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1、Mathematical English 2: Geometry and TrigonometryMathematical EnglishDr. Xiaomin ZhangEmail: 2.2 Geometry and TrigonometryTEXT A Why study geometry?Why do we study geometry? The student beginning the study of this text may well ask, “What is geometry? What can I expect to gain from this study?”Many
2、leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools.Geometry had its origin long ago in the meas
3、urements by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The Greek word geometry is derived from geo, meaning “earth”, and metron, meaning “measure”. As early as 2000 B.C. we find the land surveyors of these people re-establishing vanishing landmarks and bo
4、undaries by utilizing the truths of geometry.Geometry is a science that deals with forms made by lines. A study of geometry is an essential part of the training of the successful engineer, scientist, architect, and draftsman. The carpenter, machinist, stonecutter, artist, and designer all apply the
5、facts of geometry in their trades. In this course the student will learn a great deal about geometric figures such as lines, angles, triangles, circles, and designs and patterns of many kinds.One of the most important objectives derived from a study of geometry is making the student be more critical
6、 in his listening, reading, and thinking. In studying geometry he is led away from the practice of blind acceptance of statements and ideas and is taught to think clearly and critically before forming conclusions.There are many other less direct benefits the student of geometry may gain. Among these
7、 one must include training in the exact use of the English language and in the ability to analyze a new situation or problem into its basic parts, and utilizing perseverance, originality, and logical reasoning in solving the problem. An appreciation for the orderliness and beauty of geometric forms
8、that abound in mans works and of the creations of nature will be a byproduct of the study of geometry. The student should also develop an awareness of the contributions of mathematics and mathematicians to our culture and civilization.TEXT B Some geometrical terms1. Solids and planes. A solid is a t
9、hree-dimensional figure. Common examples of solid are cube, sphere, cylinder, cone and pyramid.A cube has six faces which are smooth and flat. These faces are called plane surfaces or simply planes. A plane surface has two dimensions, length and width .The surface of a blackboard or a tabletop is an
10、 example of a plane surface.2. Lines and line segments. We are all familiar with lines, but it is difficult to define the term. A line may be represented by the mark made by moving a pencil or pen across a piece of paper. A line may be considered as having only one dimension, length. Although when w
11、e draw a line we give it breadth and thickness, we think only of the length of the trace when considering the line. A point has no length, no width, and no thickness, but marks a position. We are familiar with such expressions as pencil point and needle point. We represent a point by a small dot and
12、 name it by a capital letter printed beside it, as “point A” in Fig. 2-2-1.The line is named by labeling two points on it with capital letters or one small letter near it. The straight line in Fig. 2-2-2 is read “line AB” or “line l”. A straight line extends infinitely far in two directions and has
13、no ends. The part of the line between two points on the line is termed a line segment. A line segment is named by the two end points. Thus, in Fig. 2-2-2, we refer to AB as line segment of line l. When no confusion may result, the expression “line segment AB” is often replaced by segment AB or, simp
14、ly, line AB.There are three kinds of lines: the straight line, the broken line, and the curved line. A curved line or, simply, curve is line no part of which is straight. A broken line is composed of joined, straight line segments, as ABCDE of Fig. 2-2-3.3. Parts of a circle. A circle is a closed cu
15、rve lying in one plane, all points of which are equidistant from a fixed point called the center (Fig. 2-2-4). The symbol for a circle is . In Fig. 2-2-4, O is the center of ABC, or simply of O. A line segment drawn from the center of the circle to a point on the circle is a radius (plural, radii) o
16、f the circle. OA, OB, and OC are radii of O, A diameter of a circle is a line segment through the center of the circle with endpoints on the circle. A diameter is equal to two radii. A chord is any line segment joining two points on the circle. ED is a chord of the circle in Fig. 2-2-4.From this definition is should be apparent that a diameter is a chord. Any part of a circle is an arc, such as arc AE. Points A and E
