/sci/ - Science & Math

>implying that wasn't taught to me in high school calculus the day we defined the derivative.

Fun fact: Newton loved circular coordinates a lot more than Cartesian ones

>>1594746
>implying I didn't have shitty teachers, as mentioned earlier

>>1594749
>implying you understand math if you were in high school for 6 years

That's not surprising. That's almost obvious from the definition of standard differentiation.

>>1594746
>implying I was even lucky enough to get the chance to learn even algebra at my high school
>I'm 20, in college, and still can't even divide
In case you're asking: Yes, I was a student for the US school system

>>1594761
>In case you're asking: Yes, I was a student for the US special ed school system

>>1594773
Pfft, I wish.

>>1594761
>>>>Implying the US doesn't have the world standard in education

>>1594761
They're even taking algebra away you Amerifags? And your kids don't even know what the equal signs means as well? Dear lord guys.

>>1594781
>implying the US public school system isn't the shittiest one in the 1st world

>>1594781

US has the world standard... in higher education. Meaning that everything good about it, the average citizen (which most likely includes almost everyone here) won't be able to enjoy.

>>1594781
http://news.nationalgeographic.com/news/2006/05/0502_060502_geography.html
http://tamunews.tamu.edu/2010/08/10/students%E2%80%99-understanding-of-the-equal-sign-not-equal/

Well, yeah, because the rate of change in volume is the rate of change of radius times the surface area, since you consider an infinitesimally larger shell.

Still, yes, the shit teachers don't teach because they suck at teaching.

>>1594781
That's for their universities you cunt! *slap* Their public, tax-payed education is FUBAR'd beyond FUBAR.

>>1594795

are you kidding?

4chan is 95% middle class white guys, most everyone here will get a college degree eventually

>>1594810
Yeah, because an associates/bachelors still means something these days.

>>1594746
Right, you learned the derivative and then learned about it on

If you learned about that the first day, then your teacher is the most scatter-brained jackass ever. There are plenty of more interesting and useful 2D Cartesian examples.

>>1594810

Sorry, I was talking about the actual top-tier institutions such as MIT and Harvard. The ones which are the best in the country but with acceptance rates so low your chances are pretty slim whether you got a 36 or 2400 on the SAT or ACT or not.

>>1594761
Lol. My algebra teacher in 9th grade always went on these little rants about how they're dumbing our education because "it's too hard" for most students, and yet the faculty dumbing it down still expected these students to be able understand it by high school or college (in which most cases they don't), and how this is going to disable them from much education further on. I guess he was kind of right.

>>1594819

mine does. if yours doesn't then you should have probably thought about doing a different major.

What is sin(0)? What is the tangent line of cos(0)?

>>1594851

What is cos(0)? What is the slope of the tangent line of sin(0)?

I remember when I figured that out the first time. I was blown away too. Too this day, most of my peers don't know it.

>>1594738

More like they're integrals. lrn2calc2 and read from left to right.

but dude

the area of a square is <span class="math">A^2[/spoiler] and the perimeter is <span class="math">4A[/spoiler].

the volume of a cube is <span class="math">A^3[/spoiler] and the surface is <span class="math">6A^2[/spoiler].

so you can't just differentiate volume to get surface area, the fact this happens with circles and spheres is some kind of coincidence

>>1594781
>actually thinks the US education system is anywhere near "good."
http://www.apa.org/monitor/mar05/scores.aspx

meh, none of my teachers ever pointed it out either. i'd point it out to my friends when tutoring them and it was like they had an epiphany. When will we start requiring our teachers to actually major in their subjects?

God damn OP!

>>1594886
it's not a coincidence; it's a consequence of its shape. but yeah it's not something you can just apply to any 3D shape. that'd be bad lol

>>1594886
>>1594898
This is because both of the objects are symmetrical across the x and y axis. This is the only reason.

>>1594913
so is a square you fucking idiot

>>1594876
the area of a circle is the integral of its circumference, the volume of a sphere is the integral of its surface area

>>1594919
lolllllll.... if you read the posts you'd understand
excuse me as I herp derp your herpy derp.

<span class="math"> \int V = SA [/spoiler]

ITT pretend that the surface of a shape is the derivative of its volume to troll me

>>1594939
ITT: doesnt understand Cal 3

>>1594934
>SA = surface area

HOLY FUCKING FUCK

THE AREA UNDER ANY OF THE HUMPS IS 1

MIND = BLOWN

trust the internet to teach me more in one picture than my math teachers in 17 years

<span class="math">\coprod = upside down capital PI[/spoiler]

>>1594886
No. No it's not. It's just a little simpler with a circle, because you need only differentiate in the radial dimension. For a square, you have to differentiate in both the x and y direction, because it's not radially symetrical, so you get 2A + 2A = 4A.

Strange, I majored in math and I never noticed that or had it pointed out.

Thanks OP.

>>1594988
You majored in math, and never once tried to derive the formula for the volume of a sphere or the area of a circle?

>>1594974
tetrahedron next then I will believe you

>>1594988

Similar story here, OP. I'm not a math major, but I'm certainly enthusiastic about math and math puzzles. And I'd never noticed this either, thanks.

Are there any other shapes/forms that exhibit this same behavior?

>>1595011
There you have sides that are not oriented along independent axes, so it will get complicated. However, for any shape, the area must = the integral of the perimeter as it expands. It's just simplest to figure out if it expands radially, because then there's only one axis and variable, r.

I have a PhD in circular geometry and I never put 1 and 1 together, thanks OP.

>>1594948
>PhD in math
>can calculate <span class="math">2 \cdot 1[/spoiler]
>$1000 welfare check

>>1595005
You don't need to realize the relationships OP pointed out to derive any of the formulas.

I learned this in Integral Calculus...

>>1594886
OTOH if you define r as shown in the pic...

the area of a square is <span class="math">4r^2[/spoiler] and the perimeter is <span class="math">8r[/spoiler].

the volume of a cube is <span class="math">8r^3[/spoiler] and the surface is <span class="math">24r^2[/spoiler].

Of course, you can't just apply this blindly; you have to know why it works.

God here, I created circles and area but I never noticed how exactly they were related. Thanks op.

Here's one I found out on my own.

There are 2pi radians per circle.

The circumference of a circle is 2pi * radius.

A radian is the same length as a radius.

>>1595087
wow good discovery, especialyl because THATS THE DEFINITION OF A RADIAN

>>1595093
Too bad nobody ever told me that.

>>1594947

area under the 2nd hump is -1 dooface.

>>1595095
Its one of those types of things, when you find out you say "holy shit this makes sense" but in hind sight it should be obvious. and if nobody ever tells you, it takes a while.

>>1594913
wow. I noticed ops observation but couldn't quiet get my head around why. That helped. Thanks.

what the fuck? why does everyone buy this, ITS NOT TRUE YOU FUCKING IDIOTS

>>1595060

The length of an infinitesimal arc segment is represented by <span class="math"> r d\theta [/spoiler]. To determine the circumference, integrate between <span class="math"> 0 [/spoiler] and <span class="math"> 2 \pi [/spoiler] to get:

<span class="math">\int^{2\pi}_0 r \;d\theta = 2\pi r[/spoiler]

For area, there is also a radial variance, as we want the radial contributions to come into play. We integrate between 0 and R, for example.

<span class="math">\int^{R}_0\int^{2\pi}_0 r \;d\theta \;dr =\int^{R}_0 2\pi r\; dr = \pi r^2[/spoiler]

That clearly proves that due to the geometry of circles, the integral of the circumference with respect to radius is the area.

>>1594888
The day that school systems are actually capable of writing their own curricula instead of buying them from publishing companies that are waaaay more interested in making a buck than in making students smart.

Which would require communities of North Americans that send their kids to those schools to be able to make informed decisions about the information being taught.

In other words, not gonna happen.

>>1594948

<span class="math">\int SA = V[/spoiler]

<span class="math">\int P = A[/spoiler]

Welcome to the world of calc.

>>1594795
mfw fags still think that only those born into a relatively high socioeconomic class can get into higher education, like it's still the 1800s or some shit and we haven't invented student loans yet.

>>1595123
>mfw negative area

>>1595327

mfw he doesn't realize loans are just a form of slavery to keep the middle class, middle class

>>1595478
No, most loans are a means of making money for doing nothing but sending someone else a number. They don't care what class people are.

>>1594738
I remember figuring this out on my own during a calc 1 final exam when I forgot the formula for finding the volume of a cylinder and tried to come up with it on the fly. Made me feel smart although that was short lived since I failed to come up with the formula for the fucking cylinder.

Took BC calc in highschool.
Yea it's kind of weird how we were never taught they are derivatives/integrals (depends on which direction you go from). I was in physics and we were talking about how you only really needed to know 1 equation for objects falling and how to find the other ones by using derivatives (sorry this was 3 years ago and I'm not majoring in science :(). Next day, I was thinking about derivatives and had a sudden realization that I only needed to memorize the circumference of a circle in order to find the area/volume/etc. My mind was blown and I felt so happy since my memory sucks!

I thought this was kind of important to teach to students; seems very fundamental and it teachers us that we need to be more aware of how we came up with certain theories/laws! This revelation made me look at life in a different way.

Now I'm just an artschool fag. :(

>>1595584
lolwut I thought art kids cringed at matth.

>>1595626
Yeah, I was always fascinated with math and science (namely biology) in high school. Couldn't get enough of it. Now I'm in art college and I'm kind of regretting it. The education isn't that difficult and I'm not learning anything I couldn't find online. A degree in the arts is practically useless unless you want to teach.

I should have just taken the easy route and went into accounting since now I'm worrying about my financial future. That way if art didn't work, my degree was actually useful.