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=== Blaschke-Santaló diagrams ===
The set <math>\mathcal{K}^2</math> of all planar convex bodies can be parameterized in terms of the convex body [[Diameter#Generalizations|diameter]] ''D'', its inradius ''r'' (the biggest circle contained in the convex body) and its circumradius ''R'' (the smallest circle containing the convex body). In fact, this set can be described by the set of inequalities given by<ref name=":0">{{Cite journal|last=Santaló|first=L.|date=1961|title=Sobre los sistemas completos de desigualdades entre tres elementos de una figura convexa planas|journal=Mathematicae Notae|volume=17|pages=82–104}}</ref><ref name=":1">{{Cite journal|last1=Brandenberg|first1=René|last2=González Merino|first2=Bernardo|date=2017|title=A complete 3-dimensional Blaschke-Santaló diagram|url=http://mia.ele-math.com/20-22|journal=Mathematical Inequalities & Applications|language=en|issue=2|pages=301–348|doi=10.7153/mia-20-22|issn=1331-4343|doi-access=free|arxiv=1404.6808}}</ref>
<math display=block>2r \le D \le 2R</math>
<math display=block>R \le \frac{\sqrt{3}}{3} D</math>
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