Year 2014 - Volume 50
2020 - Present

One of the most fashionable research pursuits of our time, in the mathematical sciences, is Big Data Science. Fashionable pursuits attract a great deal of interest and funding, which creates more interest and funding, so that fashionable pursuits can quickly dominate research effort.

Congwen Xu
In 1899, more than a century ago, Karl Pearson, Alice Lee, and Leslie Bramley-Moore discovered an interesting phenomenon, in wihch it was found that a statistical association between two different groups was reversed when the groups were combined.

Michael A. B. Deakin
In my last column, I introduced a technique of proof known as "mathematical induction". It is a powerful technique, aimed at proving general formulas, by showing that each instance of the formula implies the truth of the next.

Q1441. Hundreds of millions of pebbles were deposited on the foreshore of a beach. Every high tide, 20% of the pebbles are transported from the deep end to the shallow end.

Q1431. Find a four-digit number with the following property: if the last digit of the number is moved to the front and 7 is added to the result, the answer is exactly twice the original number.

It is with a deep sense of loss and regret that we let you know about the death of Michael Deakin on 5 August 2014. Michael contributed enormously to mathematics enrichment in Australia over several decades.

Michael A B Deakin
Back in 2005, I devoted two of these columns to the history of complex and imaginary numbers. Here I return to the theme, but take a different slant on it, telling how an initially suspect notion became respectable.

Farid Haggar
It is natural to look for relationships between the roots of a polynomial and the coefficients.

Q1451 Use the ideas of the solution to problem 1443 (later this issue) to find without calculus the maximum value of
x(x2+a2)2,
where a is a positive real number.

We begin with the solution to problem 1440 from volume 49, issue 3, which was inadvertently omitted last issue.

Q1440 Let f(x) be a polynomial with degre 2012, such that
f(1)=1,f(2)=1/2,f(3)=1/3,…,f(2013)=1/2013.

With this issue we celebrate 50 years of continuous publication of Parabola. The essential aim of Parabola at the time it was launched was to inspire students, through articles and problems, about the timeless beauty, power and relevance of mathematics.

Peter Donovan
Suppose that a weather recording station started operations in 1871 and has complete records from then onwards. These may well include the noon temperature on each day. The mean noon temperature for any year may then be calculated.

Thomas Britz, Adam Mammoliti and Henrik Kragh Sørensen
Just like any other cultural group, mathematicians like to tell stories. We tell heroic stories about famous mathematicians, to inspire or reinforce our cultural values, and we encase our results in narratives to explain how they are interesting and how they relate to other results.

Michael A. B. Deakin
In my last column I described how, at the cost of some apparent artificiality and seemingly needless complication, the imaginary numbers eventually became respectable. Here I describe the analogous process with the real numbers.

Junior Division - Problems and Solutions
Solutions by David Crocker, UNSW, Australia.
Problem 1
Find
S=1+11+111+⋯+11…1⏟2014 digits.

Competition Winners - Senior Division
Damon Zhong Shore School 1st Prize
Praveen Wijerathna James Ruse Agricultural High School 1st Prize

Parabola incorporating Function would like to thank Sin Keong Tong for contributing problem 1464.

Q1461 As in problems 1442 and 1452, a particle is projected from one corner of a 2014 x 1729 rectangle.

Q1451 Use the ideas of the solution to problem 1443 (previous issue) to find without calculus the maximum value of
x/(x2+a2)2,
where a is a positive real number.