Geometry and Trigonometry

Geometry and Trigonometry — page 7 — Euclid works with a compass a tool used in drawing circles in a 14th century marble panel on the Campanile bell tower of Santa Maria del Fiore in Florence Italy A Dagli Orti De Agostini Picture Library Getty Images 12

Geometry and Trigonometry — page 8

Geometry and Trigonometry — page 9 — Geometry and Trigonometry provides a simplified universe where points and lines obey believable rules and where conclusions are easily verified By first study ing how to reason in this simplified universe people can eventually through practice and experience learn how to reason in a compli cated world Geometry in ancient times was recognized as part of everyone s education Early Greek philos ophers asked that no one come to their schools who had not learned the Elements of Euclid There were and still are many who resisted this kind of education It is said that Ptolemy I asked Euclid for an easier way to learn the material Euclid told him there was no royal road to geometry The same message applies to readers today They will not learn what geometry is all about What they will learn is the basic shapes of some of the fig ures dealt with in geometry and a few facts about them It takes a geometry course with textbook and teacher to show the complete and orderly arrangement of the facts and how each is proved POINTS LINES AND ANGLES Geometric figures are based on points and lines Euclid began his Elements with a series of definitions starting with these two A point is that which has no part A line is breadthless length 14

Geometry and Trigonometry — page 10 — EUCLIDEAN GEOMETRY Because he had not explained the words part breadth or length he was not defining these figures in terms of simpler things The fact is that points and lines are so simple that they cannot be defined perfectly but other things can be defined in terms of them Definitions in this volume will not be stated in full detail as they would be in a geometry text book but they will be described briefly to show how they are linked lead ing from points and lines to very special figures A line is usually drawn with arrowheads to show that it extends without end in both directions A ray is half of a line with just one Some different geometric figures are from top endpoint Two rays to bottom a line a ray an angle a straight with the same endpoint angle and a right angle The latter two are also shown as an open book Encyclopaedia form an angle If the Britannica Inc rays are the two halves 15

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