The Art of Geometry (Classic Reprint)

The pedagogy of Geometry is divisible into three parts, the Science of Geometry (the facts), the Logic of Geometry (the framework), and the Art or Technique of Geometry.

The Science and Logic of Geometry are presented in the current text-books.

The Art of Geometry is given in the following pages.

One of the great causes of complaint among students of Geometry is the lack of a systematic course of procedure. The student has no guide as to what to do next, and is generally unable to give any reason for the different steps he takes, except that they are logically correct and that they produce an answer. On the other hand, he ought to know why each step in the proof is taken. Only thus can he proceed with real understanding and be prepared to attack intelligently a new and unknown problem. Thus in the problem. To compute the length of the bisector of the angle of a triangle, the first step given by all the text-books is, draw the circumscribing circle. But why? What suggests such a step? What preparation has been given to the student to lead him to such a construction? No text-book has yet answered the question.

The following pages will show not only what suggests the circle, but will provide the student with such a course of procedure (technique) that he could not miss it if he would.

The current text-books supply the student with propositions and a logical proof of their correctness, but they do not put him in a position to deduce his own propositions nor to build a proof independently for himself.

Tags: lines line geometry construction diagram points equal circle segments tools operation metrical tool straight triangle angles base equations consequences similar
Category: Mathematics - Geometry

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