We actually don’t fully understand the properties of Pi (or it’s bigger brother Tau). There are open questions about digit distribution that relate to information in Pi (so to speak).
Having more digits let’s us check if our thinking matches observation and look for other patterns.
Also, Pi (Tau/2), like many numbers, is just beautiful. [See here.](https://www.google.com/amp/s/www.washingtonpost.com/news/wonk/wp/2015/03/14/10-stunning-images-show-the-beauty-hidden-in-pi/%3foutputType=amp)
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