Volume 50

2014

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.

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.

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.

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 $$S = 1 + 11 + 111 + \cdots + \underbrace{11 \ldots 1}_{\text{2014 digits}}.$$

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 $$\frac{x}{(x^2 + a^2)^2},$$ where $a$ is a positive real number.