MF75: Cubics and the prettiest theorem in calculus

[richiedon100]

When you have to solve the cubic equation for (r-x) couldn't that

lead to an irrational value for r?

[njwildberger]

@richiedon100 It is better to say: we cannot necessarily solve for r-x. But when we can, there is at most one solution---that is the key point. Irrational values/numbers don't really exist. A modern mirage!

[richiedon100]

@njwildberger I've heard you briefly mention sqrt2 and sqrt3. And what about

pi. Don't we need that for volume and area problems?  So I'm still a bit confused

by irrationals.

[njwildberger]

@richiedon100 Don't worry, the confusion with pi and related so called irrational numbers is a widespread phenomenon. This year I will try to clarify some of the issues in this series.

[savio2006]

There is a typo on page 5 (@13:40) at the example: it should be T(1, 1) p = 8 - 8(alpha)

[teavea10]

Does the disjoint tangent conic theorem carry up to any higher degree polynomials?

[Toxie207]

Very nice - so this leads us to the idea of polarity?

[njwildberger]

@Toxie207 I think the idea of polarity is more closely hinted at by the last video on Line and parabolas II. However it is a very important notion that I will be talking about at some length in the future.

[MrElephantMemory]

You have a beautiful handwriting, which is one of the rarest things in mathematicians. Besides, you are very talented at explaining things and speak clearly. All in all, you are an excellent instructor.

[paul1964uk]

Amazing result. Very elegant.

[NielsHProsch]

Nice!

[alquiora]

wow...that is interesting

[Kurtlane]

Bravo!