can someone run me down on the main difference between those two? like when I would use 丸 or 円
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円い is typically for flat circular objects.
丸い is typically for spherical objects.
Dictionaries often have this information noted.
The 補説 (supplementary explanation) says “丸い is often used with regard to balls, fruits, and other spherical objects.”
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I see, thank you very much!
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If you need a mnemonic to tell those apart, just remember that 円い objects are shaped line a 円 coin. 
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Yet 丸 is used for the sun (日の丸).
Was there an ancient knowledge/intuition that celestial bodies are spherical?
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From what I was able to research, there’s no definitive answer, but from historical context purely, 丸 was used in old Japanese to describe circular shapes in a more poetic/artistic way (It also appears in names of things like ships, “日本丸” or “日本郵船丸”. And then 円, tends to carry a more geometric or mathematical connotation, which could make “日の円” sound like a precise sun-shaped circle rather than a poetic representation of the sun.
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