Proof in Geometry With

Proof in Geometry With "Mistakes in Geometric Proofs"

by ;
ISBN13: 9780486453545
ISBN10: 0486453545
Format: Paperback
Pub. Date: 2006-11-17
Publisher(s): Dover Publications
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Summary

This single-volume compilation of two books,Proof in GeometryandMistakes in Geometric Proofs,explores the construction of geometric proofs. In addition to offering useful criteria for determining correctness, it presents examples of faulty proofs that illustrate common errors. High-school geometry is the sole prerequisite. 1963 edition.

Table of Contents

Introduction 1(2)
1. First student's question
1(1)
2. Second student's question
1(1)
3. Third student's question
2(1)
4. How to find the answers
2(1)
CHAPTER 1. What Is a Proof? 3(4)
5. Induction and deduction
3(2)
6. Application to geometry
5(2)
CHAPTER 2. Why Are Proofs Necessary? 7(6)
7. The law of sufficient reason
7(1)
8. Dangers of "obviousness"
7(3)
9. Dangers of particular cases
10(1)
10. Geometry as a scientific system
11(1)
11. Summary
12(1)
CHAPTER 3. How Should a Proof Be Constructed? 13(24)
12. Correct reasoning
13(2)
13. Incorrect reasoning
15(1)
14. Converse theorems
16(2)
15. Distinguishing between direct and converse theorems
18(1)
16. Conditional and categorical statements
19(1)
17. Avoiding particular cases
20(3)
18. Incomplete proofs
23(2)
19. Circular reasoning
25(2)
20. Requirements for a correct proof
27(1)
21. How to find a correct proof
28(1)
22. Analysis
29(3)
23. Synthesis
32(1)
24. Direct and indirect proofs
33(4)
CHAPTER 4. What Propositions in Geometry Are Accepted without Proof? 37
25. Bases for selection of axioms
37(1)
26. Properties of a system of axioms
38(1)
27. Analogy from algebra
39(2)
28. Axioms of connection
41(1)
29. Axioms of order
42(4)
30. Axioms of congruence
46(2)
31. Axioms of continuity
48(4)
32. Theorems based on the axioms of continuity
52(2)
33. Axiom of parallelism
54(1)
34. Reduction of the number of axioms
54(1)
35. Summary
55

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