Why are the surface area and volume of a sphere not dependent on pi squared?

Because Pi is a constant, and you integrate (opposite of derivate, not sure of the translation) following the R dimension for the volume.

For the surface, you integrate Pi*R around an axis on [0; 2*Pi]


Edit : I am missing something, oh boy it's old. Don't do math on the fly. Second shot for the surface : double integration is the way to go.

True, but the surface area and volume of a 4-dimensional sphere are dependent on pi^2. The same for a 5-dimensional sphere. At six dimensions, it jumps again to pi^3. The same for seven. What is it about spheres that makes the pi-dependence increase every other dimension?

I'd have imagined the increases to be more... symmetrical?

edit:
In case anyone is curious about the relevant formulas:
http://en.wikipedia.org/wiki/N-sphere

Ooh. Interesting indeed. Thanks for the link that's kind of refreshing.
To answer this question, I would say that in my mathematical experience, you often found harmony where you'd least expect. It's a great gift to be able to feel the mathematics.

I agree! I don't think it's a gift I have, but I'd still like to understand it in a visceral sense. Maybe if I actually do the work and fight through all the integration myself*, something will become clear. It would be encouraging, though, to first hear that someone else "gets it".

*Actually, I'd ask my wife to do it.

Here is a good guess

wow, thanks and +1

how did you find this?? ... wait maybe you're an hot dog&bun conspirancy employee who distract us from the truth by spreading this propaganda!!

LOL Embrace the baking square and the meat pound of unevenness, comrade. It will all work out if you buy enough of both ;)

this, when read by itself, is the most random string of nonsense ever. awesome.

And if you picture it...................oooh boy! Some things cannot be unseen, and others.........can´t be unthought.

I saw an interesting advert at the mall today. Some human-sized cardboard display at a hair salon read:

2 for $26 Liters

I stared for a bit and I certainly understood the price accurately. Still, part of me was thinking, "Wow, that's a lot [of liters]!" Even though I knew the ad was deceptive, it was having an effect on me.

I wonder if it will catch on. Sorry, not really a question.

Here is a real question that I'm a bit ashamed of not knowing the answer to:

How does an O.S. measure CPU use? The only way I can think of would be extremely CPU intensive as it would need to emulate the CPU.

OS is the conduit between hardware and the user; it, itself, is a user.

It knows how, and to where, it directs information to be processed, so it just measures the load of what it passes. ie, To which core, etc.

I kind of get that but not really. If I were to write a program in machine language and run it on a modern multitasking O.S., surely not every CPU instructions would be handled to the O.S. before getting to the CPU? That would reduce machine language to the speed of an interpreted language. Me not understanding might be because my electronic and programming background CPU wise are on the 6502 and 8080 CPUs with absolutly no O.S. between me and the metal.