UKMT Maths Circle Review
We visited Aston University for an educational event that would broaden our mathematical perception and allow us to explore different avenues within mathematics. This event was split up into 2 days of focus and here is the summary…
Thursday:
This first day was great with us messing around with shapes and defining algebra as an essential translating language in mathematics. We started off the day by attempting a mathematical crossword (or number) puzzle which integrated all types of numbers from perfect to triangular and factors to multiples. We then moved on with the first of 4 people who were to try and explain to us their love of maths. We began with a series of complex problems that could be solved easily with clever implementation of algebra. We were taught how we needed to use algebra as a “mathematical language” and translate the problem through its means.
Followed by a short break we explored how problem solving becomes much easier when the same problem can be explored in different ways. We were given 4 different problems like dyck paths and mountain making which had the same solutions. On inspection we saw how those seemingly different problems were the same! We then moved onto the second part of the day focused on geometry. We explored unique shapes like the Reuleaux Triangle and how these shapes are able to maintain the same width all around with the exception of a non-fixed centre. This was followed by the last on how shapes are related almost in a family tree eg. a rectangle can be a square, but a square cannot be a rectangle. By exploring several different properties of quadrilaterals, we were able to seek out these connections which may usually be overlooked in school curriculum. The course of the first day really unlocked some of the ideas around mathematical interpretations and set us up for a whole new day to follow!
Friday:
Another day waiting to be explored. This day was going to include a lot more puzzling uses of mathematics. As a starter, we were given a code cracking task, where each letter represented another. Our first thought was to spot out repeated letters or groups of letters, which corresponded to other common letters. Through this, we were able to figure out the code representative for ‘THE’, which allowed us to complete much more of the code. Five minutes, and a load of trial and error later, we managed to crack the code. Our next task was to come up with the largest possible number that could be written on paper in 2 minutes. The lecturer acknowledged a variety of methods we could have used, ranking them, with the most efficient using iterations.
After the fifteen-minute break, we moved onto the midpoint theorem. Using the information obtained from the previous day, we proved a list of geometric statements, through the means of logic and angle rules. The next activity was probably the most exciting, where we explored how Tetris pieces, Candy Crush and hydrocarbon molecules were all linked. This was because of the finite ways of connecting a certain number of items. The final task was calculating the amount of ways to travel from one grid square to another, being limited to moving just right and down. To wrap the day up, we filled in feedback sheets and gave a round of applause to everyone.
Overall our perspective on this subject has widened, exploring the multiple ways maths is used in day-to-day life as well as more theoretical ideas.
We would like to take this opportunity to thank the Maths department and especially Miss Drage for arranging this great trip and ultimately a wonderful learning experience.
Thank you!
By: Jasbinderbir Singh & Yusuf Sakhawat
