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== Definition ==
 
== Definition ==
{{Geomag-construction|Title=Suspended Circle|Filename=Suspended Circle.jpg|Type=[[Suspended Circle|Abstract]]|Squares=44|Rods=353|Spheres=131|Author=[[User:Jeffkoslo|Jeffkoslo]] 22:05, 3 May 2007 (UTC)}}
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{{Geomag-construction|PageTitle=Suspended Circle|Title=Suspended Circle|Filename=Suspended_Circle.jpg|Type=[[Suspended Circle|Abstract]]|Squares=44|Rods=353|Spheres=131|Author=[[User:Jeffkoslo|Jeffkoslo]] 22:05, 3 May 2007 (UTC)}}
   
 
A fully suspended closed circle on two support legs. The loop is composed of 34 segments, alternating trianges with pyramids.
 
A fully suspended closed circle on two support legs. The loop is composed of 34 segments, alternating trianges with pyramids.
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# Continue adding segments upwards to complete the entire circle.
 
# Continue adding segments upwards to complete the entire circle.
 
#* Keep the two sides balanced as you are building upwards.
 
#* Keep the two sides balanced as you are building upwards.
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{{clr}}
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== Calculations ==
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Let alpha = arcsin(1/sqrt(3)) = 35.264 degrees, be the semi-apex angle of an equilateral square-based prism.
   
== Properties ==
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(A mnemonic for this is that the inclination of a face is 54.7 degrees, which is the complement, and is half the well-known "bond angle of methane" at 109 degrees 28 minutes, which I've always remembered for some reason).
   
* Structure is fully supported on the two support legs, which can be made longer if desired.
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Then each segment of the curve moves through 2*alpha - 60 degrees = 10.528 degrees
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So, 34 segments move through 357 degrees, which is just 3 degrees short of a complete circle, and easily close enough for the structure to absorb the error.
   
 
== Examples ==
 
== Examples ==
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<gallery>
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Image:SS_0.JPG|Segment detail
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Image:SS_1.JPG|Arc with support legs
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Image:SS_2.JPG|More than half way
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Image:SS_3.JPG|Almost there
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Image:SS_4.JPG|Complete circle
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Image:SS_5.JPG|More arcs
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Image:SS_6.JPG|Alternate view
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</gallery>
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== Other Builder Notes ==
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I just built this for the first time: boy it's tricky! It collapsed a couple of times on me before I hit on the idea of supporting the base of the arc during construction. I used a book, and opened just enough pages to offer firm support to the base panel.
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With just five panels to go, I built the last five segments 'off piste', then dropped it in place (with the help of an assistant).
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I'm excited to report that this is one of those models that achieves a magical strength once completed, and with care can be picked up and moved.
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[[User:Karl Horton|Karl Horton]] 22:20, 23 June 2007 (UTC)
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[[Category:Polyhedron]]
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[[Category:Ring]]

Latest revision as of 00:06, November 4, 2009

Definition Edit

Suspended Circle
Suspended Circle
TypeAbstract
Panels 44 × Geomag square panel icon
Rods 353 × Geomag rod icon
Spheres 131 × Geomag ball icon
Author Jeffkoslo 22:05, 3 May 2007 (UTC)


A fully suspended closed circle on two support legs. The loop is composed of 34 segments, alternating trianges with pyramids.

Building Instructions Edit

  1. Create the bottom arc of 9 segments.
  2. Add the support legs downward from the ends of the arc.
  3. Continue adding segments upwards to complete the entire circle.
    • Keep the two sides balanced as you are building upwards.


Calculations Edit

Let alpha = arcsin(1/sqrt(3)) = 35.264 degrees, be the semi-apex angle of an equilateral square-based prism.

(A mnemonic for this is that the inclination of a face is 54.7 degrees, which is the complement, and is half the well-known "bond angle of methane" at 109 degrees 28 minutes, which I've always remembered for some reason).

Then each segment of the curve moves through 2*alpha - 60 degrees = 10.528 degrees

So, 34 segments move through 357 degrees, which is just 3 degrees short of a complete circle, and easily close enough for the structure to absorb the error.

Examples Edit

Other Builder Notes Edit

I just built this for the first time: boy it's tricky! It collapsed a couple of times on me before I hit on the idea of supporting the base of the arc during construction. I used a book, and opened just enough pages to offer firm support to the base panel.

With just five panels to go, I built the last five segments 'off piste', then dropped it in place (with the help of an assistant).

I'm excited to report that this is one of those models that achieves a magical strength once completed, and with care can be picked up and moved.

Karl Horton 22:20, 23 June 2007 (UTC)

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