## Archive for July 2010

### Circling the drain – Geometry is going to drain your will to live!

July 24, 2010

Circles have fascinated since the beginning of time – cave art includes circular designs, early humans arranged giant stone circles such as stonehenge, Greek mathematics, Mandalas, Leonardo da Vinci’s Vitruvian Man, all the way through to crop circles, as shown on the left. For those of you of the opinion that crop circles are alien-created messages, please re-think!.

As part of your studies of mathematics, you have to learn the definitions of circle sections, as well as a set of circle theorems that explain the different relationships between angles within a circle.

### Colouring outside the lines…

July 14, 2010

Colours are amazing – a world without colour would be truly uninspiring. We even describe something that is depressing or unimpressive “grey” or “colourless”. But what is colour, scientifically speaking? Well, for a start, red is not made up of red waves – colour is a response of the human eye to a specific range of frequencies. The part of the electromagnetic spectrum that can be perceived by the human eye as colour is called the visible light spectrum:

### Going round and round until you are dizzy

July 5, 2010

Trigonometry is all about circles – from the start to the end of your study in this maddening topic, you will be coming back to the same point: circles. In other words, you will be getting dizzy:

DIZZY!

The Unit Circle is part of your previous studies, and you are expected to undestand it at this time. For those of you who need a refresh on this topic, here are a few links (1, 2, 3, 4) (note that 3 and 4 are particularly good!)

This year, we continue to look at the three primary trigonometric functions, and the ways in which they can be distorted (either by stretching, compressing or translating them). The basic form for all trigonometric functions is below (we’ll use sine as an example)

### Wave bye-bye to your sanity…

July 5, 2010

Paradoxes are fun – if you understand them. Watching others attempt to reconcile the conflict between the irreconcilable is amusing. For example:

The following sentence is false.

The previous statement is true.

Which of these statements are correct? If your head is beginning to hurt, then you had better go and buy a very large box of panadol, because you are going to need it during the next unit of work. We are beginning your investigation into the properties of light, and it only gets weirder (and more paradoxical) the further in you get. The truth of the matter is that physicists don’t really know (absolutely) what light is. Scientists rely on a set of models (models are ways to explain why light behaves the way it does), but the porblem is that light doesn’t play nice. Certain models explain some behaviours, but not others. In fact, no one model explains all of the properties of light. Over the course of the next unit, we will look at two models:

1. Ray Model
2. Wave Model