Angled lego pieces

Written by William. LEGO elements, especially bricks and plates, are often viewed as being incredibly square.

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Angled lego pieces

In this new series of posts, I will try to use math to explain how some of these techniques work suggestions are always welcome for the techniques I should cover next. The first thing that draws your attention to this modular building is its unusual triangular shape. LEGO as we know is based on a regular square grid of stud locations and so how did they pull this shape off and can we figure out the math behind it? If you read my post on angled walls , you will see that the trick to placing LEGO pieces at any angle other than 0 or 90 degrees relative to the LEGO grid is by ensuring that the studs at the two ends of the brick or plate line up with studs on the LEGO grid. The smallest Pythagorean triple set of numbers that satisfies the theorem is 3, 4, 5 and that is the one the Boutique Hotel uses. But it uses the triple in a way that is not immediately apparent. In fact, if you look at the angled walls in this build, you can count not one but 6 separate 3, 4, 5 triangles including two 4 and 6 that even intersect each other. The hypotenuses of triangles 5 and 6 are at right angles to the line connecting the hypotenuses of triangles Even more interesting is the fact that the floor sections separating the 3 levels of the building as well as the roof section are built using regular plates and wedge plates and somehow their angled sides line up perfectly with the angled walls of the building. I think not.

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In this new series of posts, I will try to use math to explain how some of these techniques work suggestions are always welcome for the techniques I should cover next. The first thing that draws your attention to this modular building is its unusual triangular shape. LEGO as we know is based on a regular square grid of stud locations and so how did they pull this shape off and can we figure out the math behind it? If you read my post on angled walls , you will see that the trick to placing LEGO pieces at any angle other than 0 or 90 degrees relative to the LEGO grid is by ensuring that the studs at the two ends of the brick or plate line up with studs on the LEGO grid. The smallest Pythagorean triple set of numbers that satisfies the theorem is 3, 4, 5 and that is the one the Boutique Hotel uses. But it uses the triple in a way that is not immediately apparent. In fact, if you look at the angled walls in this build, you can count not one but 6 separate 3, 4, 5 triangles including two 4 and 6 that even intersect each other. The hypotenuses of triangles 5 and 6 are at right angles to the line connecting the hypotenuses of triangles Even more interesting is the fact that the floor sections separating the 3 levels of the building as well as the roof section are built using regular plates and wedge plates and somehow their angled sides line up perfectly with the angled walls of the building. I think not.

Angled lego pieces

There are quite a few as you can imagine, but each time the studs of the brick have to line up with the studs of the baseplate under it. That is just how LEGO works. Suppose you are building a castle out of LEGO and one of your walls needs to be at a 45 degree angle, are you out of luck?

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Pretty neat, eh? Now we attach a six-long piece over those plates and find it works! We often say LEGO is great for building something square. A right angled triangle with a 45 degree angle is called the special right triangle. Building sideways will work the same, it is just a bit more involved making sure everything lines up. The big number is the hypotenuse, or the angled leg of the triangle. I enjoyed. Make the house even more realistic by adding LEGO dolls that live in the house. The stud on its side is near the top edge which means you have a half plate thickness gap at the mottom. I tend to use trial-and-error when trying to build with angles, but I really should start using my math skills instead. That is especially true since right triangles have a very square component to them.

Note: An updated version of this post has been published here.

Loved your explanation on using the hypotenuse, that technique is way clearer in my head now than it used to be! Again my solution for this is to use those bricks that are five plates high, typically used in Brickheadz, stack them all up, then figure out what you need to remove in order to leave the studs you want. On the other side in section B, is a brick height which is 3 plates or 0. Fingers crossed. The side that was 5 long is now 9 and the side that was 9 is now 5. This works. Basically, I flip the numbers. In a right angled triangle for either of the smaller angles, the ratio of the length of the side opposite the angle to the side adjacent to it is called the tangent and this ratio is fixed for a given angle regardless of the size of the triangle. September 24, , AM. Pretty neat, eh?