MAGIC OF MATHS

MATHS GOES TO THE MOVIES

Maths goes to the movies

Got your popcorn? Picked a good seat? Are you sitting comfortably? Then let the credits roll…

MATHEMATICS PROUDLY PRESENTS…

We have all marvelled at the incredibly life-like computer generated images in the movies. What most of us don’t realise is that the dinosaurs of Jurassic Park and the wonders of Lord of the Rings — particularly the star turn of Gollum — would not have been possible without mathematics.
But how are these amazing images made? Computer graphics and computer vision are huge subjects. In this article we will take a simplified look at some of the mathematics it takes to get to a final product. First we’ll create the world seen in the movie, and then we will bring it to life.

SETTING THE SCENE

First objects are modelled as wire skeletons made up from simple polygons such as triangles.
The first step…

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MAGIC OF MATHS

Finding your way home without knowing where you are

The life of a foraging ant is tedious and boring. It involves nothing more than repeated trips between food sources and the nest. These trips are arduous and long. A single foraging trip of an ant, one of many in a day, might be hundreds of metres. We can put this in human terms by comparing this foraging distance to the body-length of an ant. A 200m journey for an ant represents a distance of over 26,000 body lengths. For a human of average height that would equate to a trip of 30 miles. An ant forager will repeat this journey until she drops dead from exhaustion.

The foraging trips aren’t just long, they also follow complex zig-zag paths. So how do ants manage to find their way back home? And how do they manage to do so along a straight…

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MAGIC OF MATHS

TO PROVE OR NOT TO PROVE

INTRODUCTION

There is a legendary story of the sage who posed the question: ‘A normal elephant has four legs; if an elephant’s trunk is called a leg, how many legs does it have?’ He asked a mathematician, who continued to stare at a pile of paper on which he was scribbling as he muttered: ‘four and one make five’. Next to him a philosopher mused enigmatically and puffed for a few moments on his pipe before observing: ‘The fact that it is called a leg, doesn’t change the fact that it is not a leg, so the answer isfour ‘. ‘Excuse me,’ said a passing zoologist, ‘if a trunk is classified as a leg, clearly this will also apply to the tail, so it has six legs, and it’s an insect’. A logician joined the conversation: ‘A normal elephant has four legs…

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