Geometry: A Contemporary Course pdf epub mobi txt 电子书下载 2024

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[美] Harry Lewis

D. Van Nostrand Company, Inc.

1968-1-3

678

Hardcover

9780442047634

图书标签: 欧式几何数学几何 geometry

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发表于2024-11-22

Geometry: A Contemporary Course epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

Geometry: A Contemporary Course pdf epub mobi txt 电子书下载 2024

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This book arises from mature experience allied with an appreciation of contemporary trends of thought, it has been tested under classro om conditions, it requires high standards of thought on the part of both pupil and teacher, and it has a number of novel aspects without breaking with traditional methods.

In recent years, the trend in our syllabuses up to the Ordinary Level in the G.C.E. has been to reduce the number of formal theorems asked. The teacher has had little to learn as his ability in rider work has so greatly transcended the ability of his pupils: he has perhaps allowed himself to be bored. This may account for the fact that the attention of reformers has been drawn towards facets of work in algebra, as being a more obvious field in which change would be acceptable, by challenging our teaching skill in the presentation of new material.

In spite of the American style which inclines to put a number to every postulate, definition and theorem, Dr. Lewis's text does much to bring a happy marriage between so called "modern mathematics" and the content of our geometry syllabuses up to the standard of our fifth forms and a little beyond. The author investigates the need for definitions and postulates, first in everyday situations and then in mathematics generally. Point, line and set then appear as undefined terms whose properties need to be made clear by examples: there follow the ideas of betweenness, line segment, ray and angle. The postulates needed for the four elementary operations are followed by those of the reflexive, symmetric and transitive properties of equality. Congruence appears as a one to one correspondence between the vertices of two polygons such that (a) all the corresponding sides are equal and (b) all the corresponding angles are equal. Ratio is defined as the quotient of the measure of two quantities, when the quantities are expressed in the same unit. A locus of points is the set of those points and only those points, that satisfy given conditions.

The elements of set theory, particularly intersection and union first appear in connection with the building of figures, and later along with loci and cartesian geometry. There is a careful examination by Venn diagrams of the relations between the statements (i) If p then q, (ii) If q then p (iii) If not p then not q (iv) If not q then not p This comes first with general and then with geometrical situations. The relationships are later established by truth tables. The set theory and the logic are developed on formal lines but only so far as they are needed for practical purposes in the book.

The text itself is very readable and smooth, in many places quite informal without being familiar, and without the slightest trace of looseness, triviality or "writing down to a level". The preface mentions grades 10 and 11 in the U.S.A., corresponding to the 15 and 16 year old grammar school pupils in this country, so the level of writing would be a little difficult for younger pupils. On the other hand, the author has increased the pace at which a pupil may move by his deliberate policy of providing readymade diagrams for the first half of the riders in each exercise.

The less usual parts include chapters on coordinate geometry, in which set notation is used skilfully but not obtrusively, some formal solid geometry and an eight page incursion into non-euclidean geometry with three theorems and eight tangible riders.

The format of the book is large being 9.5 in. by 6.3 in., the printing, layout and symbolism are clear and most attractive, the book is profusely illustrated and two colour printing is used for both diagrams and text. A good index is provided, but there do not appear to be teachers' copies with answers. In my opinion, this book represents an important contribution to the teaching apparatus of any school and copies should be widely available for use by school staffs, if not for rotation amongst classes.

Geometry: A Contemporary Course 下载 mobi epub pdf txt 电子书

著者简介

Dr. Harry Lewis was principal of Arts High School, Newark, New Jersey. He was formerly the chairman of the Mathematics Department of Ease Side High School of Newark, having taught mathematics for many years in the Newark Public School System. He is the coauthor of textbooks on business mathematics and has taught at the New York University School of Education.