I'd like to know What does ' turned out' mean? in this phrases
this problem has widely studied by many of researchers and many geometric properties have turned out to be useful to determine an upper bounded.
Thanks in advance
This is the phrasal verb to turn out. It means "to happen" or "to become known to happen in a particular way".
So in this sentence it means that many geometric properties have become known to be...
it means "it appeared...." or "we found out... "