He discovered it because he was a very great mathematician of ancient history. He was smart and developed the discovery of Pi to better the world as it is today.
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Archimedes first used the symbol PI because he was the first one to discover it so he wanted to investigate about it.
i think Archimedes was the first to discover pi (3.14) or leonhard euler by brichelle xD
Archimedes made pi more precise
Archimedes