Geometry/Chapter 1

Chapter 1: An Introduction to Geometry

Introduction

Geometry comes from two words: geo which means Earth and metry meaning measure. Therefore, geometry means "measuring the Earth". This branch of mathematics deals with the understanding of point and lines and their combinations. In other words, geometry is a type of maths used to measure things that are impossible to measure with devices. For example, no one has been able take a tape measure around the Earth, yet we are pretty confident that the circumference of the planet at the equator is 40,075.036 kilometers (24,901.473 mi). How do we know that? The first known case of calculating the distance around the Earth was done by Eratosthenes around 240 BCE. What tools do you think current scientists might use to measure the size of planets? The answer is geometry.

However, geometry is more than measuring the size of objects. If you were to ask someone who had taken geometry in high school what it is that s/he remembers, the answer would most likely be proofs. If you were to ask him/her what it is that s/he liked the least, the answer would probably be proofs. A study of Geometry does not have to include proofs. Proofs are not unique to Geometry. Proofs could have been done in algebra or delayed until calculus. The reason that High School Geometry almost always spends a lot of time with proofs is that the first great Geometry textbook, "The Elements," was written exclusively with proofs.

This textbook is based on Euclidean geometry. Euclidean refers to a book written over two thousand years ago called The Elements by a man named Euclid. In this book Euclid provides methods using just a compass, ruler and a protractor to prove geometrical statements. His method influences the way geometry is taught today. Euclid's book was part of the math curriculum until the beginning of the twentieth century.