C091105-karlhorton Self Intersection [challenge]

C091105-karlhorton Self Intersection [challenge]

Postby karlhorton » Thu Nov 05, 2009 2:35 pm

C091105-karlhorton build a stable, self supporting model with at least one self-intersecting rod.

A self-intersecting rod is a rod that passes through the triangle formed by three other rods.
The solution I have in mind works best with the new longer bars,
because there is more space, but is completely build-able using classic Geomag.
It does not involve panels, and uses fewer than thirty rods.

As this is the first post to the challenges group we have no guidelines yet, so I'll propose some:
  1. Challenge name - of the form Cdate-handle, so that it can be referred to easily
  2. Challenge solution should be posted 1 week after the initial post
  3. Threaded keep discussion about a challenge all on the same thread

Hint: In the bad old days before panels you could stabilize square faces with
triangles making pyramids. The obvious thing to do is to orient the apex of the pyramid outwards.
But what if you pushed the spike inside?
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Re: C091105-karlhorton Self Intersection [challenge]

Postby Wim » Tue Nov 10, 2009 6:18 pm

So if I understand this correctly, you're looking for a model that has a rod passing through a triangle, is stable and self-supporting?

Is this one construction that consists of two intersecting parts? Or is it something that is simply has a bar going through a triangle as part of its own stabilizing structure? I'm having a hard time visualizing the objective. It doesn't help that I don't have any Geomag at my desk at the moment.

Is there a general shape you're looking for other than that it has at least one square face?

I have one made with Supermag (desk toys, since my Geomag is at home), but I really don't think it'll be possible with Geomag... Don't have a camera with me, so I can't take a picture at the moment either. But the outside is 4 triangles and 3 4-sided edges. One of the 4-sided shapes is braced with 4 other bars like a pyramid, while the triangle that is on the opposite side of the structure intersects three of the four triangles of that bracing pyramid. Only the triangle at the bottom of the bracing pyramid does not have an intersect, and the 4-sided side there is the most square of the different 'walls'. However, even with the tapered ends of Supermag it is tight and the connections aren't perfect. The structure is stable, but quite ugly :). I suppose if I grab some larger spheres I can make it work.

Combined part count: 9 balls, 12 bars for the walls, 7 bars for the bracing (19 total).
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Re: C091105-karlhorton Self Intersection [challenge]

Postby Wim » Mon Nov 23, 2009 4:37 pm

This was the 'solution' I talked about:

IMG_3330.JPG
My solution


I'm pretty sure that's not what you were looking for though.
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Re: C091105-karlhorton Self Intersection [challenge]

Postby karlhorton » Tue Nov 24, 2009 4:14 am

Wim, I have to give that one to you .... even though you used Supermag, hopefully
Peter "rod & ball purity" Jepsen won't delete your post!

My solution is very close: it's a square antiprism with inward-facing supports.

Whichever way you cut the cake it has steric interference with Geomag: it's a fundamental
limitation of the system - balancing large strong magnets with small balls.

Here are a few ways to make it more elegant:

1. use double-length Geomag rods.
2. use those wonderful long Supermag bars
3. use the new Geomag kids
4. use the new Geomag kids with 5/8" balls

Solution 4 does look quite elegant: pictures soon.
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Re: C091105-karlhorton Self Intersection [challenge]

Postby Wim » Tue Nov 24, 2009 4:12 pm

Thanks Karl. I'm looking forward to seeing your pictures. Speaking of which, I was messing around trying to recreate one of your Flickr images and couldn't get it done. I noticed this morning that it was on the Wiki as well (which I can access at work, so I figured I'd try it during my lunch break). Sadly enough, I forgot to bring the box of Geomag I had prepared for this so it will have to wait another day.

As far as using Supermag, I hope Peter won't have a problem with it either. And it's not like the brand still exists anyway so it's not the competition anymore :).
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Re: C091105-karlhorton Self Intersection [challenge]

Postby Peter Jepsen » Tue Nov 24, 2009 6:19 pm

Nah, I don't have a problem with Supermag being mentioned here in this context. I have a nice collection of Supermag at home too, the 'classic' with only two different lengths.
But certainly, if a user made a post trying to sell or advertise that or another competing product, someone up in Management would probably have a fit and the banhammer would be swung. And I'd be put in the corner with the Dunce hat for the rest of the day. This Forum is for and by the fans, but internally in the Geomagworld company it is my baby.
Regarding the Supermag brand not existing anymore, I don't think that's true. The web site is alive and well and as our 'colleagues' I hope they are getting by just as we are.
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Re: C091105-karlhorton Self Intersection [challenge]

Postby Wim » Tue Nov 24, 2009 6:31 pm

Ah. Thanks Peter. Odd... I tried a month or two ago and the related websites could not be reached, and every link I tried from Google failed so I assumed that they were gone, just like the GeomagSA website was at that time. And like Geomag it's not in stock in any store in the US either, hence my conclusion.

Speaking of stores... Hopefully I'll be able to find a brick and mortar store in The Netherlands that sells Geomag next time I'm there. I have some Euros to use up :).

Heh. And don't worry about me trying to sell anything. I'm a pack rat. :D
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Re: C091105-karlhorton Self Intersection [challenge]

Postby Peter Jepsen » Wed Dec 02, 2009 3:05 pm

Is this one qualified?
DSC01568.jpg
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Re: C091105-karlhorton Self Intersection [challenge]

Postby Wim » Wed Dec 02, 2009 4:36 pm

That's a very cute model. I like it.

However, it looks like it's two models intertwined, and as such not a "stable, self-supporting model", since it's the table that supports both parts instead of it supporting itself (yes, it can support itself too, but then it's not stable as it'll be wobbly :)).

However, that leads me to thinking. If you take the classic tetra with 4 spheres locked inside it, and you connect rods to those spheres, would that count as intersecting? Because that could certainly become self-supporting and stable... Although I can't try it right now, and the rods may not connect perfectly at the spheres given the thickness of the rods.
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Re: C091105-karlhorton Self Intersection [challenge]

Postby cappells » Thu Dec 03, 2009 11:06 pm

I did it with 24 rods. Met all the criteria, especially the free-standing, self supporting using Geomag. I'll post pictures later.

Here is the picture as promised:
intersect2.jpg
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