How to Build Angular Structures

Lego is primarily designed for building parallel and in right angles. Therefore building off-grid can be fairly challenging. However, there are certain techniques that allow you to build stabile angled structures.

This tutorial will show you some of the techniques that can be used to build angular in the horizontal plane.

Using the Pythagorean Theorem

As you probably know, the Pythagorean Theorem is a formula which is valid in all right-angeled triangles.
It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

a²+b² = c²

Probably the easiest example for this is a triangle with 3, 4 and 5 as side lengths:

3²+4²=5²--> 9+16=25

Here in Lego form:

As you can see 9 (orange plates) + 16 (green plates) = 25 (blue plates). How is that useful for building with Lego? With these dimension you can now build a right angled triangle which is indeed useful in many ways:

Of course this works for all side lengths as long as they have the same ratio. In this one for example all side lengths were multiplied by 3. (now they are 9, 12 and 15)

With these techniques you can for example build a diagonal wall on a normal base plate.

Using Diagonals

As you know the diagonals of rectangles and squares have in each case the same length. This can be used for your advantage in building.

As you can see in the picture above it does not matter which way the orange plate is turned since the diagonals are the same. It also doesn't matter how big/small the orange plate is.

You can then connect everything together eith hinge plates and for instance create a "curved" window.

Wedge Plates

Angled plates or "wedge" plates as they are often called can also be used to create angled builds. While not as stable as the other techniques from above they still can be used in many ways.

If you repeat the technique from above you can buld a circle:

'Illegal' Techniques

Of course there are also other possibilities for building angularily which are mathematically not perfect or simply "illegal". That, however, does not prevent them from being useful in building. Recently I found one that is quite handy.

This was especially designed for fighter plane wings.

Thanks for reading!

Do not forget to do the poll on top to let us know whether you find this useful. Also feel free to share your thoughts in the comment section and to suggest any other building technique that you think should be added.