Benchmark #1: List of Potential Transformations
A poem that doubles the lines each time
Exponential y= # of lines x= Stanza
A bloodline of creatures that increase by one creature per pair
Linear y= # of creatures x= Generation
A painting where two drops of blue paint are added to the green each time
Linear y= # of tries x= Drops added since start
A bloodline of creatures that increases by two creatures per pair
Exponential y= # of creatures x= Generation
Exponential y= # of lines x= Stanza
A bloodline of creatures that increase by one creature per pair
Linear y= # of creatures x= Generation
A painting where two drops of blue paint are added to the green each time
Linear y= # of tries x= Drops added since start
A bloodline of creatures that increases by two creatures per pair
Exponential y= # of creatures x= Generation
Benchmark# 2: Linear and Non-Linear Transformations
1. I obtained my data by first starting out with the lowest numbers possible, and then using arithmetic to build myself up. I didn’t need to ‘obtain data through experimentation,’ because my project is just based off of multiplying and adding things together, regardless of the starting number.
(X) Generation | (Y) # of creatures (Exponential)
1 2
2 6
3 14
4 30
5 46
(X) Generation | (Y) # of creatures (Linear)
1 2
2 4
3 6
4 8
5 10
3. I can give evidence that my relationships are linear and exponential by looking at the number growth in the y-axis. In the linear growth, the numbers increase at a steady rate at first, and the shoot up with numbers that are further and further apart from each other. The linear one is more of a gradual growth, with the numbers being 2 numbers away from each other at all times.
My Exponential Graph
My Linear Graph
Benchmark #3: Creative Piece
A picture of my final Exponential Art Piece. Notice the quickly multiplying dragons.
A picture of my final Linear Art Piece. Notice the steady growth of dragons.
A picture of both my creations posted up on the wall alongside their graphs.
Benchmark #4: Project Reflection
1. Three habits of a mathematician that I have experienced throughout this project are searching for patterns, patience and persistence. They have strengthened my knowledge by helping me to complete projects in greater and complete detail, where as a person without these skills would produce a much blander product.
2. My experience on exhibition night while interacting with the guests about math was a bit of a challenge. Since the math project had no connects to any of our other projects, it was hard to find a way to introduce it without confusing the audience. However, I simple guided the guests as best I could towards the area where my math was being displayed, talking about it and answering any questions that they had.