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- Isoperimetric_ratio abstract "In analytic geometry, the isoperimetric ratio of a simple closed curve in the Euclidean plane is the ratio L2/A, where L is the length of the curve and A is its area. It is a dimensionless quantity that is invariant under similarity transformations of the curve.According to the isoperimetric inequality, the isoperimetric ratio has its minimum value, 4π, for a circle; any other curve has a larger value. Thus, the isoperimetric ratio can be used to measure how far from circular a shape is.The curve-shortening flow decreases the isoperimetric ratio of any smooth convex curve so that, in the limit as the curve shrinks to a point, the ratio becomes zero.For higher-dimensional bodies of dimension d, the isoperimetric ratio can similarly be defined as Bd/Vd − 1 where B is the surface area of the body (the measure of its boundary) and V is its volume (the measure of its interior). Other related quantities include the Cheeger constant of a Riemannian manifold and the (differently defined) Cheeger constant of a graph.".
- Isoperimetric_ratio wikiPageID "48509016".
- Isoperimetric_ratio wikiPageLength "2497".
- Isoperimetric_ratio wikiPageOutDegree "18".
- Isoperimetric_ratio wikiPageRevisionID "691034766".
- Isoperimetric_ratio wikiPageWikiLink Analytic_geometry.
- Isoperimetric_ratio wikiPageWikiLink Area.
- Isoperimetric_ratio wikiPageWikiLink Category:Analytic_geometry.
- Isoperimetric_ratio wikiPageWikiLink Cheeger_constant.
- Isoperimetric_ratio wikiPageWikiLink Cheeger_constant_(graph_theory).
- Isoperimetric_ratio wikiPageWikiLink Circle.
- Isoperimetric_ratio wikiPageWikiLink Convex_curve.
- Isoperimetric_ratio wikiPageWikiLink Curve-shortening_flow.
- Isoperimetric_ratio wikiPageWikiLink Dimensionless_quantity.
- Isoperimetric_ratio wikiPageWikiLink Invariant_(mathematics).
- Isoperimetric_ratio wikiPageWikiLink Isoperimetric_inequality.
- Isoperimetric_ratio wikiPageWikiLink Jordan_curve_theorem.
- Isoperimetric_ratio wikiPageWikiLink Length.
- Isoperimetric_ratio wikiPageWikiLink Riemannian_manifold.
- Isoperimetric_ratio wikiPageWikiLink Similarity_(geometry).
- Isoperimetric_ratio wikiPageWikiLink Surface_area.
- Isoperimetric_ratio wikiPageWikiLink Two-dimensional_space.
- Isoperimetric_ratio wikiPageWikiLink Volume.
- Isoperimetric_ratio wikiPageWikiLinkText "Isoperimetric ratio".
- Isoperimetric_ratio wikiPageWikiLinkText "isoperimetric ratio".
- Isoperimetric_ratio wikiPageUsesTemplate Template:Math.
- Isoperimetric_ratio wikiPageUsesTemplate Template:Mvar.
- Isoperimetric_ratio wikiPageUsesTemplate Template:Pi.
- Isoperimetric_ratio wikiPageUsesTemplate Template:Reflist.
- Isoperimetric_ratio subject Category:Analytic_geometry.
- Isoperimetric_ratio hypernym http://dbpedia.org/resource//.
- Isoperimetric_ratio comment "In analytic geometry, the isoperimetric ratio of a simple closed curve in the Euclidean plane is the ratio L2/A, where L is the length of the curve and A is its area. It is a dimensionless quantity that is invariant under similarity transformations of the curve.According to the isoperimetric inequality, the isoperimetric ratio has its minimum value, 4π, for a circle; any other curve has a larger value.".
- Isoperimetric_ratio label "Isoperimetric ratio".
- Isoperimetric_ratio wasDerivedFrom Isoperimetric_ratio?oldid=691034766.
- Isoperimetric_ratio isPrimaryTopicOf Isoperimetric_ratio.