## History of Mathematics: A Supplement1 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. |

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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 |

263 | |

### Andre utgaver - Vis alle

### Vanlige uttrykk og setninger

algebraic angle appeared apply approximation assume Biography calculator century chapter Chinese circle cited coeﬃcients compass complete conclude conic consider constructible Corollary correct course cubic curve derivative determined diﬀerent discussion distinct divides edition Elements equal equation Euclid example existence fact Figure ﬁnd ﬁrst follows geometry given gives Greek Hence History of Mathematics Horner’s includes integer interest intersection known later Lemma length less look magnitudes mathematicians means method multiple negative Newton’s obtain original pair polynomial positive positive roots present Press problem proof prove published Pythagorean rational real roots reference regular Rule of Signs ruler Science sequence sides sign changes similar solution solve sources square stamps Suppose textbook Theorem theory translation triangles University volume whence write yields