It's all maths, you see

[pne]

Yesterday, I was playing around with some of Amy's Lego, and was placing some fences on a board.

I was surprised to find that the fence, which I had placed at a random angle rather than horizontally or vertically, seemed to fit perfectly! Since diagonals are not, in general, a whole number of units long, I found this surprising... perhaps the distance was close to a whole number? But it fit rather too well for it to be chance.

It was only after a looked at the result more closely and counted that I realised what was happening. (I was also, at first, misled by an off-by-one problem: the number of bumps that are "covered" by a fence are not, of course, the number of spaces between bumps.)

Here are a couple of pictures. (From after I had placed some more fences; at first, there was only one of the short white fences.)

(How quickly) can you figure it out?

Comments

[arthur-sc-king.livejournal.com]

a = 3, b = 4, c = 5. Thanks, Pythagoras!

[ubykhlives.livejournal.com]

The joyous joys of the smallest Pythagorean triple, of course!

(...darn, looks like I was beaten to it. And I was so proud of noticing, too.)

[pthalo]

another vote for pythagoras

[elgrande.livejournal.com]

Wow. So it comes as no surprise that the fences are and must be 5 units long. I always thought they just chose a random length.

[pne.livejournal.com]

I always thought they just chose a random length.

That would have surprised me with Lego -- most things are designed to work together, so it would make sense that the bottom feet would fit over a standard nob and be a whole number of nobs apart. (And typically an odd number of nobs apart, since most boards and bricks have an even number of nobs on each side.)

[ubykhlives.livejournal.com]

It's odd, because (apparently as pne also had) I'd always thought of them as being six units long, counting each nub as being a unit, perhaps because one can get blocks that only cover one nub; it's hard to think of such blocks as having zero length.

Usually Lego blocks are 1, 2, 4, 6 or 8 nubs in length; 3 nubs is rarer, and 5, 7 etc. are never seen. (Almost. I have seen propellor blocks whose wingspan is 5 nubs. Of course, the Technic sets have 10-, 12- and 16-nub blocks also, but they're a different story altogether.)

[pne.livejournal.com]

(Possibly) interestingly, there are also varied opinions on how to specify certain sizes.

I remember disagreements with a friend when I was a kid on whether a 4x2 block was to be called an "Achter" or a "Vierer" (i.e. with a name derived from "eight" -- the total number of nubs -- or "four" -- the number of nubs along the long side, with two being the number along the short side by default). (I don't remember which side I was on, though, or what I'd call such a block now, other than "regular", since I consider it the most common basic block.)

[pne.livejournal.com]

with two being the number along the short side by default

A consequence of this is that I consider a 1x2 block to be one nub "long" and two nubs "wide", even though this means that the length is smaller than the width.

[tungol.livejournal.com]

We had confusion over how to name the lengths of Lego blocks too, but it was over what counted as one unit.
There was confusion over whether a 'onesie' was 1x1 or 2x2, and whether a 'twosie' was 1x2 or 2x4 - since most blocks were two wide, it was easy to think of a 4-bump square as being a single unit. Also possibly we met the 1-wide blocks later than the 2-wide ones.

[sparkofcreation.livejournal.com]

Looks like a 5-4-3 triangle to me, but I admit I discovered the same thing with my Legos as a child.

[mendel.livejournal.com]

I looked at it expecting a 3-4-5 triangle, but then I counted 6 nubs and got thrown off track, having made an, erm, appropriate error. :-)