The Useless Number - Numberphile

One of the first people to stumble over imaginary numbers (namely the square root of -15) thought it was "subtle" and "useless". More links & stuff in full description below ↓↓↓ Featuring...

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Well, I'm going to bring you back to the sixteenth century first.The Italians, especially, were interested in cubic polynomialsx cubed plus, oh, five x plus seven, something of that sortNow I'll draw you the graph of any of these cubic polynomialsThat is to say I'll draw it qualitatively. Unless you're particularly perversein your choice of cubic polynomial it's gonna look sort of like thatBrady: this kind of distinctive wiggleBarry Mazur: there's a wiggle there. There's a ... it looks like it's getting to a maximumand then it changes its mind, then goes to a dip there, and then it thinks 'oh gosh this is a valley' and thenespecially if the coefficient of the X cube is positive it&#...
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