/sci/ - Science & Math

Seriously this shit is making me mad.

>>2128229

I don't want to talk to no mathematicians. you know them fuckers lying and be gettin me pissed.

inb4 fractal bullfuck arguments including infinitesimal geometry by high school fucktards who've never been to an analysis lecture

Consider making a cross shape. Now consider leaving the arms of the cross the same length, but the width of the arms skinnier and skinnier. The perimeter remains the same, but the area decreases toward 0.
Moral: you can make any arbitrary shape with an arbitrary area with a given perimeter. The fact that the perimeter doesn't decrease is an indication that you're doing it wrong.
The triangle argument works for computing <span class="math">\pi[/spoiler] because the perimeter goes down with each step.

>>2128224
here you go
>>2128030

protip: the picture assumes a certain theorem about the convergence of arc lengths of a sequence of curves.

A circle by definition has no edges. Every time a "chunk" is taken from the perimeter of the square, the square is not significantly changing in relation to the circumference of the circle. No matter how many corners are removed, the circle must still be a smooth curve in relation to the jagged perimeter. There is no such thing as a perfect circle in nature

>>2128224

bump

>>2128279
what the fuck, "computers"? you pretentious fucking narrow minded idiot, if you've even taken a single god damn higher level computer science course you would say the right fucking opposite of "computers in /g/"

>>2128320
someone's butthurt.

mind = blown

Primary school explanation:
A circle is a collection of dots that are all the same lenght away from another dot in the middle.
What you are getting with that procedure is a jagged circle that has dots at different lenghts from the center, even if it's by infinetly small amounts.
Therefore, you no circle get.

Therefore, you were wrong. Again.

>>2128372
plus, there aren't no such infinetly small amounts.

0.999... == 1 etc. pp.

>>2128279
engineering=/cm/ /y/
You , please, post it on /b/, /b/ is for troll

>>2128372
ahhh, but you actually do.
d(point in squiggly, (0,0))=k + d
where |d|<E for all E>0
so no matter what range of distances you allow, I can come up with some E which will get all the points in the curve closer to the circle than you choose. This process continues all the way to zero.
So in a limit, they are in fact the same. however the limits of the perimeters are different. Now isn't that a mindfuck?

>>2128395
nice troll
the whole point of maths is inventing things that "don't exist"...
If you define them, they exist.the end

>>2128279
>engineering = cm y
i lol'd

Taxicab geometry != euclidean geometry

>>2128407
>the whole point of maths is inventing things that "don't exist"...
wat?

>If you define them, they exist.the end
But you didn't define anything. You just spouted random bullshit from the top of your head.

>>2128466
what does the taxicab metric have to do with this at all?
The iteration converges to the circle, the perimeter however does not.

What, in the name of fuck, does that have to do with the manhatten metric? Please, do tell us.

Archimedes here. Yes, I do have a problem with your argument. You have provided no rigorous definition of "repeating to infinity." No matter how many times you repeat your process, all of your polygons will have a perimeter longer than the circumference of the inscribed circle. Therefore, while your diagram shows that the circumference is less than 4, you have not set any lower limit to the circumference. I would encourage you to read about my own technique of calculating the ratio of circumference to diameter, which uses both circumscribed and inscribed polygons to set both lower and upper limits on the circumference. Using my method, I have found said ratio to be between 223/71 and 22/7.

by his logic pi would equal 2 due to the equation for the circumference being 2*pi*r. Therefore all your arguments regarding error being a factor are invalid

>>2128841
Yes, the equation for the circumference is indeed 2*r*pi, and since the diameter is 1, we have 2*r = 1, so the perimeter is fucking pi you 12 year old shitfucking scumfuck.

yeah cuz the perimeter of a circle is pi.
fucking idiot

>>2128877
the perimeter of a circle is d*pi where d is the diameter. Since d = 1 in this case, you're right.
You really are a fucking idiot.

-It infinitely approaches the area, not the perimeter

-It assumes that there is a rule present in manhattan geometry that allows for diagonals, which there isn't

-The circle has a right angle in it, as the angles never disappear because the lengths of the triangles that make up the sides are still real values

-repeated an infinite number of times causes it to lose its perimeter length, this can be proven by taking the limit of a function that has a definite length to a specified coordinate.

-It's a violation of the Pythagorean theorem

-the hypotenuse of each and every tiny triangle is slightly curved, therefore making it not a right triangle and not having the same perimeter

Pick one, /thread

pi = C/D
so if your perimeter is 4, and diameter is 1
oh dear

>>2128279
>>2128279

What's with the Engineering hate?

>>2128955

But pi is just the amound of radians in 180 degrees so being 4 would make no sense.

>>2128963
how can you get any better then engineering? it's the top of the food chain

>>2128224
for the same reason that these 2 lines are not equal length.

>>2128982
>Top of the Food chain

I guess if your into homosexuality

>>2128982

>>2128991
but what's higher then engineer explain this to me what is better then being an engineer in science!?

>>2128998
What is the best position then!?

>>2128986
you're just as retarded as the 0.999.. != 1 folks.

Just saying.

>>2128996
>Whats higher then engineering

Science in general
Biology, Chemistry, Physics, Mathematics.

Engineering is usually classified as shit-teir, as they learn little if no math. Engineering is akin to a "trade", like plumbing. It is needed in society, but it is still just considered specialized grunt work.

>>2129014
what, so equally retarded... which is zero?
because 0.999... DOES equal 1.
and i already know i'm right, and theres no point arguing this, its been done countless times, its practically a /sci/ based troll copypasta, so i'm not gonna argue about it.

>>2129021
But technologists and technicians are lower on the food chain and engineers learn math where the fuck did you hear they didn't? You design and build...

>>2129021
It's just a troll folks, let's move along now.

Explanation:

the perimeter approaches to that of a circle, it's okay.

the radius however, is not defined properly. when you have a polygon with each side tangent to the circle, the DISTANCE from the origin to EACH SIDE is the the same.
in here the distances are different. you can't use the original r. you can use the mean of the distances from the origin to the MIDDLE POINTs of each side as a radius. and it will show that pi approaches to its actual value.

why is this true? because a circle is defined as points with the same distances from the origin. if a polygon consists of sides with the same distances to the origin, in whatever why, it can be used to approximate the circle.

>>2129021

What the hell? I'm in Engineering Physics and our degree consists of an Honours Physics degree along with an Electrical Engineering degree. Where'd you get your information?

>>2129050
I'm going into EE and I was thinking the same thing O-o

>>2129006
>Underage faggot detected

There is no "best". However there are some fields that are obviously shittier then others.

Engineering doesn't contribute to man's fundemental understanding of shit. Engineering is just application of science (by definition). No discovery, no new knowledge.

Engineering = homosex Teir

>>2129050
>Where'd you get your information?

It's common knowledge, go to any university dumbshit. Everyone knows engineering is shit Teir. Not sure what "engineering physics" is though. If its just "Technical physics", then you should be fine.

Also, when did you come out of the closet?

>>2129059
Gay PRIDE

>>2129050
Bisexual?

>>2129064
>>God tier: Atheism

Irony anyone?

>>2129116
lol, oh wow... i honestly didnt spot that before. :)

but what kind of job do i get with chemistry biology and physics? Research, working in a lab, and being a butt monkey.

That is no circle. That is a roundish squareamajig.

Proof: consider the set of all points that intersect the circle and the roundish squareamajig. These points have a one-to-one mapping to a set of real numbers between zero and one inclusive (proof: map one of the points to zero, then take the angle away from that point in the circle as the value, then multiply by a constant to get the highest valued number equal to one)

Now, consider this set of real numbers, compared to the set of real numbers generated by following a similar procedure with the entire circle. If you do this with the entire circle, you get all real numbers between zero and one inclusive - since for any real number, you can choose that as an angle, and get a point on the circle.

For the roundish squareamajig, if you pick an arbitrary real number between zero and one, there's no guarantee that the circle intersects with the roundish squareamajig at the corresponding angle. We know this because the sizes of infinity are different for the number of points on the roundish squareamajig that intersect a circle and the number of real numbers between zero and one. Specifically, there are only 2^(n+1) intersecting points, where n is the number of times you repeat the corner-removal process. As n goes to infinity, you get countably many points. There are an uncountable number of real numbers between zero and one.

OP's picture is a clever troll, good thing there are cleverer mathematicians.

>>2129145
just show us your tits already

>>2129050
>>2129059
>>2129034

you must be new here
don't feed the trolls

>>2129155
see >>2129165

>>2129029
>because 0.999... DOES equal 1.
Yes, it fucking does. The symbol "!=" means "does not equal". It's used in programming languages a lot.

But you're the kind of retard that would have to argue that 0.999.. is at all times still infinitely small away from 1, which is retarded.

Just like saying that the limit of the given iteration does not approach a circle, but instead a fractal-like object with infinitely small jagged edges in it.

tl;dr: you're a fucking retard.

>>2129174
obey me, woman.

>>2129034
>engineers learn math

You sir are the true JOKER
I tip my hat to you

>>2129177
>agrees with me, then calls me a retard. laughingfaggots.jpg

>>2129213
I don't agree with you at all, you illiterate fucktwit.


you posted >>2128986
as an "explanation" of why OP's picture failed. But the picture you posted implies that OP's iteration will indeed NOT converge to the circle (which it obviously does. There's no such thing as infinitesimally small right angles. The fucktardation, jesus).

Thus you're a retard. Did you understand it this time or shall I mail it to you?

OP If you ever did grade 12 advanced functions you should know that what you are saying is stupid.

>>2129222
i meant that we are on the same side of the 0.999... = 1 argument.
>the picture you posted implies that OP's iteration will indeed NOT converge to the circle (which it obviously does....)
nope, it does not converge to make a circle.

>>2129259
cool story, bro.

Would you like to give any arguments? Please do tell us why the iteration would NOT be a circle in the limit.

>>2129148
>That is no circle. That is a roundish squareamajig.
The "repeat to infinity" step isn't well-defined, so any "proof" you have about the result is utter, utter bullshit.

Here we go again...

Fractals, not converging, octogonal shape, infinitesimal bullshit, taxicab geometry circlejerk brainfart.

>>2129148
we had that argument before, it's wrong.

For example consider <span class="math">f_n(x) = x^n[/spoiler] on [0,1] -> [0,1]. This converges pointwise to <span class="math">f([0,1)) = 0[/spoiler] and f(1) = 1. Yet, in every step of the iteration <span class="math">f_n[/spoiler] has only 1 point in common with the limit function.

You can now leave.

>>2129305
oh, actually there's 2 points in common for every f_n and the limit f, but who gives a flying fuck.

It's a finite (even constant!) amount of points.

>>2129291
Sure, the take to infinity thing is well defined. First you remove the corners once, then you remove the remaining corners, etc, etc. Each time, you double the number of points that are in contact with the edge of the circle.

>>2129305
Your example is unrelated. My proof is built around the fact that the square corner removal technique is isomorphic to the set of all fractions in the form of x/2^(n+1), where x is between zero and 2^(n+1) - 1. If the roundish squareamajig is actually a circle, then all real numbers between zero and one can be expressed by repeated multiplication and addition. We know that there are real numbers which cannot be represented this way, so this is a contradiction. So by proof by contradiction, the roundish squareamajig is not a circle.

>>2129344
>Sure, the take to infinity thing is well defined.
Then define it.

>First you remove the corners once, then you remove the remaining corners, etc, etc. Each time, you double the number of points that are in contact with the edge of the circle.
That only defines the shape after a finite number of steps.

There is no such thing as the shape after an infinite number of steps. We can only speak of limits as the number of steps approaches infinity.

>>2129344
shut the fuck up you semi-informed idiot.
You wrote:
>Specifically, there are only 2^(n+1) intersecting points, where n is the number of times you repeat the corner-removal process. As n goes to infinity, you get countably many points. There are an uncountable number of real numbers between zero and one.

I repeat:
>As n goes to infinity, you get countably many points.

This is fucking retarded. I showed you an example where you have one 2 points in common between every step of the iteration and the resulting limit.

>If the roundish squareamajig is actually a circle, then all real numbers between zero and one can be expressed by repeated multiplication and addition
They sure can, if you allow infinite series. In fact, every real number can be expressed as the infinite series of its decimal digits. What are you, fucking retarded?

Yes, there's a limit process. Yes, you don't understand limiting processes. Is that bad? I'm not sure. But it is a fact.

Stop looking like an idiot online.

>>2129356
Squares are curves in R^2. Curves are functions. Take to infinity means take the limit function. The limit function parametrizes the circle. Derivatives are not necessarily preserved in the limit, thats why the longitude isnt preserved. Engineers are fags.

>>2129382
>In fact, every real number can be expressed as the infinite series of its decimal digits. What are you, fucking retarded?

>http://en.wikipedia.org/wiki/Computable_number

>>2129421
I didn't say you need an algorithm you raging fucktard.

Do you even know how the reals are constructed?
Equivalence classes of rational cauchy sequences for example. For every real number you most certainly have the cauchy sequence of partial sums of the decimal digits. Again, are you retarded? Are your parents brother and sister?


You are now confirmed for being 12 years of age.

>>2129441
>doesn't understand limits, open sets, compactness.

>>2129464
You don't need to know anything about compactness to see what's wrong with the reasoning. Limits, yes.

Jesus christ man, why can't anyone give an explanation that non-mathematicians such as myself can understand

>>2129561
Just because the polygons get closer and closer to the circle doesn't mean their perimeter gets closer and closer to the circle's circumference.

>>2129561
Repeating things to infinity does not necessarily preserve stuff. Take >>2129441 for example. 1 > 0, 1 x .5 = .5 > 0 and so on. If you have one positive number, then that number divided by 2 is still positive. However, the limit (which is 0) is not positive.

LIMIT OF CIRCUMFERENCE IS NOT CIRCUMFERENCE OF LIMIT

\thread

>>2129561

really, even though it may look like the square became circular, to cover its perimeter, you would still have to make all those little turns onthe grooves and end up covering the same amount of distance as when it was a square.

taking the diagonal to save time only works if you actually take the diagonal, not if you take smaller and smaller turns.

>>2131204
no it wouldn't shut the fuck up. the square converges uniformly onto the circle.

see >>2131185
>>2131185
>>2131185

for an Actual answer.

Another example would be how if a series of functions converges to a function, their integrals don't have to be the same, I.e. limit of integrals is not integral of limits.

Or sometimes we cannot say the limit of some measure is the measure of the limits.

Or sometimes we can't switch derivatives (limits)

THE FUCKING LIMIT OF THE FUCKING CIRCUMFERENCE IS NOT THE FUCKING CIRCUMFERENCE OF THE FUCKING LIMIT AND THAT'S THE ANSWER GOD DAMNIT

>>2129561
>Jesus christ man, why can't anyone give an explanation that non-mathematicians such as myself can understand.

Long story short, the picture assumes the existence of a theorem such as "if a sequence of curves c_n tends to a curve c, and the lengths l_n of the curves tend to a length l, then the length of c is l".

But there is no such theorem. It sounds plausible, but it's not true. The OP is a counterexample, and proves that such a theorem does not exist.

>>2131219
no faggot, it's just that the limit of circumferences is not the circumference of the limits.

>>2131222
I just said that in more generality, you dummy.

how the fuck is saying "no such theorem exists" more generality? can you PROVE that no such theorem exists? hell no you can't. i said it in more generality when i said that the limit of measures is not measure of limits.

>>2131218

hahaha fuckin retard

look up "taxi cab geometry"
basically the triangle inequality doesn't hold

so given two points a and b. the fastest route between them is equal in length to the route taken by creating a right triangle with them.

It doesn't matter the number of turns you make or how tiny they are, to only cross the diagonal distance (which is usually root(2) shorter) you must actually move diagonally.

>>2131239
you're an idiot. go get a phd in math then we'll talk