wacky notions

1. Rationaloids and irrationaloids. A rationaloid is an irrational number that “looks like” a rational number when you blur it a bit. Start with 1/1029384905433049501, and in every repeating block of digits, randomly permute two digits. The resulting number never repeats, but if you kind of apply a blur filter to it, it looks like a rational number. An irrationaloid is a rational number that consists of say, 15000 100 digit blocks that get closer and closer to something and then in the 15001 and thereafter digit block it’s all the same. Again, apply a blur filter to it and it looks like an irrational number, but it’s not.

2. Absurd way of calculating the Dottie number D if r_{n+1}(\theta)=\cos(r_{n}(\theta)) and r_{0}(\theta)=\theta

D = \sqrt{\left[\frac{1}{\pi}\prod_{n=2}^{\infty} \frac{\int_{0}^{2\pi} r_{n+1}^{2}(\theta) d\theta}{\int_{0}^{2\pi} r_{n}^{2}(\theta) d\theta}\right]}

3. making sense of divergent series. A divergent series converges to a point on the other side of the Riemann sphere, the value it diverges to tells you where, exactly, it diverges to.


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