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Pantheism and the Nautilus
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April 20, 2015, 02:49:37 AM
#15
Looks a bit like an Artist's Impression of the Big Bang.

By the way, I enclose a picture of a Romanesco - allegedly a bit like a cauliflower-broccoli blend.   Anyway it contains cones on its surface ranging medium to large - and arranged according to a logarithmic spiral ...

BUT ALSO,  each cone has a set of mini- cones varying small to medium, all ALSO arranged in mini-spirals ?

I am guessing this would be a great opportunity to use a block :)   
cheers

PS Then of course there is the humble pinecone ...  where the same pinecone can have spirals going in two directions. (jpegs refer) - As you say, depends how you look at it.
« Last Edit: April 20, 2015, 03:05:30 AM by samdavo »

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April 21, 2015, 09:02:41 PM
#16
Anyone familiar with the Fibonacci spiral  - made with quadrants (and a compass).   The first rectangle is drawn with an aspect ratio of  1.618034:1 (golden ratio).

It is interesting that a golden spiral (logarithmic - drawn with progressive spokes at 15 degree intervals, (24 in a circle), each 1.08356 times longer than the previous) and a Fibonacci spiral (made with quadrants) are near as dammit identical.

http://en.wikipedia.org/wiki/Golden_spiral

I calculate that the ratio of lengths of spokes in the same direction (after another revolution) would be 1.08356^24 = 6.86. (PS and btw, 1.08356 is the 6th root of the golden ratio 1.618034)

Also, just looking at those Fibonacci quadrants, the linear scaling between each "similarly oriented rectangular shape" is also 6.854 - (PS which incidentally is the golden ratio 1.618034 to the 4th power). (2 cents)

« Last Edit: April 22, 2015, 12:28:39 AM by samdavo »

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April 28, 2015, 04:12:46 AM
#17
I find this interesting "Archimedes Spiral Gears"  (nothing to do with logarithmic spiral).
https://www.youtube.com/watch?v=bbp0SYEpjrg
This  gearbox keeps changing between 1st gear and overdrive with each revolution.  Boy would that be a bumpy ride lol .
cheers

PS I thought I could draw one module ( consisting of two spokes and three cogs) and use circular array to get the full spiral - with a radial .   But as the radius ratio of 2.   But I find that as the radius increases, so too does the distance between the modules - so that in effect cogs are missing.  ( 2 cents)


Ahh ... I think what you have to do is set two handles on said module, and then it would work, and you would have neat gears around the rim.   For another day.  Maybe someone else knows the best way to draw those gears (?) :)

« Last Edit: April 28, 2015, 05:19:36 AM by samdavo »

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April 28, 2015, 08:12:08 PM
#18
ok, a serious question.
That set of Archimedes gears ( 3 parts) were apparently 3D printed. 
Presumably (?) you could do that WITHOUT the need to be able to disassemble into 3 parts, i.e. they could be wrapped around each other from the getgo (?)  Including axles and bushes at each gear centre (?)

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