Year 2017 - Volume 53
2020 - Present

Thomas Britz

Dear Readers, welcome to this year’s first issue of Parabola, dedicated to my colleague Peter Brown. In this issue you will find three excellent articles, beautifully-set problems and, as something new, a book review.

Michael Brand

It was quite a surprise when it was recently found that Friedman numbers have a density of 1 within the integers. In this paper, we describe how this result is reached.

Peter Brown

How do we find all points with integer coordinates on the hyperbola x2−8xy+11y2=1 ? One approach is to use continued fractions.

Travis Dillon

Our system for writing integers relies on ten symbols. When we write an integer that is less than ten, the rule is easy: write the corresponding symbol; for example, “nine” is expressed as “9”. However, for integers greater than or equal to ten, the rules are more complicated.

Thomas Britz

The book under review, Mathematical Doodlings - Curiosities, conjectures and challenges is a personal and passionate affair. Most of the book forms an ode to numbers and their patterns, a lifelong love affair that the author has enjoyed as non-professional mathematical doodler and thinker.

David Angell

Q1521 Solve the equation √x+20 + √x = 17 .

David Angell

Q1511 In a certain country, every pair of towns is connected by a highway going in one direction but not by a highway going in the other direction. A town is central if it can be reached from every other town either directly, or with just one intermediate town.

Thomas Britz

Dear Readers, the articles in this special issue of Parabola were written by high school students and introduces the comic 2Z Or Not 2Z. I dedicate this issue to my colleague Susannah Waters.

Tyler Gonzales and Daniel Bungert

We present a epsilon-delta definition of limits for real functions and we show how to derive proofs that use this useful definition. A brief section on continuity with the epsilon-delta definition is also included.

Olivia Burton and Emma Davis

The Dalivian coordinate system presents a new way to graph points in a coordinate plane, using the non-origin intersection of two parabolas, x = ay2 and y=bx2 .

Michael Kielstra

When a number k has the property that all prime numbers greater than k are of the form kn±1 where n is an integer greater than 0, we say that k is a prime determinant. In this paper, I will prove that 1, 2, 3, 4, 6 are prime determinants, and give reasons why no other numbers are.

Phu Nguyen and Ngan Le

In this paper, we are going to explore how many dimensions it takes to embed a wheel graph with multiple hubs in Euclidean space.

Robert Schneider

An odd comic about even numbers

Peter Brown

Q1531 Take any four consecutive whole numbers, multiply them together and add 1. Make a conjecture and prove it!

David Angell

Q1521 Solve the equation √x+20 + √x=17.

Thomas Britz

Dear Readers, welcome to Parabola! This issue, published near year's end, reflects at the past and looks to the future.

Martina Štěpánová

This survey presents several constructions of a regular pentagon inscribed in a given circle together with proofs, old and new, of their correctness.

Benjamin M. Altschuler and Eric L. Altschuler

We show that Old Babylonian problem tablets contain a geometric proof of the irrationality of 2‾√ predating the Greek discovery of this profound mathematical fact by more than a millennium.

The traditional Collatz Conjecture states that, for any number, if you divide by 2 if the number is even and, if odd, then multiply by 3 and add 1, and repeat, you will eventually reach 1.

Robert Schneider

An odd comic about even numbers.

David Angell

Q1541 Consider 29x+30y+31z=366 where x,y,z are positive integers with x
(a) Without writing or using a computer, find such x,y,z.
(b) Prove that there is only one solution.

Peter Brown

Q1531 Take any four consecutive whole numbers, multiply them together and add 1. Make a conjecture and prove it!

Denis Potapov

The problems from the 56th UNSW School Mathematics Competition.

Thomas Britz

The winners of the 56th UNSW School Mathematics Competition. Well done to you all!