Plastic number/ Harriss spiral

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 From:  bemfarmer
8351.1 
Plastic number fractal:

https://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/13/golden-ratio-beautiful-new-curve-harriss-spiral

Based upon the plastic number, this spiral is essentially the same as the Harriss spiral, but instead of using a
side ratio of 1/1.325, uses the ratio 1/1.32471795724474602596, 1/plastic number.
The golden ratio of ~1.61803 is a solution of the equation x*x = x+1.
The plastic number is a solution of the equation x*x*x = x+1.

MoI was used to construct the fractal spirals.
A base line along the x-axis of 50 cm was used.
An end point was scaled by entering 1/1.3257...
The resulting point was rotated 90 degrees to create the upper left corner of a rectangle.
This single scaling was enough to establish the plastic ratio rectangles.
Orient LineLine was used extensively to lay out the rectangles, which also did scaling.
Arcs were placed, and or swept, and again Orient LineLine was used.
Trims and Booleans were used.
BlendCap was used.

- Brian



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 From:  bemfarmer
8351.2 In reply to 8351.1 
I used free 7Zip because it makes a much smaller file than zip,
and I have used up attachment allotment of ~56MB, despite spring house cleaning:-)
- Brian
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 From:  Frenchy Pilou (PILOU)
8351.3 In reply to 8351.2 
yes but sometime unzip an 7zip 7zp don't work very well! ;)
Classic zip is more sure!
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 From:  futagoza (STEFAN)
8351.4 
Hi Brian,

maybe a file storage service like Dropbox etc. can help.

Regards
Stefan
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 From:  Frenchy Pilou (PILOU)
8351.5 
Or Mediafire : 50 Gigas Free!
---
Pilou
Is beautiful that please without concept!
My Gallery
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 From:  TOM (SIRTOM)
8351.6 In reply to 8351.1 
Beautiful ! Never heard the term "plastic" in relation to geometry. Where does it come from ?
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 From:  bemfarmer
8351.7 In reply to 8351.6 
Re: Plastic name:
See history and Hans van der Laan:
https://en.wikipedia.org/wiki/Plastic_number
- Brian

Also mathematical interest:
http://mathworld.wolfram.com/PlasticConstant.html
I may try for a Snub Icosidodecadodecahedron :-)

EDITED: 19 Mar by BEMFARMER

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 From:  bemfarmer
8351.8 In reply to 8351.7 
One of the 75 uniform polyhedral.

Simple .obj file of DodecaDodecaHedron solid. Import with Max's _ImportObj script.
Can change color on non-triangles.
The pentagrams are indented, whereas paper models show planar pentagrams.
The coordinates are here, but must be edited to get an .obj file.
Vertices must be indexed by 1, not zero.
- Brian

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