The Best Writing on Mathematics 2013 by Unknown

Author:Unknown
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2013-03-19T16:00:00+00:00

FIGURE 2. Fiona Ross, A Thread in the Labyrinth, 6″ × 6″, 2011, Micron ink on Denril paper.

FIGURE 3. Fiona Ross, Blue Introverted Unicursal Labyrinth, 14″ × 8″, 2010, Ink on Yupo paper.

3. A Historical Perspective of the Jordan Curve Theorem

Just as the JCT artwork in the previous section shows that curves can tell a tale, the JCT itself is an interesting story. The JCT says that the plane is separated into two components by a Jordan curve.

We traditionally call the bounded component the “interior” and the unbounded component the “exterior.” Bernard Bolzano [8,13] realized that the problem was nontrivial and officially posed it as a theorem needing a proof. Here is Bolzano’s “prophetic version of the celebrated Jordan curve theorem” (8, p. 285):

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