Master Math: Geometry (Master Math Series) | 
 enlarge | Author: Debra Anne Ross
Publisher: Delmar Cengage Learning
Category: Book
List Price: $18.95
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Sales Rank: 330947
Media: Paperback
Edition: 1
Pages: 384
Number Of Items: 1
Shipping Weight (lbs): 0.9
Dimensions (in): 8.5 x 5.6 x 0.6
ISBN: 1564146677
Dewey Decimal Number: 510
EAN: 9781564146670
Publication Date: July 28, 2004
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Condition: S-F-22 Brand new-never been opened.
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Product Description
Master Math: Geometry and the Master Math series as a whole are clear, concise, and yet comprehensive reference sources. They are designed to allow quick access to clearly presented and easy-to-understand explanations of concepts, principles, definitions, examples, and applications. This book was written for students, teachers, tutors, and parents, as well as for scientists and engineers who need to look up principles, definitions, explanations of concepts, and pertinent examples. It provides everything a high school or first year college student needs to know including: explanation of deductive reasoning, how to perform proofs, definitions, theorems, and postulates, Examples pertaining to points, lines, plans, angles, and ratios, coverage on triangles, quadrilaterals, polygons, and much more!
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Introduction and TOC August 8, 2007
Ming
6 out of 6 found this review helpful
Geometry is present in nature, art, architecture, surveying, navigation, cartography, biology, chemistry, physics, geology, astronomy, all fields of engineering, and in the structure of the smallest bits of matter to the grandest galaxies. The study of geometry is like detective work-you are given bits of information and use logic and reasoning to determine what you want to know. Becoming proficient in geometry will train your mind to solve problems in a creative and efficient way-like a detective.
In forming the field of geometry, ancient mathematicians developed the postulation system in which one begins with a set of unproved statements or postulates, and deduces using logic, other statements or theorems. Accordingly, the development of logic and deductive reasoning was instituted to prove geometric statements. Geometry was used by ancient people including Babylonians, Egyptians, Romans, and Greeks in practical applications such as land measurement, surveying, construction, navigation, and astronomy. Information and facts pertaining to geometry were organized and developed by Greeks between 600 and 300 B.C., and described by Euclid in his famous book Elements in approximately 300 B.C. Euclidean geometry combines related elements using the methods of logic and reasoning, and the tools of axioms, postulates, definitions, theorems, and constructions in order to prove, describe, calculate, generate, or use information pertaining to geometric objects. Euclid provided five primary postulates which can be described as: (1) One straight line connects any two points; (2) Any straight line can be extended infinitely in either direction; (3) A circle can be drawn with any center and any radius; (4) All right angles are equal; and (5) Given a line and a point not on the line, only one line can be drawn parallel to that line through the point. The process by which mathematicians attempted to verify this fifth parallel line postulate led to non-Euclidean geometries.
Euclidean geometry describes the world we think we see around us in which the shortest distance between two points is a straight line, the angles in a triangle always sum to 180 , and parallel lines lie in the same plane, remain equidistant, and never intersect even if they are infinitely long. Non-Euclidean geometries are less obvious. In spherical geometry, which takes place on a sphere and is used by pilots, ship's captains, and astronomers, no parallel lines exist, the angles in a triangle sum to greater than 180 , and the shortest distance between two points is a great circle (the largest circle that can be drawn through any point on a sphere). In hyperbolic geometry, which can be represented in two dimensions as saddle-shaped, the angles in a triangle sum to less than 180 , and through a point not on a line, there is more than one line parallel to that line. Euclidean geometry provides an excellent repre-sentation for part of the universe that we observe, but in the study of certain aspects of our universe, or the universe itself, non-Euclidean geometries may provide a more accurate portrayal. For example, in Einstein's Theory of General Relativity, matter produces curved space-time. Compare a Euclidean triangle, a Hyperbolic triangle, and a Spherical triangle!
Another branch of geometry developed in the 17th century by Rene Descartes is coordinate geometry, also called analytic geometry, which is the study of geometry using the analytical methods of algebra. This approach involves placing a geometric figure into a coordinate system illustrating a proof, and obtaining information about the figure using algebraic equations.
Today, geometry has been joined with computers and computer-aided design and is used in fields such as automobile manufacturing, computer vision, robotics, video game programming, virtual reality, aerospace, and architecture. Architecture examples include the innova-tive work of Frank O. Gehry in his Guggenheim Museum in Bilbao, Spain, and Norman Foster's striking glass and steel London City Hall.
Master Math: Geometry provides everything a high school or first year college student needs to know including an explanation of deductive reasoning, how to perform proofs and constructions, as well as definitions, theorems, postulates, and examples pertaining to points, lines, planes, angles, ratios, proportions, triangles, congruence, similarity, quadrilaterals, polygons, circles, surface area and volume of geometric solids, and coordinate, or analytic, geometry. Master Math: Geometry is part of the Master Math series, which is comprised of Master Math: Basic Math and Pre-Algebra, Master Math: Algebra, Master Math: Trigonometry, Master Math: Pre-Calculus and Geometry, and Master Math: Calculus. This book and those previously listed are written to provide clear, easy to understand, comprehensive reference sources that allow quick access to explanations of concepts, principles, definitions, examples, and applications. Master Math: Geometry is written to assist high school and college students, teachers, tutors, and parents, as well as to serve as a reference for scientists, engineers, architects, or anyone needing a basic reference.
Table of Contents
Introduction
CHAPTER 1: Deductive Reasoning and Proofs
1.1. The language of geometry
1.2. Deductive reasoning
1.3. Theorems and how to write a proof
1.4. Key axioms and postulates
1.5. Chapter 1 summary and highlights
CHAPTER 2: Points, Lines, Planes, and Angles
2.1. Points, lines, and planes
2.2. Line segments and distance
2.3. Parallel lines
2.4. Perpendicular lines
2.5. Distances and bisectors
2.6. Rays and angles
2.7. Chapter 2 summary and highlights
CHAPTER 3: Ratios and Proportions
3.1. Ratios and proportions
3.2. Proportional segments
3.3. Chapter 3 summary and highlights
CHAPTER 4: Triangles, Congruence, and Similarity
4.1. Triangle definitions, interior angle sum, and exterior angles
4.2. Types of triangles
4.3. Parts of triangles, altitude, bisector, median, and Ceva's Theorem
4.4. Inequalities and triangles
4.5. Congruent triangles
4.6. Similar triangles: Congruent angles and sides in proportion
4.7. Similar right triangles
4.8. Right triangles: Pythagorean Theorem and 30 :60 :90 and 45 :45 :90 triangles
4.9. Triangles and trigonometric functions
4.10. Area of a triangle
4.11. Chapter 4 summary and highlights
CHAPTER 5: Polygons and Quadrilaterals
5.1. Polygons
5.2. Sum of the interior and exterior angles in a polygon
5.3. Regular polygons and their interior and exterior angle measures
5.4. Quadrilaterals
5.5. Parallelograms
5.6. Special parallelograms: Rectangles, rhombuses, and squares
5.7. Trapezoids
5.8. Area and perimeter of squares, rectangles, parallelograms, rhombuses, trapezoids, other polygons, and regular polygons
5.9. Congruence, area, and similarity
5.10. Chapter 5 summary and highlights
CHAPTER 6: Circles
6.1. Circles: Definitions
6.2. Arcs, central angles, and inscribed angles
6.3. Chords, arcs, and angles
6.4. Secants, angles, arcs, and segments
6.5. Tangents
6.6. Circumference and area of circles and sectors
6.7. Circumscribed and inscribed polygons
6.8. Chapter 6 summary and highlights
CHAPTER 7: Geometric Solids: Surface Area and Volume of Three-Dimensional Objects
7.1. Solids
7.2. Prisms: Cubes, rectangular solids, and oblique and right prisms
7.3. Pyramids
7.4. Cylinders
7.5. Cones
7.6. Spheres
7.7. Similar solids
7.8. Cavalieri's principle
7.9. Chapter 7 summary and highlights
CHAPTER 8: Constructions and Loci
8.1. Introduction
8.2. Constructions involving lines and angles
8.3. Constructions involving triangles
8.4. Constructions involving circles and polygons
8.5. Construction involving area
8.6. Locus of points
8.7. Chapter 8 summary and highlights
CHAPTER 9: Coordinate or Analytic Geometry
9.1. Rectangular coordinate systems: Definitions
9.2. Distance between points
9.3. Midpoint formula
9.4. Slope of a line including parallel and perpendicular lines
9.5. Defining linear equations
9.6. Graphing linear equations
9.7. Chapter 9 summary and highlights
Index
The best basic geometry book written! September 25, 2007
Happy Camper
7 out of 7 found this review helpful
The best presentation of geometry I have ever seen. The topics are presented in a logical manner so that they build, are in context, and make sense. It explains logic and proofs in a way students can really understand. Definitions are provided in the beginning so you can orient yourself and understand the jargon of geometry from the start. It presents concepts three ways: a description, a picture, and a description of the picture. It makes learning so easy! There are plenty of real-world and fun examples and tidbits of information that makes learning fun. It is clear, concise, and the topics have a flow and context that makes is easier to learn the material whether you are taking geometry for the first time, are older and need a review, or are taking higher level math, science or engineering classes and need to quickly look something up and understand it. Learning geometry does not need to be a frustrating experience! Everything you need for basic geometry is in this book! Master Math: Basic Math and Pre-Algebra, Master Math: Algebra, Master Math: Trigonometry, Master Math: Pre-Calculus and Geometry, and Master Math: Calculus are also fantastic!
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