2+2=4
do you have any hard math problems?
>>8172669
1+1
>>8172669
Use chords to split a circle into equal area pieces that are all non-congruent with each other
>>8172673
1+1=2
proof?
>>8172679
IIRC someone wrote a 400 page proof that 1+1=2
>>8172676
just do n vertical slices for n>2 where you vary the distance between slices. simple integrals to get the distances between slices
>>8172686
Russel. 360 pages.
>>8172698
disregard this, i suck cocks.
>>8172686
Bertrand Russel and J.E. Whitehead wrote "Principia Mathematica," where they tried to derive all of mathematics from first-order logic. The book contained a full formal proof of 1+1=2, in addition to a lot of other stuff. Gödel's incompleteness theorems ended up demolishing the project.
I think there's still a team of researchers trying to figure out how to formalize pic related.
Here is a problem for you guys: is there a function that takes two natural numbers (a,b) and yields the number of connected components of Top[S^a, S^B]?
>>8172707
explain your notation
>>8172705
>
m a t h
>>8172714
The connected components of the space of maps from the a-sphere to the b-sphere (which is automatically a CW-complex).
>>8172717
They tried to formalize philosophical abstract concepts to build math.
Prove or give a counter-example of the following statement:
In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.
>>8172705
NOW THAT'S WHAT I CALL MATH, volume 1.
Would anyone buy such a book?
>>8172676
Is it possible to do this by inscribing a triangle in the circle?
>>8172749
Only if it had a Pug smoking a cigar while reading a paper about the Banach-Tarski theorem on the cover
>>8172669
1/1(1*1)1/1(1*1)1/1
NP=P :^)
>>8172766
>doing it in the easy way
pshhh
>>8172771
There was a anon on /g/ that said his professor was reviewing a paper that might prove that P != NP
>>8172780
His professor shouldn't be sharing that information.
>>8172826
That information is hardly enough to get "scooped" -- I suspect the majority of mathematicians are convinced that P != NP and it's not helping them prove it any faster.
>>8172833
No, you aren't supposed to talk about papers you're reviewing.
intergral of (e^x^e^x^e^x^e^x^e^x^e^x)/(666*(-69)^sqrt(-i))
>>8172755
No, you can't get equal area pieces if you inscribe a triangle.
>>8172766
No, if you only used vertical chords that don't intersect then the pieces on the side must be congruent in order to have the same area.
The area a chord divides the circle into determines its position relative to the center of the circle. For example, if a chord divides a circle into parts that are 1/3 and 2/3 of the circle's area, then the angle between the radii which touch the endpoints of the chord is the solution to the equation
x - sin(x) = 2pi(1/3)
Such an equation will always have only one solution between 0 and 2pi, but can only be solved numerically. Let's call it the "position angle".
In order to describe any combination of chords, we must determine a similar kind of angle that describes the separation between the radii touching the endpoints of intersecting chords based on the area they together delineate. Let us call this the "separation angle" This is a bit more complicated. The separation angle is the solution to
cos(z/2) cos(x-y/2) csc(x-y/2-z/2) (1-cos(y/2) sec(x-y/2))^2-sin(x) cos(y/2) sec(x-y/2)+x = 2pi F
Where y and z are position angles of the two intersecting chords and F is the fraction of the total area delineated by the intersecting chords. This of course can only be solved numerically.
So it seems rather difficult to prove that it is impossible for such a set of chords to exist. I have proven by exhaustion that it is impossible for this to be done in 5 chords or less.
>>8172676
Divide the circle with a horizontal line in two. For the left side use the horizontal line trick, for the right side draw chords from a single point at the top of the circle, and end of each chord in appropriate points on circumference of the right half circle.
>>8172918
Could be done in 3 chords I suppose?
>>8172918
Yeah did you not read what I said? Look at the two chords at the ends. They must be congruent with each other since the only thing that determines their shape is the area they delineate, which is equal.
I'm trying to find the name of this problem (or just formulate it better).
A circuit is a graph of components and traces. For a given circuit, find the configuration that has the least jumpers over traces (in 2D space).
>>8172926
Dunno about a name, but I believe you're asking for the circuit with the least self-intersections in 2d space?
>>8172923
So if you're allowed to cut the circle using only chords that don't intersect, doesn't that mean you'll always end up with at least 2 figures being circular segments, thus proving such division impossible?
>>8172931
>So if you're allowed to cut the circle using only chords that don't intersect
Where did I say they aren't allowed to intersect? Of course they are, or the problem would be trivially impossible.
>>8172884
So is the seperation angle, the angle of the intersection of the two position angles of the intersecting chords?
So you basically created these equations for all groups of three from the five chords and then ran all of the equations through some program to show there is no solution for 5 chords?
>>8172936
Groups of two*
>>8172936
>So is the seperation angle, the angle of the intersection of the two position angles of the intersecting chords?
Yes, exactly.
>So you basically created these equations for all groups of three from the five chords and then ran all of the equations through some program to show there is no solution for 5 chords?
Groups of two you mean. Yes, essentially that's what I did. There are some things that help reduce the problem space. Anything where a cycle of intersections is made, like three chords intersecting to form a triangle in the middle, doesn't work because it's an overdetermined system.
>>8172928
Getting there
A circuit is a planar graph of components and traces. Find the _____ that minimizes self-intersections.
What do you call a transformation where edges still connect to the same vertices?
>>8172875
>intergral of (e^x^e^x^e^x^e^x^e^x^e^x)/(666*(-69)^sqrt(-i))
easy peasy m8
>>8172943
Why does an overdetermined system mean there are no solutions?
>>8172936
Here is the simplest division that breaks symmetry. It would be a solution if that small chord at the top left didn't cross that other chord.
>>8172963
Because it has negative degrees of freedom. In other words, it has properties that can't all be true at the same time.
>>8172963
A stupid example of an overdetermined system:
x = 5
x = 2
There is no such x, that solves this system.
The only way such a system (x=a, x=b) is if two of the equations where linearly dependent (if a=b)
I'm probably explaining this horribly
>>8172971
Okay, makes sense.
>>8173002
>Nothing says an overdetermined system can't have a solution.
It's generally intended that way by anyone with a brain, as an overdetermined system with a solution has unnecessary constraints that can be simply discarded to yield an equivalent system that is not overdetermined.
If you want to be a pedant, be less of a brainlet asshole.
>>8173007
>interpreted
The definition seems pretty clear to me.
>>8173073
>greentexting with a different word than i used
I didn't disagree with the definition, see:
>If you want to be a pedant, be less of a brainlet asshole.
You can show an inverse square law with triangular numbers sequence.
Show us how it's done.
