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# SQRT(2) Lego

 (+8) [vote for, against]

Lego, but with the blob spacing exactly the square root of 2 times bigger than usual, so that it links with normal Lego, but at a 45° diagonal.
 — hippo, Mar 05 2011

Diamond Shreddies -> Diamond Lego? http://meanwhile.wo.../diamond-shreddies/
Could the same concept be applied to Lego, thus baking the idea? [AntiQuark, Mar 05 2011]

Hippo Lego http://www.brothers...2/06/i-like-hippos/
[Ling, Mar 14 2012]

Lego Geometry Document (MS Office .doc Format) http://www.brickshe...ry/legogeometry.doc
[zen_tom, Mar 14 2012]

The (very good) book "Badass Lego Guns" has an excellent diagram of all the angles that 'Technical Lego' struts can be made to interconnect. This is what [Alterother] means. It's not quite the same as this idea though. [hippo, Mar 14 2012]

Hippasus got a raw deal. [+]
 — 2 fries shy of a happy meal, Mar 05 2011

Just make them N-dimensional. Easy!
 — RayfordSteele, Nov 08 2011

 Erm, *pure* genius. Here's a V¯2 croissant [x]

What, and how much would the machine cost that you'd need to injection-mould a whole bunch of these?
 — zen_tom, Mar 14 2012

I have no idea.
 — skinflaps, Mar 14 2012

I like the ideo of an art project that riffs on legos. There are enough lego ideas on the HB to fill a category.
 — bungston, Mar 14 2012

Firstly, there are already Lego pieces that connect at 45 degrees and many other angles on several axes, and secondly, isn't the square root of two an irrational number?
 — Alterother, Mar 14 2012

 There are, but they don't allow the continuation of an angled side. So if you imagine a base of 100x100 studs - you can only place bricks orthagonally - but a piece with root2 spacing on its base and regular spacing on its surface, you'd be able to start off a diagonal wall.

 Other piece types might include ones that translate from regular bottoms to root2'd tops, and various mitred arrangements for dealing with the connections between straight and diagonally aligned pieces.

On the second point [Alterother] - yes it is - but then so is pi, and that hasn't stopped us from successfully enjoying wheels, biscuits and other circular technology.
 — zen_tom, Mar 14 2012

I think I see what you're getting at, but (I may be wrong) you still can't build a physical model of an irrational number. It would be like trying to make the spacing aspect ratio 1:pi.
 — Alterother, Mar 14 2012

 No, fair enough, there's always going to be some tolerance - but root2 is the ideal if you want to create a range of bricks that would be integrated with the larger system.

I think you'd need to also introduce a new range of bricks with normal spacing tops and bottoms, but who's lengths were multiples of root2. So if there's currently bricks of length 1, 2, 4, 8 and 16 - you might also want to introduce ones of 1V¯2, 2V¯2, 4V¯2 etc which would allow you create neat diagonally (i.e. NE, NW, SE, SW) oriented walls who's edges would line up (perhaps with neat little mitres) nicely with traditional (N,E,S,W) walls.
 — zen_tom, Mar 14 2012

 Sorry--I know you can get it really close, but I'm a stickler when it comes to practical geometry. Too much fabrication and machining will do that to you.

The idea is good, but unless I'm entirely missing the point I still think it's doable with regular Lego. It might require some hard-to-find or discontinued pieces; I haven't messed around with them since the '90s. I can't remember what they were called, but the special bricks with the rows of holes all along could be configured in almost any position using the little connector pegs. Of course, using those to build a multiaxial structure might get pretty bulky. Your way would be much more elegant.
 — Alterother, Mar 14 2012

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