History of Mathematics: A Supplement

Forside
Springer Science & Business Media, 10. des. 2007 - 274 sider
1 An Initial Assignment I haven’t taught the history of mathematics that often, but I do rather like the course. The chief drawbacks to teaching it are that i. it is a lot more work than teaching a regular mathematics course, and ii. in American colleges at least, the students taking the course are not mathematics majors but e- cation majors— and and in the past I had found education majors to be somewhat weak and unmotivated. The last time I taught the course, however, themajorityofthestudentsweregraduateeducationstudentsworkingtoward their master’s degrees. I decided to challenge them right from the start: 1 Assignment. In An Outline of Set Theory, James Henle wrote about mat- matics: Every now and then it must pause to organize and re?ect on what it is and where it comes from. This happened in the sixth century B. C. when Euclid thought he had derived most of the mathematical results known at the time from ?ve postulates. Do a little research to ?nd as many errors as possible in the second sentence and write a short essay on them. Theresponsesfarexceededmyexpectations. Tobesure,someoftheund- graduates found the assignment unclear: I did not say how many errors they 2 were supposed to ?nd. But many of the students put their hearts and souls 1 MyapologiestoProf. Henle,atwhoseexpenseIpreviouslyhadalittlefunonthis matter. I used it again not because of any animosity I hold for him, but because I was familiar with it and, dealing with Euclid, it seemed appropriate for the start of my course.
 

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Innhold

Introduction
1
Annotated Bibliography
11
Foundations of Geometry
41
The Construction Problems of Antiquity
87
Conic Sections
100
Quintisection
110
Algebraic Numbers
118
Petersen Revisited
122
Descartes Rule of Signs
196
De Guas Theorem
214
Concluding Remarks
222
Some Lighter Material
225
A Poetic History of Science
229
Drinking Songs
235
Concluding Remarks
241
A Small Projects
247

Concluding Remarks
130
A Chinese Problem 133
132
The Cubic Equation
147
Examples
149
The Theorem on the Discriminant
151
The Theorem on the Discriminant Revisited
156
Computational Considerations
160
One Last Proof
171
Horners Method
175
Inscribing Circles in Right Triangles
248
cos9
249
Using Polynomials to Approximate π
254
π a la Horner
256
Parabolas
257
Root Extraction
260
The Growth of Science
261
Index
263
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