Geometry and Trigonometry

Geometry and Trigonometry — page 1 — Intro duction his book covers a broad collection of the principles of geometry and trigonometry inside a nice compact format for the middle school and early high school student Colorful diagrams bring the principles to life The topics are enriched by references to famous mathematicians who discovered these prin ciples and also snapshots of these principles at work in the real world Seldom does a math book bring the story of so many topics in such a comprehensible way The student will find a wonderful resource that can always be consulted for quick help and location of ideas that arise even years later during formal math study and beyond Of course math discoveries are fascinating in themselves and when they lead to wonder ful useful inventions one sees why people study these ideas in the first place For instance could a basic geometric shape be used to stop excruciating pain Perhaps Euclid didn t have disease in mind when he began organizing the simplest of geometric figures such as points lines and curves But over the years other mathematicians took his shapes and proved that certain geomet ric properties had qualities that today make people feel better even if those individuals happen to be doubled over in pain from what are called kidney

Geometry and Trigonometry — page 2 — INTRODUCTION The particular geometrical shape required for medical healing in this case is called an ellipse featured in this book Inside the ellipse or its three dimensional relative an egg shape or ellipsoid is a point called a focus near one end of the shape Another focus appears near the other end of the shape Scientists found ALL In lithotripsy a lithotripter uses an ellipsoid and a focus point to send sound waves to shatter a patient s gallstones or kidney stones into miniscule pieces Southern Illinois University Photo Researchers Getty Images

Geometry and Trigonometry — page 3 — Geometry and Trigonometry that shooting sonar waves from one focus makes sounds that bounce off the inside walls of the ellipsoid and they all strike the other focus at once like a gentle hammer That's how doctors use those sounds special instruments such as a lithotripter machine and ellipsoids to help break up kidney stones in the patient No surgery is needed The patient makes a faster recovery than if surgery had been used His or her kid ney stones are painlessly shattered with no harm to the kidney and the patient might go to school or work the very next day When readers enter the pages of this book and see the basics of geometry and trigonom etry it pays to ask themselves with each figure they see could they discover some great inven tion with this shape Could they save lives Could they ease pain Could they somehow use it to create a new invention What prob lem might they solve with it Students will discover why trigonometry is called that and they ll see a math topic begin to unfold that strangely they have already used quite a bit even though they might not have been aware of it Trigonometry is embedded in the software of computers When people have played a computer game where their car for instance spins and misses trouble on the road the joystick is really telling the computer

Geometry and Trigonometry — page 4 — INTRODUCTION to use trigonometry formulas to get the car to do what the players want So the math comes alive for these individuals They'll encounter in this book some basics of trigonometry often fondly called trig Finally readers will also find fascinating information on great mathematicians who made the ideas of geometry and trigonome try apply to wonderful discoveries that have changed the world they live

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