Recent content by Curious3141

Until the singularity occurs. :biggrin:

Have you just proven we don't exi...(poof) :oldbiggrin:

The most common way of solving a problem like this in an elementary fashion is to try to get it into the form of a polynomial equation that can be easily solved. Of course, the question has to be set specifically so that it's "easy" to solve that way, and in this case, it is. You need to be...

I would rewrite it as ##\displaystyle \frac{1}{2a}[\int(2ax + b)\sqrt{ax^2 + bx + c}dx - b\int\sqrt{ax^2 + bx + c}dx]## The first integral is of the form ##\displaystyle \int f'(x)g(f(x))dx## and can be solved easily by either inspection or applying the sub##\displaystyle ax^2 + bx + c = u##...

To put it succinctly, that's why we live in a society. :D

It gets even better! For multiplication of 1 to 10 by 9, the tens digit is one less than the number (and the units place is easily computed 9 minus the recursive (repeated) sum of those digits, just as in your post), e.g. 6*9 = 54, 8*9 = 72, 10*9 = 90. For multiplication of 11 to 20 by 9, the...

It's applying a recursive operation, as Mentallic said. In the "classic" Casio calculators (don't know how the new ones are designed), simply pressing "=" repeatedly wouldn't do the job. Instead you needed to press the operation key, e.g. "+" or "X" twice in succession. Then a "K" symbol would...

Can't pinpoint a *first* "discovery" with any degree of precision, but I can summarise some memorable insights. When I was quite young (about 8 or so), the notion of trying to solve ##x^3 - 5x = 5## popped into my head. Mind you, I had just (autodidactically) learned basic algebra and I didn't...

Isn't anyone going to mention anything about the ethics of doing this sort of "experiment"? I'm putting "experiment" in quotes because it's a poorly designed and controlled one anyway. There's a reason that animal experimentation on a proper scale (at least that which has federal funding) has...

Well, yes, but I interpreted scenario 2 to refer to the "Universe" preventing you from changing anything in the past that would cause a paradox. In other words, the time traveller wouldn't even be able to make a change in the past that he's able to observe the immediate consequences of, while...

Actually, some stories use something other than these 3 philosophies. Case in point: the (pretty darn good, IMHO) short story "Ripples in the Dirac Sea" by Geoffrey A. Landis. You can read it here: http://diracsea.net/ripples-in-the-dirac-sea/ No paradoxes are possible because changes in the...

This one is really easy. Sub x=e^y. The rest is either that trick with the repeated integration by parts or transforming \sin y to a complex exponential form.

Currently engrossed in the "A Song of Ice and Fire" series by George R. R. Martin. About three-quarters of the way through the fourth book (A Feast for Crows), one more currently published book (A Dance with Dragons) to go, and more to come, I'm sure. I started the series a few weeks back and...

The issue of the publication of negative results in peer-reviewed journals is a highly contentious one. I am impressed by PLOS ONE accepting this publication, but I am even more impressed that they did so as a full paper, rather than as "correspondence to the editor" or even a mere footnote of...