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Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
The isoperimetric problem is to determine a figure with the largest area, amongst those having a given perimeter. The solution is intuitive; it is the circle. In particular, this can be used to explain why drops of fat on a broth surface are circular. This problem may seem simple, but its mathematical proof requires some sophisticated theorems.
Roundness = Perimeter 2 / 4 π × Area . This ratio will be 1 for a circle and greater than 1 for non-circular shapes. Another definition is the inverse of that: Roundness = 4 π × Area / Perimeter 2 , which is 1 for a perfect circle and goes down as far as 0 for highly non-circular shapes.
The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
Senate Minority Leader Mitch McConnell takes a question from a reporter during a news conference following the weekly Senate Republican policy luncheon at the U.S. Capitol on Nov. 19, 2024.