Volume 54
, Issue 2

2018

Dear Readers, welcome to this issue of Parabola!
Here, you can find three excellent articles that each showcase aspects of maths: maths as art; maths as sport; and maths as science.

Choose any function $f(n)$ and, starting at any point on a sheet of paper, draw a line interval at an angle $f(1)$ anticlockwise from the horizontal. By continuing in this way with $f(2)$, $f(3)$ and so on, we might be lucky to end up with an interesting and pretty pattern.

Given an equilateral triangle $\Delta$, what is the radius of the biggest circle contained in $\Delta$? What is the radius of the smallest circle containing $\Delta$? This article shows how to determine these radii, also for the higher dimensions.

This article serves as an introduction to the basics of what is commonly known as machine learning, focusing on support vector machines and applying them to data from a study on Alzheimer's disease.


An odd comic about even numbers.

Q1561 Let $a,b,c$ be positive numbers for which

   $\frac{a+b}c = 2018$   and   $\frac{b+c}a = 2019$.

Evaluate $\frac{a+c}b$.

We have a pattern of 34 dots arranged and may remove any three dots, provided that one of them is exactly midway between the other two; then to remove another three dots under the same condition; and so on.  If we remove 33 dots, which are the possibilities for the remaining dot?

The problems and solutions from the 57th UNSW School Mathematics Competition.

The winners of the 57th UNSW School Mathematics Competition. Congratulations, all of you!