![]() ![]() It is not possible to place a LEGO element along this side, but if we mirror the right triangle along the hypotenuse, we can create an angled wall by placing LEGO elements along the other two sides of the second triangle. The length of the hypotenuse (angled side) would be √(6 2 + 2 2) = 6.32 studs which is not a whole number. Let us start with an arbitrary right triangle – say the sides that make up the right angle are 6 studs and 2 studs long. This opens up quite a few other possibilities … There are a few other techniques where we don’t actually place any elements along the hypotenuse and can therefore disregard its length. But for this to work, the length of the hypotenuse has to be a whole number of studs and this limits our options to Pythagorean triples and near triples. The techniques we have seen so far create angled walls by placing elements along the hypotenuse (angled side) of a right-angled triangle. This article would not be complete without at least a mention of a few other ways of building angled walls using LEGO. If we were to use the method described earlier to build angled walls, there is just no good way to avoid gaps at the corners where the angled wall segments meet the regular wall segments placed along the LEGO grid. As you can see, there are not many with practical applications in LEGO builds. What are some other Pythagorean Triples ? Listed below are all the Pythagorean Triples with numbers less than or equal to 25. Any set of 3 numbers that satisfies this theorem is called a Pythagorean triple and (3, 4, 5) is the smallest such set made up of whole numbers. So the bottom line is that for any brick or plate to be placed at an angle other than 0 or 90 degrees, you need to make sure the resulting triangle satisfies the Pythagorean theorem. Then, does it make sense that we used a 1×6 brick for the longest side ? Yes, because the three sides of the right angled triangle intersect at the studs and the distance that really matters is the distance between the studs at the two ends of the 1×6 brick which is 5 studs. ![]() The triangle we created satisfies the Pythagorean theorem because 3 2 + 4 2 = 9 + 16 = 25 which is equal to 5 2. Our 1×6 brick is placed along the third (and longest) side, also known as the hypotenuse. If we count along the two sides of the baseplate starting from the corner, we see that the 1×1 plates are 3 and 4 studs away from the corner stud and make up two sides of a right angled triangle. Let’s take a closer look at where the two 1×1 plates were placed on the baseplate. Different versions of Empire State Building. ![]()
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