Elementary geometry for college students
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- Publication date
- 2006
- Publisher
- Boston, MA : Houghton Mifflin
- Collection
- internetarchivebooks; printdisabled
- Contributor
- Internet Archive
- Language
- English
- Item Size
- 1.3G
x, 519, 54, 4, 4 pages : 24 cm
Includes index
1. Line and angle relationships -- Sets, statements, and reasoning -- Informal geometry and measurement -- Early definitions and postulates -- Angles and their relationships -- Introduction to geometric proof -- Relationships : perpendicular lines -- The formal proof of a theorem -- Perspective on history : the development of geometry -- Perspective on application : patterns -- 2. Parallel lines -- The parallel postulate and special angles -- Indirect proof -- Proving lines parallel -- The angles of a triangle -- Convex polygons -- Symmetry and transformations -- Perspective on history : sketch of Euclid -- Perspective on application : non-Euclidean geometrics -- 3. Triangles -- Congruent triangles -- Corresponding parts of congruent triangles -- Isosceles triangles -- Basic constructions justified -- Inequalities in a triangle -- Perspective on history : sketch of Archimedes -- Perspective on application : Pascal's triangle -- 4. Quadrilaterals -- Properties of a parallelogram -- The parallelogram and kite -- The rectangle, square, and rhombus -- The trapezoid -- Perspective on history : sketch of Thales -- Perspective on application : square numbers as sums -- 5. Similar triangles -- Ratios, rates, and proportions -- Similar polygons -- Proving triangles similar -- The Pythagorean Theorem -- Special right triangles -- Segments divided proportionally -- Perspective on history : Ceva's proof -- Perspective on application : an unusual application of similar triangles
6. Circles -- Circles and related segments and angles -- More angle measures in the circle -- Line and segment relationships in the circle -- Some constructions and inequalities for the circle -- Locus of points -- Concurrence of lines -- Perspective on history : the value of [pi] -- Perspective on application : the nine-point circle -- 7. Areas of polygons and circles -- Area and initial postulates -- Perimeter and area of polygons -- Regular polygons and area -- Circumference and area of a circle -- More area relationships in the circle -- Perspective on history : sketch of Pythagoras -- Perspective on application : another look at the Pythagorean Theorem -- 8. Surfaces and solids -- Prisms, area, and volume -- Pyramids, area, and volume -- Cylinders and cones -- Polyhedrons and spheres -- Perspective on history : sketch of René Descartes -- Perspective on application : birds in flight -- 9. Analytic geometry -- The rectangular coordinate system -- Graphs of linear equations and slope -- Preparing to do analytic proofs -- Analytic proofs -- Equations of lines -- Perspective on history : the Banach-Tarski paradox -- Perspective on application : the point-of-division formulas -- 10. Introduction to trigonometry -- The sine ratio and applications -- The cosine ratio and applications -- The tangent ratio and other ratios -- Applications with acute triangles -- Perspective on history : sketch of Plato -- Perspective on application : radian measure of angles -- Appendix A. Algebra review -- Appendix B. Summary of constructions, postulates, and theorems and corollaries
Includes index
1. Line and angle relationships -- Sets, statements, and reasoning -- Informal geometry and measurement -- Early definitions and postulates -- Angles and their relationships -- Introduction to geometric proof -- Relationships : perpendicular lines -- The formal proof of a theorem -- Perspective on history : the development of geometry -- Perspective on application : patterns -- 2. Parallel lines -- The parallel postulate and special angles -- Indirect proof -- Proving lines parallel -- The angles of a triangle -- Convex polygons -- Symmetry and transformations -- Perspective on history : sketch of Euclid -- Perspective on application : non-Euclidean geometrics -- 3. Triangles -- Congruent triangles -- Corresponding parts of congruent triangles -- Isosceles triangles -- Basic constructions justified -- Inequalities in a triangle -- Perspective on history : sketch of Archimedes -- Perspective on application : Pascal's triangle -- 4. Quadrilaterals -- Properties of a parallelogram -- The parallelogram and kite -- The rectangle, square, and rhombus -- The trapezoid -- Perspective on history : sketch of Thales -- Perspective on application : square numbers as sums -- 5. Similar triangles -- Ratios, rates, and proportions -- Similar polygons -- Proving triangles similar -- The Pythagorean Theorem -- Special right triangles -- Segments divided proportionally -- Perspective on history : Ceva's proof -- Perspective on application : an unusual application of similar triangles
6. Circles -- Circles and related segments and angles -- More angle measures in the circle -- Line and segment relationships in the circle -- Some constructions and inequalities for the circle -- Locus of points -- Concurrence of lines -- Perspective on history : the value of [pi] -- Perspective on application : the nine-point circle -- 7. Areas of polygons and circles -- Area and initial postulates -- Perimeter and area of polygons -- Regular polygons and area -- Circumference and area of a circle -- More area relationships in the circle -- Perspective on history : sketch of Pythagoras -- Perspective on application : another look at the Pythagorean Theorem -- 8. Surfaces and solids -- Prisms, area, and volume -- Pyramids, area, and volume -- Cylinders and cones -- Polyhedrons and spheres -- Perspective on history : sketch of René Descartes -- Perspective on application : birds in flight -- 9. Analytic geometry -- The rectangular coordinate system -- Graphs of linear equations and slope -- Preparing to do analytic proofs -- Analytic proofs -- Equations of lines -- Perspective on history : the Banach-Tarski paradox -- Perspective on application : the point-of-division formulas -- 10. Introduction to trigonometry -- The sine ratio and applications -- The cosine ratio and applications -- The tangent ratio and other ratios -- Applications with acute triangles -- Perspective on history : sketch of Plato -- Perspective on application : radian measure of angles -- Appendix A. Algebra review -- Appendix B. Summary of constructions, postulates, and theorems and corollaries
- Access-restricted-item
- true
- Addeddate
- 2022年11月17日 14:01:23
- Associated-names
- Koeberlein, Geralyn M
- Autocrop_version
- 0.0.14_books-20220331-0.2
- Bookplateleaf
- 0004
- Boxid
- IA40771804
- Camera
- USB PTP Class Camera
- Collection_set
- printdisabled
- External-identifier
-
urn:lcp:elementarygeomet0000alex_o5k5_4ed:lcpdf:94d0bb27-771e-4692-b74a-dba7426205e8
urn:lcp:elementarygeomet0000alex_o5k5_4ed:epub:4d7f3341-d781-449b-9ef1-ef81a0ec20b3
urn:oclc:record:1357622976[WorldCat (this item)]
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061864525X
9780618645251
0618730680
9780618730681
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- Rcs_key
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- Republisher_date
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- Republisher_operator
- associate-shielamae-olmilla@archive.org
- Republisher_time
- 122
- Scandate
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- Worldcat (source edition)
- 74648914
- Full catalog record
- MARCXML
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