Need References That Discuss The Mathematical Number Known as Wau

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For those not familiar, perhaps this link in which Vi Hart discusses the number will be useful:

However, I cannot find any sources online that discuss the number. I'm interested in reading further about this mysterious constant but cannot seem to find anything. Is wau a constant or is it a function? If the latter, does it have any relation to the digamma function? [

I'd love to explore some external references [outside the video] if anyone can provide some useful ones pertinent to it. Thank you!

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2 Answers

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It's just the number 1. It's pretty clear that's what she's getting at in the video I think it's just meant to be misleading / funny.

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It might be cool if we work out all the computation in the video. So here is my first go:

$$ \frac{1}{ \frac{3}{\frac{3}{\dots} + \frac{1}{\dots}} + \frac{1}{\frac{3}{\dots} + \frac{1}{\dots}}} = G = \frac{1}{3G+G} $$

So $G=\frac1{2}$ and therefore $F=1$

and the second

$$ F = \frac{5}{6} + \frac{ \frac{5}{6} + \frac{ \frac{5}{6} + \frac{ \frac{5}{6} + \dots}{6}}{6}}{6} = \frac{5}{6} + \frac{F}{6}$$ $$F = \frac{5+F}{6}$$ $$F=1$$

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