It is especially ironic that you chose Pythagoras. He was the leader of a cult which had a main tenant of keeping their knowledge secret from outsiders so they

It is especially ironic that you chose Pythagoras. He was the leader of a cult which had a main tenant of keeping their knowledge secret from outsiders so they could own the benefits of those ideas. This lasted far longer than the 15 or 20 years a patent would have protected them. If Pythagoras had patented it, the patent would have expired 2600 years ago, meaning you would have had no effect from it.