Year 2010 - Volume 46
2020 - Present

B. I. Henry

This issue of Parabola incorporating Function features two articles on the history of mathematics.

Milan Pahor

Measure what is measurable, and make measurable what is not so.

Galileo Galilei

The 17th century was a revolutionary period in the development of modern science.

Michael A. B. Deakin

Some years ago, I wrote a biography of Hypatia of Alexandria, the first female mathematician of whose life and work we have a good body of reliable evidence.

Peter Donovan and John Steele

Some years ago an office building in Brisbane acquired considerable notoriety for the rate at which cancer had been detected in those who had worked in it.

Various

Q1321 Find the sum of the coefficients of those terms in the expansion of

$\left({x}^{31}+{x}^{5}-1{\right)}^{2011}$

which have an odd exponent in $x$.

Various

Q1311 Prove that $\mathrm{tan}{75}^{\circ }-\mathrm{tan}{60}^{\circ }=2$ using purely geometrical arguments.

B. I. Henry

I invite you all to look at the problems (try to ignore solutions for now) for the 49th UNSW School Mathematics Competition in this issue. How many could you do, in three hours?

Michael Deakin

In my previous column, I looked at what we can learn of the mathematical achievements of Pythagoras and Theano.  I relied in particular on an article by the Leningrad-based mathematician Leonid Zhmud, although I found his account maddeningly incomplete in places.

Samuel Power

The purpose of this paper is both to observe, understand and appreciate the link between the Fibonacci sequence and the ubiquitous mathematical constant, π. It proves the following series for π, making use of the Fibonacci numbers.

David Angell, Peter Brown, David Crocker, Ian Doust, Bruce Henry (Director), Mike Hirschhorn, David Hunt and Thanh Tran

Problem 1

Find the set of all pairs of positive integers $\left(n,m\right)$ that satisfy

Competition Winners – Senior Division

Various

Q1331 Given any positive integers $m$ and $n$ prove

Various

Q1321 Find the sum of the coefficients of those terms in the expansion of

$\left({x}^{31}+{x}^{5}-1{\right)}^{2011}$

which have an odd exponent in $x$

ANS:

Note that

$\left({x}^{31}+{x}^{5}-1{\right)}^{2011}={a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\cdots +{a}_{1}x+{a}_{0}$

B. I. Henry

In this issue we welcome a new Problems Editor, David Angell.

Detection of the arrival of important proteins at the cell surface is a problem of intense biological interest. Here we create an ideal model of the arrival of proteins at the cell membrane, as seen by a total internal reflection fluorescence microscope.

Karina de Brum

I'm no math genius. Mr Boxold always said math is about thinking up new ways of looking at things, even old problems. That's all I did.

Michael Deakin

Some years ago, in response to an altogether unusual number of reader requests, I wrote a column on the work of a woman usually called Ada Lovelace.

Various

Q1341 A lazy weather forecaster predicts that future maximum temperatures will be the average of the preceding two days maximum temperatures. The forecaster starts his forecast by noting that yesterday's maximum temperature was 23${}^{o}$C  and the day before it was  29${}^{o}$C. What is the weather forecaster's long term maximum temperature forecast?

Various

Q1331 Given any positive integers $m$ and $n$ prove that every divisor of $mn$ can be expressed as a product of a divisor of $m$ and a divisor of $n$.