David Angell
First we must introduce some musical terminology, with apologies to readers who are already familiar with it.
Ian Doust
A time series is a sequence of values x1,x2,x3,⋯ , usually representing measurements of some quantity at equal intervals of time.
Gavin Brown
Here is a problem of the sort that could possibly be set in a 4-unit paper:
David Tacon
In a recent article of Parabola (Vol. 25 No.3), Esther Szekeres showed how we could prove many geometrical results by thinking in terms of centers of mass.
Q.794 A and B are opposite vertices of a cube of side length 1 unit.
Q.782 Let \(S_N = \frac{1}{1^2-\frac{1}{4}} + \frac{1}{2^2-\frac{1}{4}} + \cdots + \frac{1}{n^2-\frac{1}{4}}\) . Simply this expression, and show that, when \(n\) is large, \(S_n\) is approximately equal to 2.
Tim Chambers
Everyone knows why they entered the actuarial field. The allure of what success as an actuary can bring - money, status, power - is a powerful attraction in anyone's book.
Peter Brown
Given a circle \(x^2+y^2=p\) , centre \((0,0)\) and radius \(\sqrt{p}\), does the circle always pass through points whose co-ordinates are rational numbers?
George Szekeres
Mathematics is generally regarded as one of the few disciplines (some would say the only discipline) which is built on rock-solid foundations.
Senior Division
First Prize: $150 and a Certificate
Le Strange, Elizabeth Teresa Sydney Church of England Girls Grammar School
The new teacher's age is an odd number which leaves the remainder 1 when divided by 3, and the remainder 9 when divided by 11. How old is the teacher?
Q.805 Solve for \(x\) and \(y\) :
\[\sqrt{x+y} + \sqrt{x-y} = 5\sqrt{x^2-y^2} \qquad\text{and}\qquad \frac{2}{\sqrt{x+y}} - \frac{1}{\sqrt{x-y}}=1\,.\]
Q.793 The vertices of a regular tetrahedron lie on a sphere of radius \(R\), and its faces are tangential to a sphere of radius \(r\) . Calculate \(R/r\) .
Michael Cowling
The subject of this paper is the mathematical theory of catastrophes. A catastrophe is a disaster. But there is, implicit in the word, the idea of a sudden change for the worse.
David Angell
We all know and have used the approximation π≃22/7. It may have occurred to you to ask why this is a worthwhile value.
Simon Prokhovnik
The geometrical proposition, named after the Greek mathematician and philosopher, Pythagoras, (~ 570-550 BC), deals with a unique property of right-angled triangles.
Q.817 Find all integers \(x\),\(y\) such that \(x(3y−5)=y^2+1\) .
Q.805 Solve for \(x\) and \(y\) :
\[\sqrt{x+y} + \sqrt{x-y} = 5\sqrt{x^2-y^2} \qquad\text{and}\qquad \frac{2}{\sqrt{x+y}} - \frac{1}{\sqrt{x-y}}=1\,.\]