The method given in the Tau Manifesto for finding the area of a circle seems unnecessarily complex. The comparison given, between how the Pi Manifesto, and how the Tau Manifesto each deal with this issue, is beyond my comprehension. The author of the Tau Manifesto seems to think that the Tauist way of figuring the area of a circle, or the volume of a cylindrical container, is somehow a better method. But I don't understand the reasons for that conclusion

Do you mean apart from the pun on Tau and Tao? The whole argument is that a full 360 degree rotation is a more fundamental natural unit than a half 180 degree rotation. Then yin-yang is a completion of the circle like that - going through the light, then the dark, to arrive back to begin the cycle again. But it seems a mention tacked on for a bit of fun and has nothing to do with the argument really.

Yeah that's similar to what I guessed but...I wish there was more. It's kind of a really~ loose symbolism.