Alexander FarrugiaApplications of the ParabolaA parabola has a very interesting feature. It has a point called the focus which has the following property: if you draw any straight line…Sep 19, 2022Sep 19, 2022
Alexander FarrugiaYou don’t need to know a lot of maths to do mathematicsHonestly, you don’t. To prove something, you barely need any of what most people think about when they hear the word ‘maths’ (numbers…Aug 26, 20221Aug 26, 20221
Alexander FarrugiaMy Summer of Mathematics Exposition 2 SubmissionLast June, 3blue1brown posted a video on the Summer of Mathematics Exposition 2 (SoME2), in which Grant Sanderson invited mathematics…Aug 17, 2022Aug 17, 2022
Alexander FarrugiaThe Missing Square PuzzleChoose four positive whole numbers a,b,c,d such that ad−bc=1. Try not to choose obvious numbers such as 1,1,1,2. Try to find more difficult…Aug 12, 2022Aug 12, 2022
Alexander FarrugiaWhy Radians?Yeah, why? After all, degrees work fine. Why do we need to split one revolution into 2π pieces? That doesn’t even make sense.Aug 5, 20222Aug 5, 20222
Alexander FarrugiaComplex Numbers: why do we need a solution for x²=-1?Prior to Cardano’s and Tartaglia’s work in the sixteenth century, mathematicians happily claimed that square roots of negative numbers did…Jul 27, 2022Jul 27, 2022
Alexander FarrugiaProving that sqrt(a)+sqrt(b) and sqrt(a)-sqrt(b) are irrationalWe assume that a and b are positive integers and that at least one of sqrt(a) or sqrt(b) is not an integer. Let x be the number…Jul 22, 2022Jul 22, 2022
Alexander FarrugiaWhy am I doing Mathematics?Often, I ask myself what am I doing exactly, when I’m doing mathematics. Am I solving problems? Discovering something? Wasting my time?Jul 9, 20221Jul 9, 20221