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 BogaertDate 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