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iscope
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There are 6 letters in ISCOPE ( C3E1I1O1P3S1 )
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Iscope might refer to |
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In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume. In * * * * n * * * {\displaystyle n} * -dimensional space * * * * * * R * * * n * * * * * {\displaystyle \mathbb {R} ^{n}} * the inequality lower bounds the surface area * * * * * s * u * r * f * * ( * S * ) * * * {\displaystyle \mathrm {surf} (S)} * of a set * * * * S * ⊂ * * * R * * * n * * * * * {\displaystyle S\subset \mathbb {R} ^{n}} * by its volume * * * * * v * o * l * * ( * S * ) * * * {\displaystyle \mathrm {vol} (S)} * ,* * * * * s * u * r * f * * ( * S * ) * ≥ * n * * v * o * l * * ( * S * * ) * * * * n * − * 1 * * n * * * * * v * o * l * * ( * * B * * 1 * * * * ) * * * 1 * n * * * * * * {\displaystyle \mathrm {surf} (S)\geq n\mathrm {vol} (S)^{\frac {n-1}{n}}\mathrm {vol} (B_{1})^{\frac {1}{n}}} * ,where * * * * * B * * 1 * * * ⊂ * * * R * * * n * * * * * {\displaystyle B_{1}\subset \mathbb {R} ^{n}} * is a unit ball. The equality holds when * * * * S * * * {\displaystyle S} * is a ball in * * * * * * R * * * n * * * * * {\displaystyle \mathbb {R} ^{n}} * . * On a plane, i.e. when * * * * n * = * 2 * * * {\displaystyle n=2} * , the isoperimetric inequality relates square of the circumference of a closed curve and the area of a plane region it encloses. Isoperimetric literally means "having the same perimeter". Specifically in * * * * * * R * * * 2 * * * * * {\displaystyle \mathbb {R} ^{2}} * , the isoperimetric inequality states, for the length L of a closed curve and the area A of the planar region that it encloses, that * * * * * 4 * π * A * ≤ * * L * * 2 * * * , * * * {\display... |