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Isoperimetric Geometry

The isoperimetric theorem states that: "Among all shapes with an equal area, the circle will be characterized by the smallest perimeter" which is equivalent to "Among all shapes with equal perimeter, the circle will be characterized by the largest area." The theorem's name derives from three Greek words: 'isos' meaning 'same', 'peri' meaning 'around' and 'metron' meaning 'measure'. A perimeter (= 'peri' + 'metron') is the arc length along the boundary of a closed two-dimensional region (= a planar shape). So, the theorem deals with shapes that have equal perimeters.

Jan Bogaert
Date Accepted: 2003-03-26 Grade Group: High School (9-12) Benchmarks: M1.4.8 M2.4.9 M5.4.2 M5.4.10 M5.4.11 Keywords: geometry shape area perimeter Microsoft Word: 01_22_03_1.docx PDF Document: 01_22_03_1.pdf