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Squares to stairs
For the problem of a growing staircase, we had to answer 3 questions;
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Deriving the Equation
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Answering the questions
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Expanding the problem
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Reflection - Habits of A MATHEMATICIAN
The two habits of a mathematician that I feel I employed the most in this problem are; conjecture and test, and take apart and put back together. I used the latter to reason out potential equations. This is most apparent in my expansion of the problem, where I attempted to put the new equation in terms of the one I created for the original problem. In the first diagram, I drew the growth of the pattern. I used the second and third to depict the pattern as a combination of two staircases through dissection. I wrote my equation off of the final figure before simplifying it to represent the whole shape. My conjectures and tests are most apparent in steps two and three of the original problem, where I experimented with different equations before arriving at the correct one.