Bonnesen's Inequality
The classical Bonnesen's inequality is the strengthened isoperimetric inequality
Here is the area of the region bounded by a closed Jordan curve of length (perimeter) in the plane, is the circumradius of the bounded region, and is its inradius. The error term on the right hand side is traditionally called the isoperimetric defect. There exists a similar strengthening of Loewner's inequality.
Read more about this topic: Introduction To Systolic Geometry
Famous quotes containing the word inequality:
“Nature is unfair? So much the better, inequality is the only bearable thing, the monotony of equality can only lead us to boredom.”
—Francis Picabia (1878–1953)