Geometry For Dummies

Mark Ryan

• Editore: For Dummies
• Anno: 2016
• ISBN:
  9781119181644
• Edizione: 3
• Argomento: Matemáticas
• Categoria: Geometría algebraica

Hit the geometry wall? Get up and running with this no-nonsense guide!

Does the thought of geometry make you jittery? You're not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you'll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time.

Geometry is a subject full of mathematical richness and beauty. But it's a subject that bewilders many students because it's so unlike the math they've done before—it requires the use of deductive logic in formal proofs. If you're having a hard time wrapping your mind around what that even means, you've come to the right place! Inside, you'll find out how a proof's chain of logic works and even discover some secrets for getting past rough spots along the way. You don't have to be a math genius to grasp geometry, and this book helps you get un-stumped in a hurry!

• Find out how to decode complex geometry proofs
• Learn to reason deductively and inductively
• Make sense of angles, arcs, area, and more
• Improve your chances of scoring higher in your geometry class

There's no reason to let your nerves get jangled over geometry—your understanding will take new shape with the help of Geometry For Dummies.

Part 1

Getting Started with Geometry Basics

IN THIS PART …

Discover why you should care about geometry.

Understand lines, points, angles, planes, and other geometry fundamentals.

Measure and work with segments and angles.

Chapter 1

Introducing Geometry

IN THIS CHAPTER

Surveying the geometric landscape: Shapes and proofs

Finding out “What is the point of geometry, anyway?”

Getting psyched to kick some serious geometry butt

Studying geometry is sort of a Dr. Jekyll-and-Mr. Hyde thing. You have the ordinary, everyday geometry of shapes (the Dr. Jekyll part) and the strange world of geometry proofs (the Mr. Hyde part).

Every day, you see various shapes all around you (triangles, rectangles, boxes, circles, balls, and so on), and you’re probably already familiar with some of their properties: area, perimeter, and volume, for example. In this book, you discover much more about these basic properties and then explore more-advanced geometric ideas about shapes.

Geometry proofs are an entirely different sort of animal. They involve shapes, but instead of doing something straightforward like calculating the area of a shape, you have to come up with an airtight mathematical argument that proves something about a shape. This process requires not only mathematical skills but verbal skills and logical deduction skills as well, and for this reason, proofs trip up many, many students. If you’re one of these people and have already started singing the geometry-proof blues, you might even describe proofs — like Mr. Hyde — as monstrous. But I’m confident that, with the help of this book, you’ll have no trouble taming them.

This chapter is your gateway into the sensational, spectacular, and super-duper (but sometimes somewhat stupefying) subject of this book: geometry. If you’re tempted to ask, “Why should I care about geometry?” this chapter will give you the answer.

Studying the Geometry of Shapes

Have you ever reflected on the fact that you’re literally surrounded by shapes? Look around. The rays of the sun are — what else? — rays. The book in your hands has a shape, every table and chair has a shape, every wall has an area, and every container has a shape and a volume; most picture frames are rectangles, CDs and DVDs are circles, soup cans are cylinders, and so on and so on. Can you think of any solid thing that doesn’t have a shape? This section gives you a brief introduction to these one-, two-, and three-dimensional shapes that are all-pervading, omnipresent, and ubiquitous — not to mention all around you.

One-dimensional shapes

There aren’t many shapes you can make if you’re limited to one dimension. You’ve got your lines, your segments, and your rays. That’s about it. But it doesn’t follow that having only one dimension makes these things unimportant — not by any stretch. Without these one-dimensional objects, there’d be no two-dimensional shapes; and without 2-D shapes, you can’t have 3-D shapes. Think about it: 2-D squares are made up of four 1-D segments, and 3-D cubes are made up of six 2-D squares. And it’d be very difficult to do much mathematics without the simple 1-D number line or without the more sophisticated 2-D coordinate system, which needs 1-D lines for its x- and y-a...