The Art of Construction
Project Overview
Many professions in the world rely on accurate drawings, like architects and graphic designers. Geometry has been used in buildings and monuments ever since the time of the ancient Greeks and Egyptians. Their accuracy in their designs created perfect circles, squares and other shapes. We learned different types of basic geometric construction that will aid us in the creation of our design. Complex, beautiful and quality designs can be constructed from only a compass and a straight edge. Our job was to create our own designs made up of geometric constructions only using a straight edge and a compass.
Many professions in the world rely on accurate drawings, like architects and graphic designers. Geometry has been used in buildings and monuments ever since the time of the ancient Greeks and Egyptians. Their accuracy in their designs created perfect circles, squares and other shapes. We learned different types of basic geometric construction that will aid us in the creation of our design. Complex, beautiful and quality designs can be constructed from only a compass and a straight edge. Our job was to create our own designs made up of geometric constructions only using a straight edge and a compass.
Benchmark #1
For our first benchmark, we had to produce a starting image that we will be creating in the form of different shapes. I chose the image of a sea turtle because I thought it would be a great challenge to recreate the turtle using only geometrical shapes. I also love sea turtles and, since they are beautiful creatures, I chose them to be the model for my geometric construction. When looking at the picture, I could see many shapes that I could create with a compass and a straight edge. So, this was the start of my journey to construct the turtle out of geometrical shapes.
For our first benchmark, we had to produce a starting image that we will be creating in the form of different shapes. I chose the image of a sea turtle because I thought it would be a great challenge to recreate the turtle using only geometrical shapes. I also love sea turtles and, since they are beautiful creatures, I chose them to be the model for my geometric construction. When looking at the picture, I could see many shapes that I could create with a compass and a straight edge. So, this was the start of my journey to construct the turtle out of geometrical shapes.
Benchmark #2
Our second benchmark required us to provide two drafts of our geometrical construction. So for me, I had to have two drawings of my turtle that was created with the available tools. Almost every geometrical shape I constructed involved a circle. The ovals, hexagons, and squares required a circle, as seen in my drawing. To construct the hexagons, I had to draw a circle, and use the radius of it to create little tick marks around the edge. Once I connected all the tick marks with a straight edge, I got a hexagon. For squares, I used my compass to draw a circle and my straight edge to draw a straight line through the middle. I had to bisect the line to create a perfect 90 degree angle, then I connected the points where the lines touched the circle to make my square. Those are some simple constructions that I used in my benchmark that helped me recreate my turtle.
Our second benchmark required us to provide two drafts of our geometrical construction. So for me, I had to have two drawings of my turtle that was created with the available tools. Almost every geometrical shape I constructed involved a circle. The ovals, hexagons, and squares required a circle, as seen in my drawing. To construct the hexagons, I had to draw a circle, and use the radius of it to create little tick marks around the edge. Once I connected all the tick marks with a straight edge, I got a hexagon. For squares, I used my compass to draw a circle and my straight edge to draw a straight line through the middle. I had to bisect the line to create a perfect 90 degree angle, then I connected the points where the lines touched the circle to make my square. Those are some simple constructions that I used in my benchmark that helped me recreate my turtle.
Steps
1. Construct a big oval for the turtle shell
2. Use half of a medium size oval for the head
3. Draw a square on either side of the shell for the start of the front flippers
4. Create an oval that will attach to the squares
5. Construct two ovals for the back flippers
6. Draw many circles inside of the shell
7. Using the circles, create hexagons
8. Around the turtle, construct four hexagons and create a petal flower
1. Construct a big oval for the turtle shell
2. Use half of a medium size oval for the head
3. Draw a square on either side of the shell for the start of the front flippers
4. Create an oval that will attach to the squares
5. Construct two ovals for the back flippers
6. Draw many circles inside of the shell
7. Using the circles, create hexagons
8. Around the turtle, construct four hexagons and create a petal flower
Benchmark #3
For benchmark #3, we had to produce a creative art piece that was constructed based on the sketches for benchmark #2. In my art piece, one can see some of the geometrical shapes I used. Like the ovals, hexagons, petal flowers, circles, and even a hint of the squares. I decided to paint my art piece on canvas paper because I thought painting my turtle would make it look like beautiful work. It is a sea turtle and I wanted to make it look like it was swimming through the water. My canvas paper is blue to also help show that the sea turtle is swimming. I added the lily pads to show that it is outside of the ocean and maybe exploring a slow moving river or pond of some sort.
For benchmark #3, we had to produce a creative art piece that was constructed based on the sketches for benchmark #2. In my art piece, one can see some of the geometrical shapes I used. Like the ovals, hexagons, petal flowers, circles, and even a hint of the squares. I decided to paint my art piece on canvas paper because I thought painting my turtle would make it look like beautiful work. It is a sea turtle and I wanted to make it look like it was swimming through the water. My canvas paper is blue to also help show that the sea turtle is swimming. I added the lily pads to show that it is outside of the ocean and maybe exploring a slow moving river or pond of some sort.
Reflection
A success I had was creating benchmark #3 because I felt that I executed it very clearly in showing my idea about the sea turtle. One challenge I had was trying to find the image of what I wanted to recreate. I struggled with that because I didn't have a clear idea of what I wanted to do, and I took a couple days to try and figure it out. One obstacle I had was creating the back flippers of my turtle in benchmark #2. I couldn't decide what shapes I wanted to use to create them, but I ended up deciding to construct ovals, which was the easiest route. A Habit of a Mathematician I felt I used successfully was "Take apart & put back together". I felt I used the habit successfully because when I looked at my benchmark #1, I took it apart in my mind and figured out what shapes I could use to recreate my turtle. I saw ovals and hexagons in my image, but I also looked for the shapes that were hidden away. If I were able to change my project, I would change how I did benchmark #3 because I feel like I could've been more creative with it. If I sat and thought about the benchmark a little more, I could've executed my benchmark more creatively and beautifully.
A success I had was creating benchmark #3 because I felt that I executed it very clearly in showing my idea about the sea turtle. One challenge I had was trying to find the image of what I wanted to recreate. I struggled with that because I didn't have a clear idea of what I wanted to do, and I took a couple days to try and figure it out. One obstacle I had was creating the back flippers of my turtle in benchmark #2. I couldn't decide what shapes I wanted to use to create them, but I ended up deciding to construct ovals, which was the easiest route. A Habit of a Mathematician I felt I used successfully was "Take apart & put back together". I felt I used the habit successfully because when I looked at my benchmark #1, I took it apart in my mind and figured out what shapes I could use to recreate my turtle. I saw ovals and hexagons in my image, but I also looked for the shapes that were hidden away. If I were able to change my project, I would change how I did benchmark #3 because I feel like I could've been more creative with it. If I sat and thought about the benchmark a little more, I could've executed my benchmark more creatively and beautifully.