Bruce Henry
Welcome to this first issue for 2009. The first article in this issue is a peer reviewed (Section A) article by Christian Aebi and Grant Cairns.
Christian Aebi and Grant Cairns
Problem 461 from Parabola (Volume 16, Issue 2, p.32) asked: Partition the set \(P_n=\{2,3,5,\ldots,p_n\}\) of the first \(n\) primes into two nonempty disjoint parts \(A,B\) and let \(a,b\) be their respective products.
David Angell
As a broad generalisation we might say that research in mathematics consists of two parts: finding out what is true, and proving that it is true.
Michael Deakin
A 2007 book tells a very interesting story. It is called The Archimedes Codex and it recounts how a lost work by that great Greek mathematician recently came to light. The authors are Reviel Netz, a mathematical historian, and William Noel, the curator of the museum that holds it.
Q1291 Show that there do not exist three primes \(x\), \(y\) and \(z\) satisfying \(x^2+y^3=z^4\).
Q1281 Prove that for any real numbers a and b there holds \[\frac{1+|a|}{1+|b|}\leq 1+|a−b|\,.\]
B. I. Henry
There has been much said in the popular media about declining standards and participation in secondary school mathematics in Australia.
Michael Deakin
It is strange that it should be so, but it is true all the same, that many of the most debated aspects of Mathematics concern matters that are really completely trivial.
Bruce Brown
The problem of how to successfully choose the partner most likely to lead to a long and happy marriage is a task which has occupied the minds of young and older people alike, men and women, among all races and cultures, throughout the ages.
Farid Haggar
A Pythagorean triad \((x,y,u)\) consists of positive integers \(x,y,u\) such that \(x^2+y^2=u^2\). Geometrically, the integers represent the lengths of the sides of a right-angled-triangle with the hypotenuse length \(u\).
Junior Division - Problems and Solutions
Competition Winners – Senior Division
First Prize
Sampson Wong James Ruse Agricultural High School
Q1301 (Suggested by J. Guest, Victoria) Solve the quartic \((x+1)(x+5)(x−3)(x−7)=-135\).
Q1291 Show that there do not exist three primes \(x\), \(y\) and \(z\) satisfying \(x^2+y^3=z^4\)
B. I. Henry
I am delighted to be able to inform you that Parabola is now available on-line. The Parabola Online project was initiated by a grant from the U-Committee of the University of New South Wales.
Michael Deakin
I was rather idly browsing the shelves of one of the University of Melbourne's libraries, when a volume caught my eye. It was entitled Les manuscrits mathematiques de Marx (Marx's mathematical manuscripts).
Bruce Henry
Mathematics is largely concerned with finding and describing patterns in a logically consistent way, and where better to look for patterns than in Melbourne Cup races . Can we use a little mathematics to help us win?
Carmen Q. Artino
Visualization is a powerful tool in any teacher's bag of tricks, perhaps even more so for the mathematics teacher who must often visually present abstract concepts. At times, though, we may be at a loss as to how to visually represent a particular notion.
Q1311 Prove that \(\tan75^\circ - \tan60^\circ=2\) using purely geometrical arguments.
Q1301 (Suggested by J. Guest, Victoria) Solve the quartic \((x+1)(x+5)(x−3)(x−7)=-135\).