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combinatorial geometry

In combinatorics: Helly’s theorem
In 1912 Austrian mathematician Eduard Helly proved the following theorem, which has since found applications in many areas of geometry and analysis and has led to numerous generalizations, extensions and analogues known as Helly-type theorems. If K₁, K₂, · · ·, K_n are…
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length, area, and volume

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length, area, and volume

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Related Topics:: geometry; volume; area; length

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length, area, and volume, Dimensional measures of one-, two-, and three-dimensional geometric objects. All three are magnitudes, representing the “size” of an object. Length is the size of a line segment (see distance formulas), area is the size of a closed region in a plane, and volume is the size of a solid. Formulas for area and volume are based on lengths. For example, the area of a circle equals π times the square of the length of its radius, and the volume of a rectangular box is the product of its three linear dimensions: length, width, and height.

This article was most recently revised and updated by William L. Hosch.

Helly’s theorem

Learn about this topic in these articles:

combinatorial geometry

length, area, and volume