 3 dimensions. Who knew?

Really great example of showing math relationships in a useful way.

some really amazing work out there.

as much as i pay attention to the rule of thirds, i don't really use the golden ratio.
I will now. =)

So i'd like to remind the lightwave user of the lil preference.

under options - display tab - composition overview - there are several settings related to the golden ratio. and some golden triangles too.
very useful =)

i'll be using it more.

spherical
02-17-2015, 03:43 AM
https://www.youtube.com/watch?v=kkGeOWYOFoA#t=207

nice - the connection between the math and the nautilus shell -just amazing. So, the nautilus is basically constructed of the golden ratio in 3 dimensions. Who knew?

Really great example of showing math relationships in a useful way.

There are lots of these out there.... Just look around, examine and absorb.

prometheus
02-17-2015, 09:59 AM
https://www.youtube.com/watch?v=kkGeOWYOFoA#t=207

nice - the connection between the math and the nautilus shell -just amazing. So, the nautilus is basically constructed of the golden ratio in 3 dimensions. Who knew?



Ivé known that for ages, (cocky me :) ) itīs also known as the fibonacci series...I recall trying to draw triangular shapes based on the golden ratio as drawing blocks for eyes and mouths, and I think I sort of got it pretty close
and then fused in the back of my bones so to speak when I used to draw.., you can build up amor curves in the mouth with proportions based on that and lotīs of other stuff, and I have found it pleasing to look at as harmonic shapes.

, 1, 1, 2, 3, 5, 8, 13, 21, 34,

I used to have a drawing book covering artists and their techniques and how they often used the golden ratio when composting etc, or drawing shapes, think Ivé lost it though.

caustics
02-17-2015, 03:40 PM
Hi,

I liked the video very much ... exceptionally well made.

Thanks for sharing.

vonpietro
02-17-2015, 03:51 PM
Been finding some real interesting stuff lately.
i knew about the nautilus, but in 3 dimensions - not really, the video hints at this though.

Slartibartfast
02-17-2015, 03:56 PM
Ivé known that for ages, (cocky me :) ) itīs also known as the fibonacci series...I recall trying to draw triangular shapes based on the golden ratio as drawing blocks for eyes and mouths, and I think I sort of got it pretty close
and then fused in the back of my bones so to speak when I used to draw.., you can build up amor curves in the mouth with proportions based on that and lotīs of other stuff, and I have found it pleasing to look at as harmonic shapes.

, 1, 1, 2, 3, 5, 8, 13, 21, 34,

I used to have a drawing book covering artists and their techniques and how they often used the golden ratio when composting etc, or drawing shapes, think Ivé lost it though.

To be even cockier :D - the golden ratio isn't unique to the fibonacci numbers. You can start with any two numbers and follow the same rule (adding the last two gives a new number) and it's approaching the golden ratio. Or so they say, I haven't been bothered to check :-)
And yeah, I've watched to many episodes of numberphile on YT :D
Anyway, I agree - the beauty of math is amazing!

KurtF
02-17-2015, 09:00 PM
Cristobal Vila's web site is full of information on his "Nature by Numbers" film. The making of is really nice.

Nature by Numbers (http://etereaestudios.com/docs_html/nbyn_htm/intro.htm)

inkpen3d
02-18-2015, 10:28 AM
There's an interesting article in the 22 December 2014 of the New Scientist titled "Is the answer to life, the universe and everything 37?", which discusses the mathematical analysis of the structure DNA carried out by Vladimir I. shCherbaka and Maxim A. Makukov. What they found was that there are about nine "patterns" or "codes within the code" embedded in the very basic structure of DNA - that is, the triplets of letters (called codons) and the chemical structure of these letters.

Here's a quote from the NS article:

"It was clear right away that the code has a non-random structure," says Makukov. "The patterns that we describe are not simply non-random. They have some features that, at least from our point of view, were very hard to ascribe to natural processes."

Exhibit A is Rumer's transformation. In 1966, Soviet mathematician Yuri Rumer pointed out that the genetic code can be divided neatly in half (see "Rumer's transformation"). One half is the "whole family" codons, in which all four codons with the same two initial letters code for the same amino acid. The AC family, for instance, is "whole" because codons beginning AC code for threonine. On the other are "split family" codons, which don't have this property.

Rumer first noted that there is no good reason why exactly half of the codons should be whole. More profoundly, he also realised that applying a simple rule – swapping T for G, and A for C – converts one half of the code into the other.That might sound inevitable, but it is not. In 1996, mathematician Olga Zhaksybayeva of the al-Farabi Kazakh National University calculated that the probability of it occurring by chance is 3.09 Ũ 10-32.

And Rumer's transformation is just one of many patterns and symmetries within the code. Another example: you can create a subset of codons including those with three identical bases (AAA, say) and those with three unique bases (GTC, say). Using a Rumer-type transformation, these 28 codons can be divided into two groups each with a combined total atomic mass of 1665, and a combined "side chain" atomic mass of 703 (see "Transformation #2"). Both are multiples of the prime number 37, which has interesting mathematical properties of its own (see "Symmetries of 37").

In fact, 37 recurs frequently in the code. For example, the mass of the molecular "core" shared by all 20 amino acids is 74, which is 37 doubled. Forget 42...

All in all, the Kazakhs have identified nine patterns in the code, which they spell out in detail in the journal Icarus (vol 224, p 228) under the provocative title "The 'Wow! signal' of the terrestrial genetic code".


The original Vladimir I. shCherbaka and Maxim A. Makukov paper can be found here: http://arxiv.org/ftp/arxiv/papers/1303/1303.6739.pdf, though I warn you, it's a bit technical. :D

Of course, as the NS article points out, this could all just be numerology: "If you crunch numbers long enough, you'll find patterns in almost anything". Food for thought though! ;)

127082 127083 127084

prometheus
02-18-2015, 01:23 PM
To be even cockier :D - the golden ratio isn't unique to the fibonacci numbers. You can start with any two numbers and follow the same rule (adding the last two gives a new number) and it's approaching the golden ratio. Or so they say, I haven't been bothered to check :-)
And yeah, I've watched to many episodes of numberphile on YT :D
Anyway, I agree - the beauty of math is amazing!

Uhmm..well isnīt that just what the fibonacci series describes by the defined sequence approach? itīs just about the sequencing, not the actual numbers themself.
so you are right about the non unique numbers, but fibonacci classification is about the serial sequence, not fibonacci numbers....I think:D

Slartibartfast
02-19-2015, 01:52 PM
Uhmm..well isnīt that just what the fibonacci series describes by the defined sequence approach? itīs just about the sequencing, not the actual numbers themself.
so you are right about the non unique numbers, but fibonacci classification is about the serial sequence, not fibonacci numbers....I think:D

No, Fibonacci begins with 1, 1 by definition. But that might not be very important in this thread :D