CONTENTS Mathematics all around us 4 Right triangles 6 Shapes and space 8 Developing numbers 10 A never-ending number 12 The Fibonacci sequence 14 Pascal’s triangle 16 Drawing graphs 18 A calculating machine 20 Symmetrical shapes 22 Count like a computer 24 Making a decision 26 Fractal geometry 28 Glossary 30 Answers 31 Index 32
MATHEMATICS ALL AROUND US Mathematics is a powerful tool that allows us to measure the world around us From simple systems of counting early mathematicians developed techniques such as arithmetic algebra and geometry to create calendars keep trade records or calculate taxes Today mathematicians use complex systems to dig into the deepest mysteries of the universe 4 1 2 10 9 5 6 3 4 7 8 Counting bases We usually count in a number system known as base 10 or the decimal system with one digit for each of our fingers and thumbs Sometimes we count in bases other than base 10 For example to count time we use base 60 Called the sexagesimal system it divides an hour into 60 minutes and a minute into 60 seconds This system was used by the ancient Babylonians 4,000 years ago Base 60 is useful because 60 is the smallest number that can be divided by 2 3 4 5 and 6 as well as 10 12 15 20 and 30 This makes it easy to divide an hour into equal parts
A clock face counts minutes in base 60 and hours in base 12 Solving equations An equation is a number sentence in which one side of the sign equals the other side 5 3 18 3 In algebra the unknown numbers in an equation are replaced by a letter The job of the mathematician is to solve the equation to find the value the letter represents y 7 2 5 therefore y 3 A formula is a set of symbols that expresses a mathematical rule Different values can be placed in the formula For example the formula to convert pounds into kilograms is y 5x 11 where y is the weight in kilograms and x is the weight in pounds The symbol means divided by 5 Mathematics in Wonderland By the 1800s new ideas had been introduced into mathematics that seemed impossible in the real world such as the square root of 1 English mathematician Lewis Carroll poked fun at many of these ideas in his 1865 novel Alice's Adventures in Wonderland In the book Alice is transported to a world in which impossible things happen all the time She tries to remember her times tables but finds that numbers behave very differently in Wonderland probably because she is no longer counting in base 10 Read on to discover the problems that mathematicians have solved through the ages The answers to each project's questions are found on page 31
