In Tessellations: The math of Tiling post, we have learned that there are just three continuous polygons that have the right to tessellate the plane: squares, it is intended triangles, and regular hexagons. In Figure 1, we can see why this is so. The angle sum of the internal angles that the consistent polygons conference at a point add up to 360 degrees.
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Figure 1 – Tessellating consistent polygons.
Looking in ~ the other consistent polygons as presented in figure 2, we can see plainly why the polygons cannot tessellate. The sums the the inner angles room either greater than or less than 360 degrees.
Figure 2 – Non-tessellating constant polygons.
In this post, we space going to display algebraically the there are only 3 regular tessellations. Us will usage the notation
In the proof, as shown in figure 1, we room going to present that the product that the measure of the inner angle the a continuous polygon multiply by the variety of vertices conference at a allude is same to 360 degrees.
Theorem: There are only three continual tessellations: it is intended triangles, squares, and regular hexagons.
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The angle amount of a polygon v
which simplifies to