The authors prove tight upper bounds for covering a triangle of side n+d with n²+k homothetic unit triangles when 4 ≤ k ≤ 2n and give optimal odd-k and even-k constructions plus a consolidated method that meets the bounds.
Yet another proof of the irrationality of √ 2.Amer
3 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 3representative citing papers
Catalan's constant is rewritten as a double integral, a single integral from a general theorem, and higher-dimensional multiple integrals expressed with the Lerch function.
Claims a proof of pi's irrationality via nested radicals of the form sqrt(2 + previous) with sample computations showing rational approximations converging to pi.
citing papers explorer
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Optimally Covering Large Triangles with Homothetic Unit Triangles
The authors prove tight upper bounds for covering a triangle of side n+d with n²+k homothetic unit triangles when 4 ≤ k ≤ 2n and give optimal odd-k and even-k constructions plus a consolidated method that meets the bounds.
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Multiple integral representations of the Catalan's constant
Catalan's constant is rewritten as a double integral, a single integral from a general theorem, and higher-dimensional multiple integrals expressed with the Lerch function.
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A proof of irrationality of $\pi$ based on the nested radicals with roots of $2$
Claims a proof of pi's irrationality via nested radicals of the form sqrt(2 + previous) with sample computations showing rational approximations converging to pi.