and e

Mathematics and other neat things

Various values of \(1^\pi\) in the complex plane. It is worth noting that the seventh value is very close to \(1\). This corresponds to \(\frac{22}{7}\) being a very good rational approximation to \(\pi\). Also very interesting: the next closest to \(1\) is the \(106^{th}\) value. This corresponds to the second convergent, \(\frac{333}{106}\), in the continued fraction expression for \(\pi\).

Various values of \(1^\pi\) in the complex plane. It is worth noting that the seventh value is very close to \(1\). This corresponds to \(\frac{22}{7}\) being a very good rational approximation to \(\pi\). Also very interesting: the next closest to \(1\) is the \(106^{th}\) value. This corresponds to the second convergent, \(\frac{333}{106}\), in the continued fraction expression for \(\pi\).

2 years ago

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