![]() ![]() ![]() If the polygon has n sides, the central angle would be 360/n. First, we will start with the central angle. Let us figure out how the apothem can be calculated if we know n (the number of sides) and the length of each side in studs. This will allow us to attach the polygonal wall firmly to a baseplate. If we create a regular polygon using LEGO pieces, we need to ensure that the distance between any pair of opposite sides (which would be twice the apothem) is close enough to a whole number of studs. Shown below is a hexagon with 6 equal sides that we will be using for illustration purposes. In a regular polygon all the interior angles are also equal. The points where any 2 adjacent sides intersect is called a vertex and the angle they make at the vertex interior to the polygon is called the interior angle. A regular polygon has n (where n is 3 or more) sides of equal length. Limiting our discussion to regular polygons (polygons where all the sides and angles are equal), how do we determine what the length of each side should be and ensure that at least one pair of opposite sides of the polygon line up with the LEGO grid (so that we have a way of attaching the polygonal wall to a baseplate) ?įor this, we will have to first review the geometry of polygons and familiarize ourselves with a few basic terms. If we extend this concept further, we should also be able to build a continuous chain of angled wall segments that form a closed shape – namely a polygon. In this earlier post we have seen how LEGO hinge plates can be used to create angled walls. These sets also have quite a bit of internal reinforcement created using Technic elements, and we will not be getting into all the details of that for this article.īefore we start diving in, we need to get a few prerequisites out of the way – namely polygon geometry, an overview of the Technic pieces used to create the inner frame in the Globe set and of course the wedge plates that are used in conjunction with regular plates to create the outer “skin” in both sets. We will try to understand conceptually how the outer shapes of the globe and the shield are put together (not necessarily following the instructions for the actual sets). And so, in this third installment of my series on ‘The Math Behind LEGO Techniques’ (the two previous installments are here and here), we will be delving into the math behind the Globe and Captain America’s Shield. I am a bit of a novice with this technique myself, but I couldn’t resist the challenge of trying to reverse engineer the two official sets (the Globe and Captain America’s Shield) to try to uncover some of this math. Michigan Avenue (John Hancock Center)Ĭlearly, there is some interesting math at play here. Different versions of Empire State Building. ![]()
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