Math Is Fun Forum

My dictionary defines science as "The intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment" (emphasis mine).

Science involves logic, but logic is not science.

Or another example, something we do constantly: image recognition. This is very, very hard to get a computer to do reliably, and is one of the things holding robotics back.

Our brains are broken in odd ways. We have a brain that stores every input it ever receives, and then promptly forgets where. Its autonomous function processing is incredibly powerful--when we train it to do things, it can do a large number of them at the same time. One example is sight-reading music. But, our higher function processing is annoyingly modal (to use a computer nerd term) - that is, only one task fits in there at a time.

I don't know how they came up with the oft-quoted figure that humans only use 10% of their brains, but it feels true to me.

The only thing I can think of is that I didn't get the biggest possible triangle. My thinking is that the largest equilateral triangle will have all three vertices touch the circle, but I can't prove that to be the case.

I'll wait for irspow to post his solution and see where I went wrong.

I had it wrong (the second part, I mean). I had thought that bocado was feminine (bocada), even though it made no sense in the context of the saying I thought I had heard (so I wrote it as india rather than indio). I actually had to research it!

"Indio" in colloquial Nicaraguan means a person that is base, crude, and rude; it's an insult. Nevertheless, the saying is not insulting. (Go figure. Languages are strange.)

The general meaning is, "I've eaten, so I'm leaving," and "I'm still here, so I must still be hungry!"

Sounds cool! Hook the panels into the lines, and throttle down the plant.

The trouble is (as has always been the case with PV) that that much photovoltaics would be prohibitively expensive. I wonder if it would be more cost-effective to put wind turbines under the lines?

It's also standards-compliant, which means nothing to most people but a great deal to web developers whose web sites work on everything BUT IE and we then must go through a horrible process of hacks to try and make it work because 80% of the web-using public uses it.

If the web devs didn't code around it, most sites would be horribly broken in IE. I sure wish we could do that--just agree to stop accomodating Internet Explorer so people would stop using it and the world would be a better place.

Unfortunately, people would blame us, not their browser, and stop visiting our sites.

Anyway, to Rod: I work at the English Language Center at Brigham Young University. Most of what I do is PHP w/MySQL, and Javascript here and there. http://www.elc.byu.edu/

I'm also working on the web site for the family business, but that's not up yet.

A mathematical paradox.

In an 8x8 game, there are 64 total squares, right? And you start with 99 flags? and 99-64 = 35?

So what's wrong with this picture? (note, I was careful to see that every flag I dropped marked a square--I know that there are a few ways to drop the flag counter without marking more squares, but I avoided them).

I'm in a college physics course that requires calculus.

Physics uses math to model reality. Some models work better than others. In that sense both are abstract, and both are real: physics is abstract until it accurately describes reality, and math is abstract until it is used to model real situations.

Don't get me started on Physics...(ignore air resistance and friction, my eye. Teach me something I can actually use, and then I might be interested.)

Close. More like, "I can't woo her because whenever I see her I forget what I was about to say..."

Edit: or perhaps even more accurate, "I can't woo her because just looking at her make me forget what I was about to say..."

Way cool.

I use Firefox primarily for web development, because the extensions are amazing (venkman, aardvark, web developer toolbar and the like). I'm waiting to DL it until I see if all my favorite plugs are supported, which I'd rather get paid to do than not. So, I'm waiting to do it at work.

Except that, isn't it the standard to put the vertex of the angle in the middle of its name? So, would "PCB" and "ACB" both have their vertex at C? That would seem to make it easier to prove that the two are equal.

Don't you love these problems where nobody knows quite what they're asking?

Nope. (e^bx)′ = (e^u)′(bx)′ = be^bx. (That's the chain rule.) The same goes for e^ax.

We know that (e^bx / e^ax)′ = be^bx / ae^ax. That is,
(b-a)e^(bx-ax) = be^bx / ae^ax

At this point, I got lazy and told my calculator to solve that for b. It spat this out:
b = a^2 / (a - e^2ax)

That's as far as I can go with it.