### Abstract

We mention in closing that even the 20th-century Algorithm CO pales by comparison with Algorithm Euclid from the point of view of robustness with respect to singularities. Consider, for example, the case where point C happens to lie at a location equidistant from A and B. Algorithm Euclid executes in this case as easily as in any other because everything is well-defined. Without special flag-waving code, however, Algorithm CO could crash attempting to draw a circle with radius zero and then intersecting two circles, one of which has radius zero.

Original language | English (US) |
---|---|

Pages (from-to) | 12-24 |

Number of pages | 13 |

Journal | The Mathematical Intelligencer |

Volume | 15 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1993 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A new look at euclid's second proposition.** / Toussaint, Godfried.

Research output: Contribution to journal › Article

*The Mathematical Intelligencer*, vol. 15, no. 3, pp. 12-24. https://doi.org/10.1007/BF03024252

}

TY - JOUR

T1 - A new look at euclid's second proposition

AU - Toussaint, Godfried

PY - 1993/9/1

Y1 - 1993/9/1

N2 - We mention in closing that even the 20th-century Algorithm CO pales by comparison with Algorithm Euclid from the point of view of robustness with respect to singularities. Consider, for example, the case where point C happens to lie at a location equidistant from A and B. Algorithm Euclid executes in this case as easily as in any other because everything is well-defined. Without special flag-waving code, however, Algorithm CO could crash attempting to draw a circle with radius zero and then intersecting two circles, one of which has radius zero.

AB - We mention in closing that even the 20th-century Algorithm CO pales by comparison with Algorithm Euclid from the point of view of robustness with respect to singularities. Consider, for example, the case where point C happens to lie at a location equidistant from A and B. Algorithm Euclid executes in this case as easily as in any other because everything is well-defined. Without special flag-waving code, however, Algorithm CO could crash attempting to draw a circle with radius zero and then intersecting two circles, one of which has radius zero.

UR - http://www.scopus.com/inward/record.url?scp=0040652841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040652841&partnerID=8YFLogxK

U2 - 10.1007/BF03024252

DO - 10.1007/BF03024252

M3 - Article

AN - SCOPUS:0040652841

VL - 15

SP - 12

EP - 24

JO - Mathematical Intelligencer

JF - Mathematical Intelligencer

SN - 0343-6993

IS - 3

ER -