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.
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.
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.
4:14 those who know 👀
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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?
At 5:55 you could have animated drawing the curve for all points P. Would have been very satisfying to watch!
Bach's Badinerie is a great choice for the end credits
You're back! Great!
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
6:48 ty for this life changing latin lesson
No mention of how the Witch of Agnesi is called the witch due to a mistranslation. smh.
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.
Me: Why would they name an innocent looking curve a witch?
*video mentions the Cauchy Distribution*
Me: Ah, yes. I agree.
That cursive greek letter Pi tho...thick.
2:22 x² + y² + e^iπ = 0
1:21 that’s what my parents call me
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.
thanks
Based ThoughtThrill video
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
but what about P.F. Changs for Bernoullis Lemniscate?
i start to wonder, this is made in canva right
But how can we get parallel lines as a conic section?
Missed the "N" in lemniscate!
lenmiscate!
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
Hey I watch these videos at night and the white background is killing me
Search 3bluebrown
Now do algebraic surfaces
bro none of the comments here were made by real people
Can confirm: not a real person.
00:10 For Jesus
first ez