Volume 58
, Issue 3

2022

Dear Readers, welcome to this issue of Parabola! It is with some excitement and with great pleasure that I present this issue to you, not least since it features the so-far greatest amount of content of any article in Parabola’s 58-year history.

We give a short introduction to group theory and present a theorem that answers the following question:
What is the probability that two randomly chosen elements in a finite group commute?

An easy-to-follow recipe for creating divisibility rules is provided, along with a gentle introduction to modular arithmetic.

We construct a wide variety of curves, all of which are dense in squares.

We express $e$ as an infinite series in a new manner, from a recently discovered relation between the uniform and the exponential probability distributions. We also provide a direction which could lead to the discovery of new representations of Euler’s number.

We outline an understanding of set theory and how it provides a foundation for mathematics, and we hint at how the Axiom of Choice contributes to a stronger foundation for mathematics. This article serves as a brief and broad introduction in a series of papers to follow, the first of which i

What is choice in mathematics? Can we make infinite choices using logic and numbers without consequence? In this paper, I will outline an understanding of the Axiom of Choice.

This paper studies a variant of the multiple subset coupon collector problem and applies it to COVID-19 testing, giving estimates for optimal numbers of test kits to be used.

In this article, we will focus on the inequality called Muirhead’s Inequality and will present some of its applications to problems which have appeared in national and international maths competitions.

The exact values of sine, such as $\sin 30^\circ = 1/2$ and $\sin 45^\circ = 1/\sqrt{2}$ are well known, but the exact value for sine for other angles such as $\sin 1^\circ$ and $\sin 7^\circ$ are not widely known.

Q1700 Find the sum of all natural numbers from 1 to 100 which have no common factor with 2022.
Also, write the product of these numbers as an expression in terms of powers and factorials.

Q1681 The recently popular game Wordle challenges you to guess a secret five–letter word. In the not–at–all well–known game Squardle, you have to guess a secret square number, and you may enter any five–digit square.

The problems and solutions from the 60th UNSW School Mathematics Competition.

The winners of the 60th UNSW School Mathematics Competition.
Congratulations to you all!