The Art of Construction
Steps For Design:
1.) Start with 1 circle in the middle.
2.) Add 5 circles of the same size around the circle, creating a rosette in the middle.
3.) Add 6 small circles, each with the middle point where the other circles overlap. (One edge should touch the inner circle)
4.) Make a hexagon by connecting the points around the rosette.
5.) From each side of the hexagon, extend two lines to meet in a point, making an equilateral triangle. (There should be 6)
6.) Through each of the petals of the rosette, make a line extending from one side of the entire figure to the other. (3 total)
7.) Through each of the spaces in between the petals, make a line extending from one side of the entire figure to the other. (3 total)
8.) Find one of the endpoints of a line that extends through a petal of the rosette, and locate the endpoint closest to it. Connect the two points.
9.) Draw a parallel line directly across from it.
10) Do the same with the remaining endpoints of the other lines. (2 sets of parallel lines)
11.) Connect the parallel lines to make 2 rectangles. (4 lines total)
Reflection:
Explain your highs and lows throughout this project.
- I think that this project went well overall, but there were some highs and lows along the way. I enjoyed that we could make any design we want and color it any way we wanted. My biggest struggle was trying to find a way to incorporate a square into my design. Otherwise, it was fun and I am happy with my final product.
How have you applied the Habits of a Mathematician throughout this project?
- The Habit of a Mathematician that I have felt that I applied the most through this project was #3, being systematic. I had to have a system and organization as I made my figure because I needed to make sure that I was consistent with the different shapes that I made so that everything would line up and overlap correctly.
How can the simplest of mathematical tools be used to create beautiful work? Why is attending to precision necessary?
- Even the simplest of mathematical tools, a compass and straight edge, can be used to create beautiful work by creating lines and circles that overlap to make detailed figures. Precision is necessary in order to attain symmetry and even work. When I made mine, precision was needed so that all of my shapes would overlap in the same places and be symmetrical.
1.) Start with 1 circle in the middle.
2.) Add 5 circles of the same size around the circle, creating a rosette in the middle.
3.) Add 6 small circles, each with the middle point where the other circles overlap. (One edge should touch the inner circle)
4.) Make a hexagon by connecting the points around the rosette.
5.) From each side of the hexagon, extend two lines to meet in a point, making an equilateral triangle. (There should be 6)
6.) Through each of the petals of the rosette, make a line extending from one side of the entire figure to the other. (3 total)
7.) Through each of the spaces in between the petals, make a line extending from one side of the entire figure to the other. (3 total)
8.) Find one of the endpoints of a line that extends through a petal of the rosette, and locate the endpoint closest to it. Connect the two points.
9.) Draw a parallel line directly across from it.
10) Do the same with the remaining endpoints of the other lines. (2 sets of parallel lines)
11.) Connect the parallel lines to make 2 rectangles. (4 lines total)
Reflection:
Explain your highs and lows throughout this project.
- I think that this project went well overall, but there were some highs and lows along the way. I enjoyed that we could make any design we want and color it any way we wanted. My biggest struggle was trying to find a way to incorporate a square into my design. Otherwise, it was fun and I am happy with my final product.
How have you applied the Habits of a Mathematician throughout this project?
- The Habit of a Mathematician that I have felt that I applied the most through this project was #3, being systematic. I had to have a system and organization as I made my figure because I needed to make sure that I was consistent with the different shapes that I made so that everything would line up and overlap correctly.
How can the simplest of mathematical tools be used to create beautiful work? Why is attending to precision necessary?
- Even the simplest of mathematical tools, a compass and straight edge, can be used to create beautiful work by creating lines and circles that overlap to make detailed figures. Precision is necessary in order to attain symmetry and even work. When I made mine, precision was needed so that all of my shapes would overlap in the same places and be symmetrical.