Tesselation Final Project





Tesselation Cover Letter

There were many topics that we discussed in Math 10 this semester. One such topic would be the question of “What is the most efficient shape and why?” and “How can we measure efficiency?” While these questions seem complex on the surface, they are very simple. We can measure efficiency by figuring out the most area per perimeter. The 2nd most efficient shape is a circle because there are no corners, and it has a very high area to perimeter ratio. The only problem with a circle is that it cannot be copied and pasted across a plane, or tesselated. A tesselation cannot have any gaps or overlap. That is why the Hexagon is the most efficient shape. The only 3 shapes that can tesselate are triangles, squares, and hexagons. Since the Hexagon has the most sides and least amount of perimeter per area, it is, therefore, the most efficient shape. We discovered that in our area hexagons lecture, hexagons could be cut up into equal triangles. Since hexagons can be split up into another shape that can tesselate, hexagons are the most efficient shape. Another topic that we discussed was finding the area of any regular polygon. One of the best ways to do this is by splitting up the regular polygons into equal triangles. If we can find the area of the triangles, then we can multiply the number of triangles by the area of them to get the total area of the regular polygon. To find the area of the triangle, we need to split it up in half and perform the Pythagorean Theorem. When we find the area of half the triangle, we multiply it by 2, then by the number of triangles in that particular polygon. To show this in class, we made a google spreadsheet calculator that can find the area of any regular polygon by entering the number of sides and the radius. To create this calculator, we first needed to find all the required variables. We need to find the Apothem (a), the number of sides (n), and the side length (L). Without these variables, it is impossible to find the area of any n sided polygon. The formula for finding the area of any n sided polygon is: ((L*a)÷2)n= A (area).


Project Reflection


My understanding of geometry has increased exponentially. There were many challenges that I faced and overcame. One such challenge was understanding all of the concepts introduced to us in this unit. One specific example would be proving how two triangles are similar. Finding out how two triangles are similar is easy when you have 2 or more sides labeled on each triangle. But when you only have a side and angle, it can get complicated. One thing that helped me deepen my understanding of how to do this was by using my previous knowledge and notes regarding creating angles and putting them to use. I worked on recreating the triangles, dilating them to be the same size, and measuring the angles. Now, I can prove is 2 triangles are similar with ease. Overcoming this obstacle of understanding geometry is very useful and reassures me that I can continue to do whatever I put my mind to.





My Final Fish Tesselation.