## Wednesday, 12 June 2013

### Mathematics is Everywhere

 Douglas Butler
On Monday 10 June 2013, Douglas Butler paid a visit to The International School of Toulouse. He joined the mathematics department for the day visiting lessons and delivering a session to our Year 9 students. Douglas, a world renowned mathematics educator and great advocator of the use of technology in the mathematics classroom, was impressed by the students, the quality of teaching and learning and the facilities at the school.  The Year 9 students, the school principal and myself enjoyed his whizz-bang lesson that I’m calling “Mathematics is everywhere!” The students used Google Earth to skip around the world and visit some places of mathematical interest. Here’s a summary of some of the fascinating discoveries we made.

### The Exmouth Hexagons

Zoom in to Exmouth Penisula in Western Australia and discover these strange hexagons in the ground. What transformations could you apply to one to get the other?Why are they there?

### Washington Airport

At each end of every runway you may notice different numbers. At Washington Airport there are numerous different runways. Why is there a 4 at the end of one of the runways and the number 22 at the other? On a second runway you will find the numbers 15 and 33. What is the mathematical significance of these numbers and if the third runway has 19 at one end what number will you find at the other?

### Melbourne Airport

Continuing on the theme of airports we used Google Earth to look at the elevation profile of the runway at Melbourne Airport. As mathematics teachers we are acutely aware how easy it is to misinterpret graphs – it is important to study them with a critical eye. Looking at the following graph what might you conclude about this runway?
 Elevation of Melborne Runway
Unless we look carefully at the axes we might be misled into thinking that the runway is quite steep. Using graphing software carefully we can see that the gradient of the straight line is not at all steep and that planes can land quite safely at Melbourne Airport!

### Denge Sound Mirrors

 Denge Sound Mirror, Kent
Returning to Europe there exist some wonderful parabolic structures in Kent. Before the invention of radar, the Denge Sound Mirrors  were intended to provide early warning of enemy aeroplanes crossing the Channel towards Britain. This mirror is shaped like the graph of a parabola (y=x² is the simplest parabola) and this was critical  in their efficiency of amplifying the sound.  Where would you stand to best hear the sound? Just like flat mirrors, the angle of incidence equals the angle of reflection. The animated gif below might give you a clue as to why they were so efficient.

You can find all the resources created by Douglas Butler for his visit here.