Oracle for Rent

An oracle ordered a prince to build a sacred building, whose space would be 400 cubits, the length being 6 cubits more than the width, and the width 3 cubits more than the height. Find the dimensions of the building.

Ars Magna, Gerolama Cardano, 1545

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The answer is: \(\sqrt[3]{190+\sqrt{35757}} + \sqrt[3]{190-\sqrt{35757}}+5 \approx 13.205\) cubits long, \(\sqrt[3]{190+\sqrt{35757}} + \sqrt[3]{190-\sqrt{35757}}-1 \approx 7.205\) cubits wide, \(\sqrt[3]{190+\sqrt{35757}} + \sqrt[3]{190-\sqrt{35757}}-4 \approx 4.205\) cubits tall

"Oracle for Rent," Convergence (April 2004)

Convergence