Project Overview
The Purpose of this project was to learn the art of construction. Many people have to create accurate drawings for their professions, most of which have sophisticated tools to use. However the Ancient Greeks only had two things to create their drawings: A straight edge and compass. Our task was to create a design made up of geometric constructions using only a straight edge and compass. We learned different terms such as an Axiom, which is a good starting point that everyone agrees on. To learn how to bisect and construct different shapes, we watched several different videos and filled out a packet for practice. Our design could basically be anything we wanted it to be as long as it had: A square, an equilateral triangle, a regular polygon, a circle, and a petal.
Benchmark #1
Benchmark #1 was to pick a design that could be based off of our research of different designs. This was the first benchmark and the beginning to this project. The deliverable for this benchmark was to be a hand drawn sketch of our design. Although this is where we decided on our design, we were could tweak it if we needed to since it was only the first benchmark. Benchmark #1 had to fit the requirements of 1 square, 1 equilateral triangle, 1 regular polygon, 1 circle, and 1 flower petal.
It took me a while to figure out what design I wanted to create for this project, but I finally created one that I liked. I chose to do this design because it is different than all of the other ones I had seen, and it had all of the required shapes in it. This is my
Benchmark # 1:
It took me a while to figure out what design I wanted to create for this project, but I finally created one that I liked. I chose to do this design because it is different than all of the other ones I had seen, and it had all of the required shapes in it. This is my
Benchmark # 1:
Benchmark #2
Benchmark #2 was the first draft of the actual construction of our design. This means that using benchmark #1's design everything was created only using a straight edge and compass, and all of the required parts are actually constructed/bisected. Several versions of benchmark #2 may be necessary for some people. The deliverables were the second draft of your construction of design, and a list of steps of how you created your design.
I did 3 different versions of my benchmark #2 until finally I got it the way I wanted it to look. The steps that I took to create my benchmark:
Step 1. Create two line segments (One vertical one horizontal)
Step 2. Place compass where the two lines intersect and draw a perfect circle
Step 3. Place point of compass in middle of one of the 4 sections of the circle and create a smaller circle
Step4-6. For steps 4-6 find the radius of the small circle you made and make three more replicas of it in the middle of the other sections
Step 7. Construct an equilateral triangle ( Create a straight line around the two bottom circles. Bisect the line by finding and matching the length of the line segment for the compass, then placing it on each end of the line segment and making marks. Then Use a straight edge to connect the points making an equilateral
triangle.)
Step8. Construct a hexagon on the top right circle by finding the radius and making it appropriate to the compass, then line it up and make six marks.
Step9. Repeat step 8 but for the bottom left inner circle.
Step 10. For both the top right and bottom left circle, make sure the compass is still the same size and then create 6 circles on all of the ticks that you made. (this
creates the flower petals)
Step 11. Place the compass where the two line segments meet again like in the beginning, then make a smaller circle. From this circle construct a perfect square
(diamond)
After doing Benchmark #1 I figured out that I made the mistake of not doing the flower petals right. This is because my circles that are supposed to make up of the flowers were not the same size as the original circle. After revising it, this is my third version of my Benchmark #2:
I did 3 different versions of my benchmark #2 until finally I got it the way I wanted it to look. The steps that I took to create my benchmark:
Step 1. Create two line segments (One vertical one horizontal)
Step 2. Place compass where the two lines intersect and draw a perfect circle
Step 3. Place point of compass in middle of one of the 4 sections of the circle and create a smaller circle
Step4-6. For steps 4-6 find the radius of the small circle you made and make three more replicas of it in the middle of the other sections
Step 7. Construct an equilateral triangle ( Create a straight line around the two bottom circles. Bisect the line by finding and matching the length of the line segment for the compass, then placing it on each end of the line segment and making marks. Then Use a straight edge to connect the points making an equilateral
triangle.)
Step8. Construct a hexagon on the top right circle by finding the radius and making it appropriate to the compass, then line it up and make six marks.
Step9. Repeat step 8 but for the bottom left inner circle.
Step 10. For both the top right and bottom left circle, make sure the compass is still the same size and then create 6 circles on all of the ticks that you made. (this
creates the flower petals)
Step 11. Place the compass where the two line segments meet again like in the beginning, then make a smaller circle. From this circle construct a perfect square
(diamond)
After doing Benchmark #1 I figured out that I made the mistake of not doing the flower petals right. This is because my circles that are supposed to make up of the flowers were not the same size as the original circle. After revising it, this is my third version of my Benchmark #2:
Benchmark #3
Benchmark #3 was the final design for this project. It was also the art portion, where we embellished our design. I chose to do my benchmark #3 on canvas paper, and use a lot of different colors to enhance the design. I chose to use a lot of different colors for my representation of beautiful work. It was petty challenging at first because I didn't know what colors to use, or how I should color it. After a while I finally made up my mind. This is my benchmark #3:
Reflection
I think that my biggest challenge was coming up with the design. It took me a really long time to find one that I liked, and so if I were to do this project again I think I could of picked a design faster so that I could have more time with my other benchmarks. Another challenge that I had was creating the flower petals. I had to revise my benchmark #2 three times, mainly because I kept doing the flower petals wrong. I soon realized/figured out that I made the mistake of not making the 6 circles the same size as the original circle. I used my resources to figure out what I did wrong. My friends helped me figure out how to create a correct flower petal. Even though I had these challenges I ended being really successful with my design. I am very happy with my design and how it ended up looking. One habit of a mathematician that I used during this project is "Starting Small'. I started to create my design using only the required shapes ( 1 of each), and then once I figured out what I wanted to do I enhanced my design by adding patterns (which is another habit of mathematician of looking for patters) and adding many of the same shapes.