Year 2021 - Volume 57
2020 - Present

Thomas Britz

Dear Readers, I hope that you are well, wherever you are, and welcome to this issue of Parabola!

Timothy Hume

At first sight, the Euler spiral map projection does not appear very practical. This article shows, however, how the Euler spiral map projection can be used to compress meteorological data.

Alon Amit

Based on your personal understanding, off the top of your head: what would a proof of the Riemann Hypothesis do to internet security? Don’t look it up. Just consider how you would generally answer this based on what you may have read or heard.

Timothy Kang

Pedestrians have been known to cause vibrations on bridges from the forces exerted by their footsteps as they cross it. This article explains the mathematics underlying this phenomenon.

Xiaoyan Hu

In the last issue of Parabola, Randell Heyman showed that cn=(1+2‾√)2+(1−2‾√)n for each natural number n.

Terry Richards

Here are two questions regarding cyclists in velodromes. Can you find clear solutions for these?

David Angell, Arnaud Brothier and Sin Keong Tong

Q1647 A monk visits temples and burns a number of incense sticks, the same number at each temple. The temples are located on different islands in a magic lake and he visits them by boat. The lake doubles the number of sticks he holds each time he reaches an island.

David Angell, Arnaud Brothier and Sin Keong Tong

Thomas Britz

Dear Reader, welcome to this issue of Parabola!

Daniel Chioffi, Stefan O. Nita, Vlad N. Nita and Bogdan G. Nita

In this paper we look at musical scales, particularly equally tempered scales. Using continued fractions to approximate irrational numbers with optimal fractions, we develop an algorithm to classify musical scales with any number of notes to an octave based on their consonance.

Jonathan Hoseana and Handi Koswara

In this note, we prove a useful general formula for limits involving two or more two square roots with quadratic radicands.

Sarthak Sahoo

Hafsa El Ibrahimi

Let me introduce to you some necessary (but not sufficient) requirements for the existence of an odd perfect number.

Noah Bergam and Teodora Kolarov

The Nobel Prize-winning Black-Scholes model (BSM) for financial derivatives pricing is inextricably linked to the study of econophysics, where concepts from statistical physics are applied to economic systems.

Eeshan Zele

In previous issues of Parabola, Randell Heyman showed that cn=(1+2‾√)n+(1−2‾√)n is an integer for each natural number n and Xiaoyan Hu derived a recursion relation for this sequence. This article extends upon these results, by providing another method to arrive at the recursive relation.

John Pollard

What is the probability that the COVID-19 virus complete dissappears? An old and simple model is used to give an answer to this question

David Angell, Arnaud Brothier and Sin Keong Tong

Problems 1651–1660 are dedicated to the editor of Parabola, Thomas Britz, and his partner Ania, in celebration of the arrival of their twin sons Alexander and Benjamin.

David Angell, Arnaud Brothier and Sin Keong Tong

Q1647 A monk visits temples and burns a number of incense sticks, the same number at each temple. The temples are located on different islands in a magic lake and he visits them by boat. The lake doubles the number of sticks he holds each time he reaches an island.

Thomas Britz

Peter Brown

I thought I would share with you a few facts about squares - some well known, and others perhaps not so well known.

Henk Tijms

A gem for teaching probability to STEM students is the game of Egg Russian Roulette. The first person who has cracked two raw eggs on their head loses the game.

Federico Menegazzo

What is the greatest product of n numbers with some fixed sum? What is the least sum of n numbers with some fixed product? These questions are answered, and applications are given.

Stefan Haesen

In this note, we determine the curve that is the set of points all of which are the third vertex of all triangles with a given side and a given incircle tangent anywhere to that side.

Xavier Gisz

In this paper it is shown that a Bilinski dodecahedron is an isohedral space-filling tessellating polyhedron, thus bringing the number of these to five.

Janelle Powell

This article presents a quick and easy method of finding π using both the methods of ancient mathematicians and basic calculus.

Ulfa Aulyah Idrus

This paper proves three elegant integer identities by algebraic proofs and by picture proofs.

Sunil Vittal

During the 1910s, A.J. Kempner proved that the harmonic series - which is divergent - became convergent when all terms relating to numbers containing 9 as at least one digit were removed. We seek to do the same thing here but generalize the result to all bases.

David Angell, Arnaud Brothier and Sin Keong Tong

Q1664 Let $a,b,c,d$ $a,b,c,d$ be four prime numbers for which $5 $5 < a < b < c < d < a + 10$.
Prove that $60$ $60$ is a factor of $a+b+c+d$ $a + b + c + d$ but $120$ $120$ is not.

David Angell, Arnaud Brothier and Sin Keong Tong

Problems 1651–1660 are dedicated to the editor of Parabola, Thomas Britz, and his partner Ania, in celebration of the arrival of their twin sons Alexander and Benjamin.

Denis Potapov

The problems and solutions from the 59th UNSW School Mathematics Competition.

Denis Potapov

The winners of the 59th UNSW School Mathematics Competition. Congratulations to you all!