Gauge Newsletter January 2020 | Page 12

Two Cops and a Drunk Theorem This is the same theorem which has another funny name, the Sandwich Theorem. The two cops and a drunk theorem has its applications in calculus where it is helpful when finding limits. The idea is simple. In a situation where two cops escort a drunk man it doesn’t matter how much he wobbles back and forth between them or what path they take, if they are able to keep him between them and both cops go to the same jail cell, the drunk man will also go to that same cell(7). Mathematically, if a function is squeezed between two other functions that have the same limit, the function in the middle will also have that exact limit. Two cops (C1,C2) accompanying a prisoner (O) Shoes and Socks Theorem This cute theorem stems from group theory. Mathematically it states that if two elements a and b belong to the same group, then the inverse of a*b is inv(b)*- inv(a) where inv() is the inverse operator(9). Notice how the order of a and b has interchanged. This is where the theorem gets its name from. First, you put your socks on and then the shoes. But if you want to inverse this operation, you have to remove (inverse) your shoes first and then the socks. Theorem of the Unconscious Statistician This theorem is also known as the Law of the Unconscious Statistician (LOTUS). LOTUS stems from the area of probability and this theorem is used very often in calculations. As this theorem is used very often, statistics students have a tendency to use this theorem as a definition without regarding it as a theorem. This very ‘unconscious’ nature of students when applying this theorem has led to its funny name (11). Chicken McNugget Theorem This oddly named theorem which belongs to the number theory states that if there are two numbers m and n, then the largest number which cannot be written in the form of am+bn is mn-m-n where a,b,m,n are positive integers. This is relatively an easy theorem to understand. The name for this theorem has a strange story of origin. In the early days, McDonald’s sold its nuggets in packs of 9 and 20. Math enthusiasts were curious to find the largest number of nuggets that could not have been bought with these packs, thus creating the Chicken McNugget Theorem (the answer worked out to be 151 nuggets) (13). Page 10 University of Peradeniya GAUGE Magazine