can you believe that YT considered this comment as not English and offered a translation that doesn't change anything beside the spacing of characters?
@@Theonewhoknocks422 No, it's not. A vertical line through the origin comprises every point that can be reached from the origin with only vertical movement, i.e., no horizontal movement. No horizontal movement means x is 0, so that line would be described by x = 0.
1:25 Wait. How do you get two parallel lines? I can't see how would you place that plane, going through the central point and producing two parallel lines.
@@chasebender7473 You said something I already knew. Go to the minute of the comment. He said: "The lines can be parallel OR intersecting". I can see how they can intersect forming and 'X' shape. But the visuals of the video and his comment claims that there is a scenario where the lines are parallel. Meaning an 'II' shape. And that is either an error of the vídeo or something that I am not understanding.
That only happens in theory if you say that a cylinder is the same thing as a degenerate cone which has its vertex at infinity. If you cut the cylinder with the plane through its infinite length, the plane will show two parallel lines where it cuts the cylinder wall circumference.
Actually the lemniscate is named after uncle Jakob (or Jacques) Bernoulli, like most Bernoulli math stuff (B numbers, B probability law…). Nephew Daniel has its name given to the Bernoulli hydrodynamic theorem.
4:48 is the cassini oval, by any chance also the curve for the equipotential surfaces for two equal point charges kept at a finite distance and its orthogonal curve, the electric field lines?
What about the Mandelbrot curves? Those are the sets of points c where the magnitude of z is equal to two after specific numbers of iterations of z starting at zero under the map z → z² + c, where z and c are complex numbers.
The boundary of the Mandelbrot set is not an algebraic curve. All algebraic curves can be broken up into finitely many smooth arcs. Since the boundary of the Mandelbrot set is fractal, it is smooth nowhere and thus not algebraic.
To understand why at 1:25 you can get three different things if the plane passes where the cones touch: 1) you get only the point if the plane passes outside both cones, let's say like horizontal through the middle; 2) you get one line if you put the plane in a way so that it touches only the outside surface of the cones, the single line will be the tangent where the cones curvature touch the plane; 3) you get two (crossing, not parallel) lines if you put the plane in a full vertical way, it will make an X figure. You cannot get two parallel lines unless you get an imaginary case in which you say that a cylinder is a degenerate cone with the vertex at infinity. In that case if your plane is vertical then the cuts in the cylinder will for two parallel lines, but that is an extreme definition case. "Cheating".
The witch of Agnesi is not a lorentzian though, as its width is not related to its height in the right way. So it is not the PDF of a Cauchy distribution.
I like how it was straight to the point
Like a cone.
straight to tips touching.. yes!
If it was _straight to the point,_ does that mean it _did_ or *didn't* go off on a tangent?
@@omargoodman2999just as Schrödinger intended
1:47(mistake)
Equation x=0 wont lie on z-axis
but rather on y-axis
and that required only Cartesian coordinate math and no linear algebra to prove.
You're back! Great!
Bach's Badinerie is a great choice for the end credits
1:21 that’s what my parents call me
No mention of how the Witch of Agnesi is called the witch due to a mistranslation. smh.
if not witch, why witch hat shaped?
4:14 those who know 👀
?
still water mango mango mango
Those who skull emoji 💀💀💀
💀💀💀💀
Knee surgery tmrw 😂😂🎉🎉🎉
1:47 y = 0
y = 0 is a vertical line that goes through the origin.
y = 0 is a vertical line that goes through the origin.
can you believe that YT considered this comment as not English and offered a translation that doesn't change anything beside the spacing of characters?
Yep, that's an error.
@@Theonewhoknocks422 No, it's not. A vertical line through the origin comprises every point that can be reached from the origin with only vertical movement, i.e., no horizontal movement. No horizontal movement means x is 0, so that line would be described by x = 0.
6:48 ty for this life changing latin lesson
Witch of Agnesi is such a banger name, mathmaticians were really cooking with that one.
It’s actually called The Witch because of a mistranslation. I think that’s pretty neat :)
At 5:55 you could have animated drawing the curve for all points P. Would have been very satisfying to watch!
desmos: 0sdzsvxb5x
1:25 Wait. How do you get two parallel lines? I can't see how would you place that plane, going through the central point and producing two parallel lines.
Not parallel lines but lines intersecting at the origin. This happens when the plane intersects the circular cross sections of the cone in a diameter
@@chasebender7473 You said something I already knew. Go to the minute of the comment. He said: "The lines can be parallel OR intersecting". I can see how they can intersect forming and 'X' shape. But the visuals of the video and his comment claims that there is a scenario where the lines are parallel. Meaning an 'II' shape. And that is either an error of the vídeo or something that I am not understanding.
That only happens in theory if you say that a cylinder is the same thing as a degenerate cone which has its vertex at infinity. If you cut the cylinder with the plane through its infinite length, the plane will show two parallel lines where it cuts the cylinder wall circumference.
@@SomeoneCommenting Thanks you so much!
@@SomeoneCommenting thank you
Actually the lemniscate is named after uncle Jakob (or Jacques) Bernoulli, like most Bernoulli math stuff (B numbers, B probability law…). Nephew Daniel has its name given to the Bernoulli hydrodynamic theorem.
They where 12
4:48 is the cassini oval, by any chance also the curve for the equipotential surfaces for two equal point charges kept at a finite distance and its orthogonal curve, the electric field lines?
What about the Mandelbrot curves? Those are the sets of points c where the magnitude of z is equal to two after specific numbers of iterations of z starting at zero under the map z → z² + c, where z and c are complex numbers.
The boundary of the Mandelbrot set is not an algebraic curve. All algebraic curves can be broken up into finitely many smooth arcs.
Since the boundary of the Mandelbrot set is fractal, it is smooth nowhere and thus not algebraic.
@patrickgambill9326 No, I am referring to the equipotential curves that converge toward the boundary of the Mandelbrot set. Those are algebraic.
@@denelson83My bad. I misread your post
Highest IQ convo in TH-cam history, including the misunderstanding.
That cursive greek letter Pi tho...thick.
The folium itself has a “paradox” where it intersects itself. How do you find the tangent lines?
But how can we get parallel lines as a conic section?
To understand why at 1:25 you can get three different things if the plane passes where the cones touch: 1) you get only the point if the plane passes outside both cones, let's say like horizontal through the middle; 2) you get one line if you put the plane in a way so that it touches only the outside surface of the cones, the single line will be the tangent where the cones curvature touch the plane; 3) you get two (crossing, not parallel) lines if you put the plane in a full vertical way, it will make an X figure. You cannot get two parallel lines unless you get an imaginary case in which you say that a cylinder is a degenerate cone with the vertex at infinity. In that case if your plane is vertical then the cuts in the cylinder will for two parallel lines, but that is an extreme definition case. "Cheating".
How can a devenerate conic be parallel lines? I don't get it.
Is a parabola a special case of a hyperbola? Or the reverse?
but what about P.F. Changs for Bernoullis Lemniscate?
i start to wonder, this is made in canva right
A pair of parallel lines is not possible on a cone. But it is possible on a hyperboloid of one sheet as well as any cylinder.
Single sided closed surface?
Surface(cos(u/2)cus(v),cos(u/2)sin(v),sin(u)),u,0,pi,v,0,pi
The witch of Agnesi is not a lorentzian though, as its width is not related to its height in the right way. So it is not the PDF of a Cauchy distribution.
2:22 x² + y² + e^iπ = 0
00:10 For Jesus
wut lol
@@sans1331 you heard me.
2:55 It's not pronounced fuck-eye but foe-sigh...
thanks
Based ThoughtThrill video
You didn't mention elliptic curves/hyper-/super- elliptic curves.
What about hyper-eliptic curves?
@ I literally said that.
Oh I meant to say omega-Hyperion-elliptical curves
can't spell "ellipse" at 4:42, horrible AI voice translation = NO SUBSCRIPTION
I don’t think it’s an AI voice
Point-slope form mentioned 🤓👆
A lemniscate is a toroidal section.
I generated one of the images used for the thumbnail of a different one of these guy’s videos lol
Me: Why would they name an innocent looking curve a witch?
*video mentions the Cauchy Distribution*
Me: Ah, yes. I agree.
Missed the "N" in lemniscate!
lenmiscate!
that concludes our latin lesson. lol
lembiscuit :)
Hey I watch these videos at night and the white background is killing me
Search 3bluebrown
Now do algebraic surfaces
2(2x*2y)=(x^2+y^2)^2
and
2(2x*2y)/(x^2+y^2)=x+y
bro none of the comments here were made by real people
Can confirm: not a real person.
It's an ai generated content.
@@rafiulalam2390It's all plagiarism, copied almost directly from Wikipedia.
first ez
1:48 y=0