Math Is Fun Forum

I've been thinking quite a bit about this (off and on) since it was first posted. When I first read the wiki, it was very much over my head, but now I think I get it. Some further thoughts (please correct me if I'm wrong):

Seeing how:

and it follows that:

for any whole number "n" is it fair to assume:

I think so. But that's easy. For my next trick I'll be using the trig identities:

I think you all probably already see where this is going:

And if "n" is expanded into all real numbers:

Is my logic sound? Does anyone have anymore half derivatives to add?

On a slightly unrelated note, what's the deal with the notation? I've never understood it... why is the second derivative:

Well my next point would be that if both pi and e were contained in that number entirely, then that means one of them has to contain the other, and that logic could be expanded to contain all irrational numbers... That just seems wrong.

As for "useful," I just meant mathematically relevant. I don't have any really strict idea of what the word should mean, just the opposite of what you meant when you said that .1234... was "utterly useless"

Very cool. He used a lot of examples that pushed his overall speech along.

The one negative thing I'd have to say is that all the examples given were only touched on, never fully explored, and it left me feeling unfulfilled. But I guess ultimately the subject was the importance of mathematics, and not to explore the individual examples. I think it's unfortunate he wasn't able to really expand on his examples, but then the overall message would have been lost. So I guess I'm retracting my original criticism, and saying that it's good that he didn't go into depth, but I'm still not happy about it (I'm not sure if that makes sense).

The coolest thing was the illustration from the children's book at the end. I really think that that speaks to our subconscious mathematician and it really shows how out thirst for mathematics is in a sense hardwired into our psyche. Even if we don't immediately know why, we can say with certainty that that picture is a bad one, to me that speaks volumes.

f(0)=0
f(50)=20
f(100) = 0

Could you maybe use a trig function? Like:

Or do you just want a quadratic like

I do the opposite of all these things. I put the book away and do something else. I let the information fester undisturbed in my subconscious. I find the more I study, the more nervous I am for a test, and the more mistakes I make.

On an odd note, I'm currently volunteering my math skills for my old high school. The AP Calculus course is right around the corner for them, and I did the best in the class last year. I remember not being nervous for my AP test, just going in doing my thing and leaving. Not really caring either way. This year I'm really nervous for their test, in fact I"m really freaking out. It's weird, but true.

Just kick back and relax. Be confident, but not arrogant, and remember that it's only a test.

And have a big breakfast.

I would think it's a combination of things. For starters, some people just have a natural talent. To give a non-math example, I knew a girl from Romania who spoke English quite fluently and when I asked her how many years she studied it, she told me she just learned from watching American TV. She learned Spanish and German this way too, but she told me she;s not as good at them (I wouldn't know I just had to take her word for it). Other people can study a language for years and never get anywhere (that'd be me). I think people are just born with certain talents.

The other thing I think is practice. When I was in high school I used my calculator for everything (because I could) but after I graduated, I got a job selling tools at Sears. After a while I got pretty quick at adding numbers (prices) in my head (for customers). I could also do percentages quickly (sales and what not) but my ability to multiply two multi digit numbers mentally never improved, because no part of my job required it. By the time I left I was known as the "mental math" kid, which is Ironic because in school I was the "calculator" kid.

As one more example (I think I'm getting carried away here) my father is a plumber and has picked up the mental math skill of estimating volumes. He's pretty good at it, but can't even do the most basic of Algebra problems. I don't think that there's anything wrong with the way he, or I, or you do math. As long as you know your strengths and weaknesses, you should be ok.

The book says:

If

then:

(can anyone show how that conclusion is reached?)

then the book says:

f'(x) = 6x-1

(obviously)

then:

y = 10 = 3x²-x

(not sure why I'm doing this)

and we get x = 2 (it says not to worry about the more difficult answer of x = -5/3)

From there we can get g'(10) = 1/11

(I pointed out the steps I'm hung up on above, can anyone push me along?)

THANKS

Cool. I knew about