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The Koch Curve: A Geometric Proof.
- Source :
- American Mathematical Monthly; Jan2007, Vol. 114 Issue 1, p61-66, 6p, 5 Diagrams
- Publication Year :
- 2007
-
Abstract
- The article presents a discussion about the Koch Curve. It states that the mathematically popular Koch curve is usually used as an example to illustrate a continuous but not differentiable function and as an example of a non-rectifiable curve. However, it emphasizes that only the fact that it is not rectifiable is proved, and the proof that it is a curve and that no point does this curve have a tangent line is disregarded. It offers a mathematical and simple geometric proof that the Koch curve is indeed an arc and that it at no point has a tangent line.
Details
- Language :
- English
- ISSN :
- 00029890
- Volume :
- 114
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- American Mathematical Monthly
- Publication Type :
- Academic Journal
- Accession number :
- 23794718
- Full Text :
- https://doi.org/10.1080/00029890.2007.11920392