The quest to find the equation of a catenary makes an ideal investigation for upper secondary students. In the modelling exercise that follows, no knowledge of calculus is required to gain a fairly good understanding of the nature of the curve. This investigation is best described as a scientific investigation--a "hands on" experience that…

An old chestnut goes something like this. The surface area of a pond in the form of an annulus is required, but the only measurement possible is the length of the chord across the outer circumference and tangent to the inner circumference. It is a beautiful example of invariance. Invariance in mathematics usually refers to a quantity that remains…

Pierre Bezier was born on September 1 in Paris, 1910. Choosing the career path of his father, he gained electrical and mechanical engineering degrees by the time he was 21 years old. He began working for the car company Renault and stayed there for the next 42 years. In 1977 he received a doctorate in mathematics. Bezier, at the age of 50 began…

One of the most remarkable devices embedded in a Microsoft Excel spreadsheet is known as the spinner. Its staggering simplicity is undoubtedly its strength. As an incrementing device that allows graphs to dance across the screen, it gives the concept of variability a whole new meaning. Spinners and their close cousins scroll bars can be grabbed…

Perhaps next time teachers head towards the fundamental theorem of calculus in their classroom, they may wish to consider Fermat's technique of finding expressions for areas under curves, beautifully outlined in Boyer's History of Mathematics. Pierre de Fermat (1601-1665) developed some important results in the journey toward the discovery of the…