Art of Construction
In the Art of Construction project we did in math, we had to design, and create an image using geometric constructions. (Geometric constructions are where you use a compass and a straight edge to make precise lines, angles, shapes, etc.) Geometric constructions were created (and mostly used) in ancient times, before rulers and protractors existed. The purpose of this project was to learn about the way people made precise shapes and angles back when math was a new concept.
For the first benchmark of this project, we focused on designing our images. I chose to design my image the way I did because, for one, it incorporates a lot of different shapes, and is pleasing to the eye. It also is symmetrical, as well as (I think) evenly spaced out. There isn't one area that is really busy. It also gets less and less complicated (and more spaced out) as it gets farther from the center point. Here is my benchmark #1 sketch.
For the first benchmark of this project, we focused on designing our images. I chose to design my image the way I did because, for one, it incorporates a lot of different shapes, and is pleasing to the eye. It also is symmetrical, as well as (I think) evenly spaced out. There isn't one area that is really busy. It also gets less and less complicated (and more spaced out) as it gets farther from the center point. Here is my benchmark #1 sketch.
Benchmark #2 was a bit more complicated. We had to not only recreate benchmark #1, but we also had to make it using constructions. The steps to making my benchmark #2 (and final product, at a bigger scale) are as follows:
- Draw a circle around a point.
- Draw a straight line through the circle - Make sure the line goes through the center point, and passes through the circle line twice. Draw the line far past the edge of the circle.
- Construct a perpendicular line through that line - Make sure the line goes through the center point, and passes through the circle line twice. Draw the line far past the edge of the circle.
- Where the two lines intersect with the circle (should be four spots) draw circles. Circles should all be the same size as the beginning one.
- The first and second lines should intersect with the far side of the four outer circles. Draw a small circle at the point where these shapes intersect. Repeat for all four outer circles.
- Inside of each of these smaller circles, construct a parallel line to the original two. Continue these lines until you make a square (using all of the small circles). Draw the line far past the vertex of the square.
- At the four vertices of the square you just created, draw circles (the same size as the original). Make sure the lines that made the square go all the way through the circles.
- Connect the bottom, left, right, and top points (Where the square's lines and the circle intersect) to create a diamond.
- Construct an octagon in each of the four circles.
- Erase construction lines, and enjoy.
This is my benchmark #3, the final creative piece. I chose to create it using watercolors because I wanted to be at least partially unique with the medium I used. Most people used marker or crayon, so I was really glad I made that choice. I chose to use the colors that I did to represent Earth and space, zooming out from the inside to the outside. The very middle is a flower, representing nature. The two greens surrounding it are Earth, the leaves, and other general greenery. The lighter blue is supposed to be the sky or ocean. In the far outer circles, the yellow is the sun, and the midnight blue and purple is space.
I think that the Habit of a Mathematician that I best used during this project was to seek why and prove. I think this, not because of the constructions, but because of when we learned about the properties of a line, triangle, and square. Most of the class already knew that a line has 180 degrees, and a triangle has 360 degrees, etc. Our teacher had the class prove why these well known facts were true. I really enjoyed that, even if I didn't arrive at the right answer (or any answer at all). I also think that I exhibited the habit of a mathematician seek why and prove while doing this. If I were to redo this project, I would have done more with rosettes and petals. I really liked the way the constructions with more petals looked, and kind of wanted to learn how to create them in bulk. A challenge that I faced during the project was not really knowing how to do the constructions at first. I didn't really piece together how the smaller constructions of angles could be put together to make a full shape. I overcame this challenge by using peer feedback and experimenting on scrap paper. At one point, an idea on how to make a shape just clicked in my mind, then the others followed.