The aim of this project was to identify, write formulae for and write proofs for patterns in reversed digit pairs of numbers (e.g. 3482 and 2843). My main accomplishments were:
- writing a formula for the difference between a reversed digit pair of numbers, and showing that the difference is always divisible by 9;
- showing that the difference between partially reversed digit pairs (where some, but not necessarily all, of the digits are reversed) is divisible by 9;
- describing why the difference between scrambled digit pairs (where the positions of the digits are changed, but not necessarily in order) is divisible by 9; and
- showing that the thinking for 1-3 held true for any base b and that the differences between reversed pairs in those bases were divisible by b-1.
I developed a few meaningful skills by engaging with this project. It gave me a lot of practice with writing mathematical proofs. This matters because it’s important to be able to communicate to others clearly and accurately about the work and thinking that I’ve done. I put these proofs together into a paper. This was my first time writing a formal mathematical paper, so I gained valuable experience in organizing, drafting and editing my paper. Lastly, to write all of the math equations and symbols in my paper, I learned how to use LaTeX, a common software used for mathematical typesetting. Knowing how to use this software will come in handy in the future when writing math or science papers with math and equations.
Overall, this fellowship allowed me to learn the start-to-end process of producing a theoretical math paper, short of journal submission.