Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal Values of Pi   We discuss the classical results of Stanis{\l}aw Go\l\k{a}b, on the values of
pi in arbitrary normed planes, including the classification of extremal values.
We reprove the result of J. Duncan, D. Luecking, and C. McGregor, which states
that any norm with quarter-turn symmetry has pi-value $\geq \pi$. We also show
that a norm is Euclidean iff it has quarter-turn symmetry in some basis and has
pi-value $\pi$.

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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: stat