Year 2022 - Volume 58
2020 - Present

David Angell

Dear Readers, mathematical problems are all around us! As Problem Editor, one of the things I most enjoy is setting problems in which ordinary everyday life leads to interesting mathematics.

Norihiro Someyama

This paper presents new inequalities related to the foci of hyperbola.

Bernard Kachoyan

This article will outline how a batting survival function can be constructed from simple building blocks of the probability of being dismissed at each run total, and the probability of scoring a particular number of runs.

Martina Skorpilová

The Butterfly Theorem is an elegant result on chords of a circle, dating back to the early nineteenth century. We present the generalization of the theorem for n circles.

Rachael Wen

I calculate the strength of the magnetic field that a person may experience if he or she were to stand below a set of transmission powerlines. My paper only uses algebra and trigonometry.

Catherine Greenhill

Knotwork is a very mathematical form of decoration which has been used in many cultures, including Roman mosaics, Islamic art, Celtic art and Ethiopian art. In this article, I will show you the basic technique and discuss a couple of mathematical points along the way.

Henk Tijms

Kelly posited a scenario in which a horse-race better has an edge: a ‘private wire’ of somewhat reliable but not perfect tips from inside information. How should he bet? Wager too little, and the advantage is squandered. Too much, and ruin beckons.

Leon Wang

In this article, we develop an interesting way to visualize the second and the third derivatives of single variable functions.

Yagub N. Aliyev

This article demonstrates a popular result from plane geometry known as Haruki’s Lemma in an unorthodox way.

David Angell, Arnaud Brothier and Sin Keong Tong

Q1679 David is designing a tiling pattern for his rectangular bathroom floor. Most people have tilings which consist of rectangles or hexagons, but David thinks this is boring, so he has decided to use pentagons.

David Angell, Arnaud Brothier and Sin Keong Tong

Q1664 Let a,b,c,d be four prime numbers for which 5

Thomas Britz

Dear Reader, welcome to this largest ever issue of Parabola

Timothy Hume

On 15 January, 2022 the undersea Hunga Tonga-Hunga Haʻapai volcano located in the Kingdom of Tonga erupted. It was the largest volcanic eruption since that of Mount Pinatubo in 1991, and created a tsunami that affected the entire Pacific basin.

Frédéric Beatrix

It is well-known that the problem of constructing π by compass and straightedge - "squaring the circle" - is impossible.

Toyesh Prakash Sharma

In this article, we use the Hermite-Hadamard Inequality to prove a powerful and applicable inequality that extends the Arithmetic Mean and Geometric Mean Inequality.

Alaric Pow Ian-Jun

I prove that any non-negative number larger than 1 can be expressed as the infinitely nested square root k+k+k+⋯‾‾‾‾‾‾√‾‾‾‾‾‾‾‾‾‾‾√‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ for some constant k>0.

Robert Schneider

Using methods from calculus, we combine classical identities for π, ln2, and harmonic numbers, to derive a nice infinite series formula for π/3 that does not appear to be well known. In addition, we give twenty-seven related identities involving π and other irrational numbers.

Emmet Houghton

This paper discusses the mathematics behind convolution and Fourier transformations.

Vedanth Nandivada

In this expository article, we show that dimensional analysis can be a powerful yet simple method for solving difficult problems.

Yagub N. Aliyev

There used to be journal called Publications of the Faculty Electrical Engineering - Series Mathematics (Publikacije Elektrotehničkog Fakulteta - Serija Matematika) which had a popular problem section.

Thomas Britz

The Golden Ratio appears surprisingly often, in surprisingly beautiful ways – in maths. This note showcases some of these surprising and beautiful ways.

David Angell, Sin Keong Tong and Mircea Voineagu

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.

David Angell, Sin Keong Tong and Mircea Voineagu

Q1679 David is designing a tiling pattern for his rectangular bathroom floor. Most people have tilings which consist of rectangles or hexagons, but David thinks this is boring, so he has decided to use pentagons.

Thomas Britz

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.

Isaac Lee

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?

Bora Demirtas

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

Kriste An

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

Mehdi Bugallo and Léo Van Damme

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.

Shreya Sinha and Rida Naveed Ilahi

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 is the article The Axiom of Choice also appearing in this issue of Parabola.

Shreya Sinha

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.

Pannawich Tangkitsiriroj, Pim Chotnapalai, Supawich Trongdee and Thanaporn Thanodomdech

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.

Soham Dutta

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.

Kyumin Nam

The exact values of sine, such as sin30∘=1/2 and sin45∘=1/2‾√ are well known, but the exact value for sine for other angles such as sin1∘ and sin7∘ are not widely known.

David Angell, Sin Keong Tong and Mircea Voineagu

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.

David Angell, Sin Keong Tong and Mircea Voineagu

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.

Denis Potapov

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

Denis Potapov

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