Introduction People use maps all the time and for good reason Maps make it easy to find out where you are and how to get to where you want to go This is called navigation the process of directing cars boats airplanes and even people When was the last time you used a map to get somewhere Can you think of ways that math relates to maps 4
If you ever find yourself in a big unfamiliar place like a park train station or shopping mall the simplest way to orient yourself is to find a map Often times a map will be posted with your locaton clearly labeled as you are here Maybe you never knew it but maps depend on math for their accuracy Most maps are created to help people travel great distances Because of this the details on a map have to be precise Math guarantees this precision DOWNTOWN NEW YORK This map shows a portion of downtown New York City 5
Considering Scale Maps are like pictures that show you places and things from angles that you don’t typically see in real life The most common angle for a map is a view from far above which is sometimes called a bird’s eye view But a map is much more than just a picture because it is meant to show very specific information Photos of New York taken from above don’t look much like maps The streets aren’t labeled Roads are not highlighted and places of interest are not identified A topographic photo showing the southwest corner of New York City’s Central Park 6
So although a map is a picture it is a picture meant to convey specific information like distance direction or elevation Calculating distance is one of the most common uses for a map Maps make this an easy task because they are drawn to scale But what does drawn to scale mean Essentially it means that the place the map shows is a different size than the map This is done for practical reasons A map of the United States that was the exact same size of the United States wouldn’t be very useful To start with you wouldn’t be able to store it anywhere Instead people rely on maps that depict large areas on a smaller scale Maps use a small measurement to depict a larger measurement 1 inch 0 5 mile A road map showing the southwest corner of New York City’s Central Park 7
