Angled lego pieces

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Written by William. LEGO elements, especially bricks and plates, are often viewed as being incredibly square. They create great straight lines, but when it comes to angles, you often need to hunt down a specialized facet brick or wedge plate for the job. Well, what if I told you there are ways to angle your most basic elements easily? The answer to this building challenge has to do with right triangles. These are triangles that have one degree internal angle.

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. We will need to get into some basic trigonometry to explain this.

If you read my post on angled wallsangled lego pieces, 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. Cheers, Chris.

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Note: An updated version of this post has been published here. If you look at a LEGO baseplate, you will see that the studs on it are arranged in a regular grid with any two neighboring studs exactly 0. However, this is true only if you are measuring the distance parallel to one of the sides of the baseplate. Herein lies the problem — you can place bricks every which way on the baseplate as long as they are parallel to one of the sides of the baseplate. But as soon as you turn the bricks to an angle different from 0 or 90 degrees, the studs no longer line up. The trick to placing bricks at a different angle with good stud connections at both ends is making sure the triangle you form satisfies the Pythagorean Theorem.

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? Remember the regular square grid I mentioned earlier? If you take any stud on the baseplate, it is exactly the same distance away from each of its neighbors on all 4 sides and that distance happens to be 0. That is because in a square, the 4 sides are of equal length but the distance between any two opposite corners is a little longer. Similarly, the distance between any two studs measured at any angle other than 0 or 90 degrees is not guaranteed to be a whole number of studs. So what exactly is going on here?

Atrioc

I think not. Now we can inflate by one to straighten out our measurements and get 10, 13, and Just make sure to have a mirror image of the first triangle if you want an angle. A right angled triangle with a 45 degree angle is called the special right triangle. Which happens to be the space distance between studs. Glad you spotted that! Triangles have three points. 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? Nofakebrick September 24, , PM. I hope their creations turn out great! September 24, , AM. The The studs on these two bricks are now able to hold a plate that is six studs long just like you get with a normal baseplate. So when I had a conversation with a friend about triangles this kind of all fell into my lap. ToyPro will keep you updated from now on. And should you have any questions or need.

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.

Nofakebrick September 24, , PM. You can place them at the bottom in between the studs instead of below the studs. The smallest Pythagorean triple set of numbers that satisfies the theorem is 3, 4, 5 and that is the one the Boutique Hotel uses. Larger plates can be handled in a couple of ways. Sideways bricks always add in an extra level of measurement sincey use what I call the 2, 5 rule. Fingers crossed. This works. Hence the inflation method. I was just using trial and error until the studs matched up, but I thought that there must be some formula for this. This puts us on the fourth stud so we add a round plate. I tend to use trial-and-error when trying to build with angles, but I really should start using my math skills instead. Basically, I flip the numbers. The reason for this is that the LEGO system is built on exact measurements. Choose a category to refine your search.