Where Does a Graph Go?

Where Does a Graph Go? — page 1

Where Does a Graph Go? — page 2 — W hen you think about mathematics you probably think about a class at school where you do calculations and answer word problems But have you ever thought about math being all around you It’s in every shape and pattern you see It’s in every song you hear It’s in every game you play and any puzzle you solve The first mathematicians realized this and they looked for ways to prove it to show how order and reason could explain much about life as they knew it Sometimes this was easy to do But other times people just didn’t get it Even some of the most intelligent people in history have struggled with math Albert Einstein once wrote to a child Do not worry about your difficulties in Mathematics I can assure you mine are still greater So how can you use whatever you know about math in everyday life When you explain your location to a friend who is meeting you at the mall make a substitution with another player in a basketball game or watch the path of a ball flying through the air you are using math These ideas are important in a branch of math known as algebraic geometry Algebraic geometry is con cerned with drawing graphs of different equations so that they can be studied Where does this branch of math show up in your own life 5

Where Does a Graph Go? — page 3 — THE LINES MADE BY ROADS ON A MAP FORM A MATHEMATI CAL-LOOKING GRID 6

Where Does a Graph Go? — page 4 — COMMON LOCATORS MUCH OF THE MATHEMATICS THAT YOU DO INVOLVES WORK ING WITH A ONE-DIMENSIONAL SET OF NUMBERS Even when you add two numbers together the final sum is just one number The same holds true for the other operations that you do The result will always be another number You are essentially just moving forward and backward on a giant number line The numbers that you calculate with can be considered points on a number line into a two-dimensional space One of the main principles of ge ometry is that two points make up a line You may also know that two points can be used for graphing in This idea expands as you get algebra but it wasn’t always that way Mathematicians were able to argue ideas in geometry and solve problems with algebra but the two branches didn’t come together until the early 17th century Think of those two points in space as being two cities The road connecting those two cities can be thought of as a line If you travel between the cities you are traveling on that line If you stay on that road to go to another city you are still just traveling in one di mension Essentially you’re mov ing along a number line by doing calculations But what happens if you want to go to a city that isn’t on the same road In real life you can use a map 7

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