Tessellation Project
This is the tessellation I designed digitally and colored physically to add texture
Question: Describe the concept of area and volume in terms of efficiency. What is the most efficient shape and why? How can we measure efficiency?
The most efficient shape is the Hexagon. It has a large area to perimeter ratio and is the shape with the most sides that can tessellate. Efficiency is determined by two factors. Being able to tessellate perfectly without any gaps or overlays. And having a lot of area without a lot of perimeter. Think of it this way. A circle has a radius of 2. If you take the radius of the circle to a square and triangle of the same dimensions as the circle the radius will go outside the perimeter of the polygons while it does not go outside the hexagon.
Question: Proving the Pythagorean theorem via construction
The Pythagorean theorem is a theorem that states that the length of the Hypotenuse of a triangle can be measured by squaring both the length of the base squared and the height squared. Proving this is simple and all you need is some graph paper. Cut a 3x3 4x4 and 5x5 square out of the graph paper. Next, arrange them like this.
The most efficient shape is the Hexagon. It has a large area to perimeter ratio and is the shape with the most sides that can tessellate. Efficiency is determined by two factors. Being able to tessellate perfectly without any gaps or overlays. And having a lot of area without a lot of perimeter. Think of it this way. A circle has a radius of 2. If you take the radius of the circle to a square and triangle of the same dimensions as the circle the radius will go outside the perimeter of the polygons while it does not go outside the hexagon.
Question: Proving the Pythagorean theorem via construction
The Pythagorean theorem is a theorem that states that the length of the Hypotenuse of a triangle can be measured by squaring both the length of the base squared and the height squared. Proving this is simple and all you need is some graph paper. Cut a 3x3 4x4 and 5x5 square out of the graph paper. Next, arrange them like this.
By looking at the length of the base and hypotenuse squared (literally) we can see that it is equal to 3^2 + 4^2 = 5^2.
My understanding in Geometry has grown a lot. I only knew the number PI as a reference and using perimeter on squares and rectangles. This unit opened my eyes in technology two teaching me how to use spreadsheets to calculate the area of different polygons. What challenged me was the math itself and grappling with new topics. I was never very good at math but these topics are way more engaging than what I have learned in the past. What deepened my understanding is the realization that geometry has connections to botany with the Fibonacci sequence and even geology with the formation of minerals.
My understanding in Geometry has grown a lot. I only knew the number PI as a reference and using perimeter on squares and rectangles. This unit opened my eyes in technology two teaching me how to use spreadsheets to calculate the area of different polygons. What challenged me was the math itself and grappling with new topics. I was never very good at math but these topics are way more engaging than what I have learned in the past. What deepened my understanding is the realization that geometry has connections to botany with the Fibonacci sequence and even geology with the formation of minerals.