In continuum theory, a dendrite is a locally connected continuum that contains no simple closed curve. A semicircle is therefore a dendrite, while a triangle is not.

The term dendrite is used by Steinhaus (1999, pp. 120-125) to refer to a system of line segments connecting a given set of points, where the total length of paths is as short as possible (therefore implying that no closed cycles are permitted) and the paths are not allowed to cross. This definition differs from the one in continuum theory since a semicircle is a dendritic continuum but is not a line segment.

See also

Dendrite Fractal, Plateau's Problem, Traveling Salesman Problem

Portions of this entry contributed by Matt Insall (author's link)

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Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, 1999.

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Cite this as:

Insall, Matt and Weisstein, Eric W. "Dendrite." From MathWorld--A Wolfram Web Resource.

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