![]() If we draw a line from the vertex (corner) opposite the longest side (or hypotenuse) so it intersects the hypotenuse at a right angle, we would get two identical right triangles with dimensions (8.5,8.5,12). So the designers chose to connect one side of the gas station island to a 2×2 tile with a hole (this attaches to the bottom of the 4×4 round plate to form a turntable) and leave the other side unconnected (it simply rests on the 2×2 black turntable base). The gas station island has two 4×4 round plates that are 6 studs apart (center to center) but there is no way to connect both these at a 45 degree angle given that there are no “near triples” with 6 as the biggest number. These posts connect the awning to the gas station island but the island itself is connected to the base in just one spot. The awning is supported by two vertical posts that are created using technic axles and axle connectors. It is attached to the angled wall of the garage using a hinge assembly consisting of a 1×3 tile with 1 finger on top (attached to the angled wall) and a 1×2 brick with 2 fingers (which is incorporated into the awning itself). Taking a closer look, we see that the awning is 16×10 studs wide with rounded corners. ![]() But it is a little less obvious how the math works here. ![]() “Near triples” also come into play in the way the awning is attached at a 45 degree angle (relative to the baseplate). The 1×2 rounded plates act like hinges and provide a firm connection while allowing a little bit of wiggle room. But the length of the hypotenuse in a right triangle where the other two sides are 12 is √(12 2 + 12 2) = 16.97 which is close enough to 17. Now, (12,12,17) is not a Pythagorean triple strictly speaking. I wasn’t aware of any official sets that used “near triples” until I looked through the instructions for the Corner Garage 10264 modular set that LEGO released in early 2019. I have used “near triples” like (5,5,7) and (7,7,10) often in my builds and some of these have the added advantage of allowing us to create walls at 45 degree angles (which is not possible with Pythagorean Triples). This minimizes the strain that you are putting on the LEGO elements when you make the connections for the angled section. When we create angled walls using “near triples”, it is always a good idea to use elements like hinges that naturally have a little bit of wiggle room. However in certain situations, it is possible to fudge the math a bit and get away with a triple (set of 3 numbers) that is not a Pythagorean triple strictly speaking, but is close enough for practical purposes. Most applications of the Pythagorean Theorem use the smallest and most common triple (3,4,5) as in the Boutique Hotel set covered here or a multiple like (6,8,10) used in the Spring Lantern Festival set. Michigan Avenue (John Hancock Center)Īs we have seen here, we don’t have a lot of options to choose from if we just limit ourselves to Pythagorean Triples.
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