Year 2011 - Volume 47
2020 - Present

B. I. Henry
Welcome to the first issue of Parabola Incorporating Function for 2011. The first article in, by John Perram, describes different meanings of equality. For example, we might write y=x2+x+1 to define y or to represent an equation.

John W. Perram
Using a computer algebra system (CAS) such as Mathematica to relate a mathematical narrative requires a more disciplined use of symbols and terms than is common in mathematical text.

Michael A. B. Deakin
When I entered my third year of university study, I was introduced to the topic of Fluid Mechanics − the mathematical analysis of the flow of liquids and gases. I found that the concept of a fluid that is analyzed in that context is not exactly that which applies to real fluids.

Various
Q1351 A city consists of a rectangular grid of roads, with m roads running east-west and n running north-south. Every east-west road intersects every north-south road.

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∘ C and the day before it was 29∘ C.

B. I. Henry
Since the last issue of Parabola Incorporating Function the mathematics world has been surprised by the appearance of a preprint, dated May 2011, by the German mathematician Gerhard Opfer who claimed to h

Catherine Greenhill
As you probably know, a Sudoku puzzle is a 9×9 grid divided into nine 3×3 subgrids. Some of the cells in the grid contain a symbol: usually the symbols are the numbers 1,2,…,9 .

Michael A. B. Deakin
Here I revisit a topic I have written on several times before, and which furthermore continues the theme of my last column.

Farid Haggar
In the latter part of year 2009, I attended a scientific talk at Sydney University about the path of a body exiting a cliff. The position at which the body lands from the base of the cliff depends on exit velocity.

Various
Q1361 Find a six digit number which can be split into three two digit squares and also into two three digit squares. (The first digit of a number cannot be zero.)

Various
Q1351 A city consists of a rectangular grid of roads, with m roads running east--west and n running north--south. Every east--west road intersects every north--south road.

B. I. Henry
Welcome to a packed issue to close the year in 2011.
Congratulations to all of the students, their parents and teachers who had success in the 50th Annual UNSW School Mathematics Competition.

Bill McKee
This article is fundamentally about the calculations behind the ways in which computers draw graphs. In the era before computers (unknown to most of you, but very familiar to me!) graphs were drawn on paper. Typically, the data points were plotted.

Michael A. B. Deakin
Let me begin by recounting a story I first heard almost fifty years ago. This is, of course, a long time and over the intervening years I have lost contact with the people involved. So it may well be that I have misremembered parts of it and the actual event may well have been somewhat different in its details.

David Angell
Many readers will at some time have played games with a pack of cards. In most games one begins by shuffling the cards so as to randomise their order. There are various different ways of shuffling, one of the most popular being the riffle shuffle.

David Angell, Chris Angstmann, Peter Brown, David Crocker, Bruce Henry (Director), David Hunt and Dmitriy Zanin
Junior Division - Problems and Solutions
Problem 1
A second-cousin prime n -tuple is defined as a set of n prime numbers {p,p+6,…p+6(n−1)} with co

Editor
Competition Winners – Senior Division
First Prize
Edmond Cheng Newington College

Various
Q1371 Consider shuffles of a standard 52 -card pack.

Various
Q1361 Find a six-digit number which can be split into three two-digit squares and also into two three-digit squares.