Recent content by arildno

For over 10 years, PF has been an important place in my life, with many joys, and challenges to solve in educating students. I am deeply thankful for having been a part of this community, and met so many wonderful people here. But, all good things will reach their natural conclusion sometime...

How does CNNs coverage of the flight catastrophe prevent them from covering other stories as well??

Probably "The Lord of the Rings" Others can make the civilization around me. :smile:

This is a very good 15-minute interview with Viswanathan Anand, whose joy is evident, but he seems levelheaded as well. As he puts it: "I needed this result as people need oxygen" When asked what might be the reason for why he managed to put the heavy blow in the World Championship behind him...

Much trigonometry (useful in both astronomy, mining (how to dig and orient shafts) and navigation). Also, a number of results that afterwards would be integrated into calculus. Various forms of equation solving were developed as well. The Wikipedia page on history of mathematics is quite good...

I believe that even if Anand loses big time against Carlsen, he has proved to himself that he still belongs in premier league. Last year, apart from the World championship matches, he hadn't really done well in top-rated tournaments since 2007-2008. Now, he'll know he is still in the top...

As it should be, since you weren't asked to prove the equivalence of those definitions. :smile:

There might, of course, be a reason behind your teacher's behaviour that might be unobvious to you as a 17-year old: While you possibly don't think of yourself in that way, you ARE, actually, a young female human ADULT. KIt is entirely natural that TEACHERS occasionally become romantically...

You are entitled to your opinions, obviously, but not to your own (historical) facts. That ends my involvement in this thread.

Aah, happy memories! Reminds me of my student days, when I and a couple of co-students became determined to prove that identity directly. We were proud of ourselves when we managed to do so, not the least because we found it rather troublesome to achieve. :smile:

"Intergral's definition is about area, it has nothing to do with 1/x's antiderivative as a function. " QUITE so. That's why it can be regarded as more fundamental, rather than as silly.

Basically, here you presuppose the conception of the derivative. Finding the area under a curve does not, and questions about how to evaluate it will occur independent of fruitful mathematical definitions of derivatives and integrals.

Nope. If you go back to 17th century maths, the question of what number would make the the area under the hyperbolic curve equal to 1 was a fairly important question.

Actually, you are the one needing to argue for the "silliness" of Integral's comment. As yet, you haven't

Why? To find the area under the multiplicative inverse function (i.e, standard hyperbola) was a MAJOR undertaking in the 17th century. That is, the gradually developed understanding of the (natural) logarithm function was a critical step in the history of the development of modern mathematics.