Question
The unsolvability of the Delian problem is equivalent to this function of two not being a constructible number. For 10 points each:
[10m] Name this odd elementary function that is differentiable everywhere except the origin. It’s not the natural log, but Heron cryptically calculated that this function of 100 is about 4.6.
ANSWER: cube root [or x to the power of one-third or one-third power of x or x to the one-third]
[10e] Heron is best known for his formula for this quantity from side lengths. This quantity equals one-half times base times height.
ANSWER: area of a triangle [prompt on area]
[10h] The unsolvability of squaring the circle was proven via a result in the theory of these numbers. Liouville pioneered the study of these numbers that are described by the Gelfond–Schneider theorem.
ANSWER: transcendental numbers [reject "transcendent"]
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Data
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2025 PACE NSC | 06/07/2025 | Y | 42 | 16.90 | 98% | 41% | 31% |