/sci/ - Science & Math

>How the fuck does it know I want area?
Oh this is going to be good.

if you believe that the area of an rectangle is a·b then it's just the interpretation of the formulas as the (limit of) the sum of rectangles which lie under the curve.
The integral itself is just an operation with variables (or rather elements of the function algebra, for example polynomials) and what it is you integrate (an area, total work, paths of a quantum field) is pure interpretation/visualization.

Two dudes called Newton and Leibniz wanted area and then looked for a way to get it. Then they went like sweet jesus's mullet on a tank top, that's it and noticed that you have to do the opposite of derivative.

A derivative is essentially a ratio, a slope. Reverse the operation, you get multiplication. Which happens often to give areas.

Math is beautiful

>>3013723
Green's Theorem (which is just a special case of Stokes Theorem).

http://en.wikipedia.org/wiki/Greens_theorem
http://en.wikipedia.org/wiki/Stokes'_theorem

Anything else?

>>3013723
>I can't comprehend something, therefore, everyone else must not.
Superiority complexes sure are funny.

>>3013748
>what it is you integrate is pure interpretation/visualization

LMFAO. No. Please take some more advanced math courses so you can learn something, instead of just making shit up.

>>3013757


\thread

>>3013757

OP is a faggot

also he's dumb

>>3013768
where do you see a problem?

Why does multiplying a circle's radius with 2pi allow me to compute the circumference? How the fuck does it know I want the circumference?

Why multiply and not divide? What's so magical about multiplication...

you can't explain it

>>3013780

>>3013777
>what it is you integrate is pure interpretation/visualization

That is incorrect, and nonsensical. See >>3013757.

>>3013780
http://en.wikipedia.org/wiki/Line_integral

\thread

WOW YOU GUSY ARE SO SMART< WIKIPEDIA LINKS EVERYWHERE

how about you try to explain it in your own words, give examples, and give reasons as to why it works

>>3013768
>>3013783
>That is incorrect, and nonsensical.
Explain to me why it is incorrect.
There is this nice visualization of the values of integrals in terms of areas and volumes, but I still don't want to root math in reality.

>>3013785
http://en.wikipedia.org/wiki/P-adic_number

It seems /sci/ doesn't know how to find information on the internet? WTF /sci/?

>>3013794

Wow, a Minxy photo that's not a 1 micron by 1 micron thumb with Gameboy Camera-quality resolution.

Fap mode engaged.

>>3013798
Shitty troll is shitty. Are you not about to read?

If you have particular questions about something you don't understand in the wiki's then ask son.

http://www.askamathematician.com/?p=6023
http://www.askamathematician.com/?p=6023
http://www.askamathematician.com/?p=6023
http://www.askamathematician.com/?p=6023

I had this exact same question OP, go to that link, srsly

>>3013833

Thanks bro. Actually explains a lot, unlike every other post in this thread.

>>3013798
You are asking why we don't do work that has already been done, and presented far better than we could?

>>3013843

better as in more accessible, yes. for instance, refer to this guy

>>3013833

5star post ^

>>3013803
You are refering to Integration as a "procedure you use", like addition, or multiplication. That is fine. But your statement makes no fucking sense then.

>what it is you add is pure interpretation/visualization

>what it is you multiply is pure interpretation/visualization

This statement is meaningless, you can say

>what it is you ______ is pure interpretation/visualization

for any _____, and get this statement that essentailly has no meaning. You actually arent saying shit.

>>3013854
you're right, it's not helpful