/lit/ - Literature

what rectangles?? what fucking rectangles????

>>19534311
Your subhuman iq threads are growing tiresome

>>19534318
Go ahead show us in ms paint buddy

>>19534311
What no pussy does to a mf

>>19534311
>>19534313
>Two right lines
Anon....

>>19534364
yes they are not wrong they are straight lines are you blind??

>>19534311
>>19534311
Sorry for how shitty this drawing is and for phoneposting but this is my best guess

>>19534364
if a "right line" is not a synonym of "straight line", what does that mean then?

>>19534423
Lines at a right angle, or perpendicular angle, to each other

I made the shitty doodle and this obviously wouldn't work without symmetry of some kind so maybe Kant also meant one of the lines had to go through the center of the circle

>>19534429
Another thought, it's a misquow2mxrte

>>19534429
>>19534417
I checked the original German and it only says "zwei Linien" without any adjective like right or straight so it's obvious he must have meant two straight lines, and nothing implies any paricular angle of the intersection. Thus your drawing, although very beautiful, is a creation of your own imagination and doesn't follow from Kant's description, not in the slightest.

>>19534429
My other guess is that he's talking about the quadrilaterals obtained by flipping these triangles about the diameter of the circle, eg, he means "rectangles" loosely

>>19534455
Oh okay. Hmm. I'll have to think about it some more while I have my coffee

>>19534455
Is there any chance he meant "symmetrical" and not "equal"? Because that would make a lot more sense

>>19534470
He used the word gleich which is exactly the same thing as equal, do what you want with it. I suggest you just go read §38 of his Prolegomena because he goes on sperging out about the geometrical nonsense, so maybe the bigger picture will help you uhh solve it

>>19534313
Well, I've drawn all three possible statuses of the lines in different colors - each intersecting the circle only once, each intersecting the circle twice, and one intersecting the circle once while its pair intersects the circle twice - and I must admit I am struggling to locate some property of possible rectangles generated by these intersections that is common to all three. In fact I am struggling to locate the rectangles at all

this is what he meant, he wrote that really poorly

>>19534507
actually no thats wrong, still not sure what hes trying to say haha

>>19534507
This is obviously false though, for this to be true the internal length of the lines would have to be the same for a start.

>>19534497
Yeah in that case I can assert with confidence that I don't know what the fuck he's talking about. I think the only Kant I've read to date is Critique of Pure Reason. Years ago. And I remember it very badly. I won't declare him wrong until I've thoroughly examined the context on my own, but this seems like a mistake on Kant's part unless he's describing a non-Euclidean geometry

>>19534516
yeah i realize that, but from the text that seems like exactly what hes saying

a rectangle is an 90 degress angle

Don't quit your day job, cunt!

>>19534565
Yes. In casual speech, though, "rectangle" and "quadrilateral" can be used as synonyms. I was being generous with that definition

If the lines are not at right angles to each other it does not seem easy to me to construct a proper rectangle with them at all. Each species of intersection >>19534506 generates different sorts of possible line segments, inside and outside the circle, but he seems convinced the property holds for all three

>>19534565
yep, this

>>19534455
Right line is an old way of saying straight line anyways. If can't didn't draw any pictures it's hard for me to see what he's describing. It's a little vague as to what segments he's referring to and how the rectangles are constructed exactly. He might be referencing some other work that explains it more clearly

>I'm drowning!

>>19534393
Usually the opposite.

>>19534311

is this what he meant by the rectangle constructed?

>>19534697
No. The lines must intersect one another

>>19534701
Where did he say that?

>>19534708
>... which intersect one another and the circle...

>>19534708
>Two right lines, for example, which intersect one another
>and the circle

In the OP, brother

You appear to have drawn them parallel, which is the only possible orientation that fails to meet Kant's criteria; all lines which are not parallel must intersect at some point, by definition

> ITT: /lit/ who are not aware of the intersecting chords theorem don't know about the intersecting chords theorem.
> https://en.wikipedia.org/wiki/Intersecting_chords_theorem
> https://www.mathsisfun.com/geometry/circle-intersect-chords.html
Seriously, you faggots really need to start with the Greeks before you try someone like Kant, this is basic fucking Geometry, read Euclid.

>>19534928
meant to write,
> ITT: /lit/ retards who are not aware of the intersecting chords theorem making fun of Kant for restating an elementary theorem of geometry.
I'm sorry, I was just so shocked that I could barely put words together. I'm calm now, but still very dissapointed.

>>19534928
The difference is the vagueness Kant uses when referencing this equation. If he was so explicit nobody would take issue with it

>>19534949
Nah, it's pretty obvious if you aren't retarded, buddy.
Anon over here >>19534507 even drew it before taking it back >>19534512 and afterwards being told that it's "obviously false" by this clueless faggot >>19534516 and saving face by agreeing >>19534530 like a retard. He was right to say that "from the text that seems like exactly what hes saying" because it was, it's just that you guys were getting filtered by basic geometry. It's okay, we're not born knowing these things, but you can still learn.
Very funny thread though. I thought OP was just being retarded but now that I think about it, he made a similar thread earlier with a quote from Russell but was immediately shut-down; I think he might be making these threads on purpose to b8 and laugh at STEMlet /lit/ards.

>>19534978
I'm not reading all that but it is vague. It's not disputable. Don't talk down to me either it's cringe. Using rectangle instead of product and not explicitly saying the lines are chords in the circle obfuscates your little elementary geometry formula. Really weird that you would try to use that to feel superior

>>19534311

God he has such a disturbing infantile appearance

>>19534429
If he meant it he should have said it

>>19534988
Spinoza also mentions this theorem in weird language, which is why I was able to recognize it when I read it.
>The nature of a circle is such that the rectangles formed by the segments of all the intersecting lines within it are equal to each other.
The original theorem is from Euclid's Elements, B3 P35:
>If in a circle two straight lines cut one another, then the rectangle contained by the segments of the one equals the rectangle contained by the segments of the other.
Sounds a lot like what Kant said, right lines is obviously straight lines. I know this post is bait, but it brought out so much sincere retardation that I'm just left feeling really disappointed.

>>19534600
>"rectangle" and "quadrilateral"
Uh, no. Nobody is going to call a trapezoid a rectangle even though they will call it a quadrilateral.

>>19534928
I'm the guy you called retarded. A chord and a line are completely fucking different geometrical objects, hence my confusion. Thanks for solving the mystery

>>19534516
>the internal length of the lines would have to be the same for a start
that’s the point of the circle. if two straight lines both cross a circle (presumably at the middle since the circle is drawn around the intersection) then the internal lengths of the lines must be equal and the rectangle constructed with those line segments always the same dimensions

>>19535071
The theorem also holds for intersections not on the center of the circle.

>>19535071
though after a little more though it seems that they don’t need to intersect the circle, just enter and leave the circle at opposite points in order to be a full diameter long. 2 diameters -> 4 radii -> 4 equal sides of rectangle

>>19535071
>howsoever they may be drawn
>presumably at the middle
And yes, I realized that if the chords are of equal length it works every time. But if the circle is drawn at some random spot they may not be of equal length.

>>19535043
That language is severely outdated

>>19535087
But because they are chords, the point of intersection must lie within the circle. That tripped me up

>>19535043
So it’s talking about the area of the rectangle as defined by the two split segments. I get it! they must be equal! makes sense. they aren’t talking about making 4 segments and forming a rectangle

>>19534988
>I'm not reading all that
Cuz ur dumb.
> it is vague. It's not disputable.
You are such a massive faggot. So, you were filtered, cool, get over it.
Stop trying to pretend like he was being an obscurantist. What does he even gain from that? Smarty pants points? It's literally an elementary geometry problem that everyone reading his book would have been familiar with already, since they all started with the Greeks, unlike you pleb.
Everyone knows that a rectangle, like a square, can be used in that exact sense because the arithmetic so obviously corresponds to the geometry.
>explicitly saying the lines are chords in the circle
From the way he described the problem it's pretty fucking obvious he meant a chord. What else could it be?
> the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides
Is that phrased too "vaguely" for you? lmao.
> https://youtu.be/pi2FFxe6AG4
>>19535033
But he didn't mean that, see >>19534928.
>>19535055
> I'm the guy you called retarded.
Kek. To be fair, you drew it so you can't be that retarded lol. You definitely deserve some credit.
> A chord and a line are completely fucking different geometrical objects
Not really, a chord is literally just a line which intersects two points on a curve (e.g. a circle). He described it well enough for you to draw, I'm sure you could have realized it was a chord by yourself at that point.
>Thanks for solving the mystery
Np.

>>19534928
Ahhh, fuck, he also meant the areas of the rectangles were equal, then, not the rectangles themselves

>>19535108
Not really, chords are just lines that intersect a circle at both its (the line's) ends. This proof is didactic enough https://youtu.be/W0iRmOs9tj0

>>19535145
Like. I wouldn't call a 2x6 rectangle "equal" to a 3x4 rectangle, but that is the sense in which Kant means it, yes?

Man this is like when I was reading Descartes and driving myself insane trying to sketch out what he was talking about and then looked it up. Good times

>>19535129
Still not reading this. Guess what, I'm smarter than you and know more mathematics than you. I didn't have to read the elements of Euclid to do that, because it's more of a historical text at this point. Cry harder, you're embarrassing yourself

>>19535159
ty!

hilarious thread. thanks for the laugh

>>19535185
>/lit/ resolves a mathematical question in record time - less than seven hours!

>>19535170
Seethe, cope, dilate, and read Euclid.

>>19535108
>But because they are chords, the point of intersection must lie within the circle
in what world
>>19534978
>it's pretty obvious if you aren't retarded
cvnt is the one who's retarded, I cannot possibly imagine explaining such a simple theorem in a more intricate way than his
>>19534928
>you faggots really need to start with the Greeks before you try someone like Kant
this has nothing to do with le start with the greeks. everyone learns about the theorem in middle school if not earlier, you're not any smarter because you know it. You merely guessed that this is what cvnt could've had in mind, bravo (You).

>>19535204
50 posts isn't too bad. /sci/ is often pretty worthless too. I bet /diy/ solves it faster.

>>19535251
>this has nothing to do with le start with the greeks.
Some people's education is so poor that explicitly starting with Euclid would, indeed, do them much good; I will also add that it is not uncommon for a mathematician to be ignorant of geometry because geometry has so fallen out of fashion these days.
>everyone learns about the theorem in middle school if not earlier
Then you should have been able to recall it, but you didn't so you're dumb.
>you're not any smarter because you know it.
Pretty sure a midwit is smarter than a retard.
> You merely guessed that this is what cvnt could've had in mind, bravo (You).
I didn't fucking guess, retard. There's a circle, there are lines intersecting the circle and each other and their segments make equivalent rectangles. Literally what else could he have meant? This guy literally drew it despite not knowing what he meant >>19534507. If you knew it, what were you missing?
>cvnt is the one who's retarded, I cannot possibly imagine explaining such a simple theorem in a more intricate way than his
Stop seething at my boy Kant, he's not retarded, you just got filtered buddy.

>>19535251
>But because they are chords, the point of intersection must lie within the circle
>in what world
Well if it lies outside of it... it's possible for that to lead to two chords of length zero, isn't it? Which preserves the theorem, but doesn't seem to say anything particularly meaningful about how the nonzero "segments" relate to each other. But at that point (heh), it is more of a point than a chord

I'll be blunt: the existence of chords of nonzero length with an intersection point outside the circle did not occur to me. I have been awake for 36 hours

>>19535379
>>19535379
Okay, so. With regard to the chords with an intersection outside the circle. Pretending that the black and green shapes are circles. If we start with the black and red situation, we can extrapolate that to the green situation, and then the gold and purple bits are the new line segments that determine the dimensions of the rectangles? yes?

>>19534311
lol