For any density function (or probability function), there always corresponds a "cumulative distribution function" (cdf). It is a well-known mathematical fact that the cdf is more general than the density function, in the sense that for a given distribution the former may exist without the existence of the latter. Nevertheless, while the density…

For at least 2000 years people have been trying to calculate the value of [pi], the ratio of the circumference to the diameter of a circle. People know that [pi] is an irrational number; its decimal representation goes on forever. Early methods were geometric, involving the use of inscribed and circumscribed polygons of a circle. However, real…

In Volume 23(2) of the "Australian Senior Mathematics Journal," Boncek and Harden present an exercise in fitting a Markov chain model to rainfall data for Darwin Airport (Boncek & Harden, 2009). Days are subdivided into those with precipitation and precipitation-free days. The author abbreviates these labels to wet days and dry days. It is…

The methods for calculating returns on investments are taught to undergraduate level business students. In this paper, the authors demonstrate how such calculations are within the scope of senior school students of mathematics. In providing this demonstration the authors hope to give teachers and students alike an illustration of the power and the…

As early as 3500 years ago, shadows of sticks were used as a primitive instrument for indicating the passage of time through the day. The stick came to be called a "gnomon" or "one who knows." Early Babylonian obelisks were designed to determine noon. The development of trigonometry by Greek mathematicians meant that hour lines could be determined…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

Calculus at the secondary school level has traditionally represented the peak of school mathematics in Australia, and has been available only to the most capable students. Until recently, many calculus curricula have focused on developing standard techniques, such as those concerned with differentiation and integration, with an emphasis on…

A derivative is the limit of a quotient. It is an abstraction of division. Since division is harder to understand than multiplication, teachers teach it later, hopefully only after a sound understanding of multiplication has been attained. For the same reason, it may make sense to teach integration first, and move on to differential calculus only…

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by implementing…

This paper presents a generic method of calculating accurate horizontal and vertical object distances from digital images taken with any digital camera and lens combination, where the object plane is parallel to the image plane or tilted in the vertical plane. This method was developed for a project investigating the size, density and spatial…

In this article, the author presents a six by six array in which individuals can obtain 182 in total even if they use a different set of numbers. The author then explain why this is possible. The author uses the k-translation of a sequence for this equation. (Contains 8 figures, 2 tables and 6 footnotes.)

In the "Sydney Morning Herald" of 23 March 2005, Ross Gittins argued that the funding arrangements for private schools positively encourage parents to move their children from the state system. The then Federal Minister for Education, Dr Brendan Nelson, in a letter to the "Herald" of 25-27 March, responded by saying that 68% of all school pupils…