As someone who failed his algebra 1 final twice and geometry once, can someone explain to me what is meant be “proving” Euclid’s postulate five? Like, the point of the postulate is two lines that cross another line will, at some point, meet if they’re angled toward each other. I get that.
What I don’t understand is why that needs to be ‘solved’ or ‘proven’. What were so many mathematicians trying to do? How would they go about ‘completing’ it? Why did it need to be completed?
In: Mathematics
It was way more complicates and verbose than thenother 4 postulates, so mathmaticians tried to “prove” it in terms of the other 4 so that they could just remove it and its verbosity.
However these days we tend to accept that the fifth isn’t “provable” and removing it results in a different, completely covalid system of geometry: non euclidian geometry (like geometry done on a curved surface)
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