Curvature formula, part 1
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- Опубліковано 19 вер 2024
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Curvature is computed by first finding a unit tangent vector function, then finding its derivative with respect to arc length. Here we start thinking about what that means.
honestly you saved my life. i was looking for mathematical prove about curvature, wondering how difference in vector can affect changes in k which is scalar.
your explanation perfectly shows how does it works!! Thank you so much.
3blue1brown!
Benjamin Rutkowski OH MY GOD I JUST NOTICED ITS MY BOI
I WAS ABT TO COMMENT THIS I RECOGNIZED HOS VOICE 1MIN INTO THE VIDEO
THE best curvature formula explanation period!
I think I’m addicted to math. It’s literally all I think about all they time.
same here dude! lol ive already got textbooks for calculus of variations and linear algebra and just can't wait to finish this and go to those.
Pluto Dagon start with p-adic Analysis after that
same here
SAME
Same
Good video I particularly appreciate the vector intangible.
However, even if that's so That's a detection only. If a building or object is still visible past all of these points it doesn't matter whether we were able to detect it or not because the building should still be below the Horizon.
Yes! But the response will invariably be the "magic" of refraction! How things magically rise from above the rear of the curvature into view! I'm here seeking a device that is capable of measuring curvature at the microscopic or even micron level if possible. With such a device one could measure the absolute lack of curvature over the surface of a large indoor swimming pool in which the water is perfectly still. This would be an awesome experiment! Here's a start! ua-cam.com/video/naXOpoRb-ws/v-deo.html - and : ua-cam.com/video/yQPUaY9t8dY/v-deo.html
Exactly
What do you use as a drawing tool? it works so well, and professors that are forced to work online need better tools like this!
btw thank you for this video! makes it so clear.
Been looping at 1:45
I love this because it shows that didn’t know about this and flat earthers need this
Turns out, that the curvature depends on the magnitude of |dT|, and the bigger |dT|, the larger ratio |dT/dS|, so why we just don't measure the length of dT itself for determining the curvature?
great lesson thank you soo much
Curvature- the degree to which something is curved; The road curved to the right.
What was that ? 1:44 to 1:46
"Y'know-I-mean-berry"
That's the vector s(T) such that the x component of that vector is t-sin(t) and y component being 1-cos(t)
how quickly unit tangent vector changes directions. this seems like this sentence summarizes the content. dT/dS is the formula of curvature. thanks~
He's good. Nice approach.
Thank you!
Can you use this to measure curvature form New York City to San Francisco?
yes...per 200metre.was 1inch
excellent but what software is khan academy using to illustrate and annotation? i'm not having success on zoom using my pad for student's notes.
That guy is good, I thing he should star a mathematics channel on youtube
He did.😂 The name is 3blue1brown. Thank me later
The earth has curvature and it has been proven
Link
Are vertical lines parallel? What is the difference between level and unlevel? Do plane surveyors and geodetic surveyors work from the same benchmarks? When you answer these simple honest questions correctly you will know the true nature of the Earth.
Wdym. And are vertical lines parallel huh?
@@c4sare4kiddos
Vertical lines are parallel they never converge together like science says they do. Most will never understand that.
@@tonyornelas9374 ok so what does that imply? And wdym that’s called intersecting lines and not parallel if they touch?
@@c4sare4kiddos
If you want to believe vertical lines can come together then whats the point of me telling you they can't? You don't agree with what I say and that’s the same as calling me a liar and I take offence to that. If you can show verified proof then I will look at it until then don't reply with your silly questions.
@@tonyornelas9374 bruh ur tweaking. I asked a question , what does parallel lines imply? (That they lie to us?) and I never said parallel lines cross , no shi they don’t that wouldn’t be called parallel buddy that would be called interacting lines like I said already.💀
I didn't know 3Blue 1Brown did your videos?
i smell infinity ahead
madisonelectronic v
Woah.. Grant!?
Grant Sanderson!!
"And this means of taking the magnitude of the rate of change of the unit tangent vector with respect to arc length just to capture that idea"
@DnB and Psy Production I understand I just find it kinda funny how long the statement is
Seems ambiguous to me, as the curve is not a circle anywhere!
Hello. I am trying to find someone to explain as well as you could mathematically the curvature formula for the earth based on a 25000mile equator. Flatearth debate would end when showing people the clear math and how to calculate...can you help and show the numbers please. If we live on a 25000mile equator how far one would need to travel before curvature drop? How much curvature in 1mile 5, 10, and so on? Please help
you might want to find a calculus textbook that explains it.. When i was in college we skipped over the section to measure lengths of circles because it was too complicating apparently.
is this sal > he sounds different
+Prateek Gurjar Please tell me you're joking.
PhysicsGuru100 Yeah listen to his old voice
it isn't sal lol
It's Grant, from the 3Blue1Brown channel.
Go watch that channel now, it's awesome!
I am sure this isn't sal..
Can anyone tell me the curvature for log(sec t + tan t)
ok'
1sec.tan+sec
How does the norm of T changes if it's a unit vector?
change in angle...
In |dT/ds| the norm is being taken of the infinitesimal vector dT(s) = T(s+infinitesimal)-T(s), scaled by the infinitesimal.
I suppose I should have expected the comment section to be filled with flat earthers
Still looking for an example that applies all this information on NURBS (with 3 or 4 control points, atleast).
Wym
1:44🤣
So you wanna see how quickly the tangent unit vector changes as the car moves.
Me: "But the tangent vector is the derivative!"
Also me: "You wanna a derivative of a derivative. Wait a minute..."
Because on normal calculus curvature is the second derivative. And now you want to take a derivative of a derivative.
Suspicious...
@@jorgealexandre4616wdym
what a crossover
i like ur beard
same
This voice seems to be of Grant from 3blue1brown
it is grant
I think I am addicted to meth!
BSc classes also upload on kaun kaun Academy please request please please and IAS IAS coaching also sir sir I will give after donation please I hopefully requested the sir I'm expecting you read this message thank for you
2500 miles from san francisco to norfolk is 2,500 miles 2,500 x 2500 = 6,250,000 miles 6,250,000 x 8 inches = 50,000,000 inches 50,000,000 divide by 12 = 4,166,666.66 feet 4,166,666.66 feet divide by 5280 = 789.14 miles ------------ so ball earth has 789 miles of drop across the united states. A plane traveling at 500 mph would have to correct the nose down 157 miles for every hour of flight to maintain the same elevation or 2.63 miles per minute to maintain elevation.................. someone correct all of my math for me so I can maintain my ballfiction please
Dont use 8 inches per square mile. That’s wrong
there is no curve to measure - sea level
@@patrickhickman8723 yes there is. Its 69.4 miles per 1 degree. And what about sea level?
explain the 2 observable forces on earth and how you measure / prove them. Clue 1, gravity is imaginary and not observable.
@@patrickhickman8723 gravity is well explained by Newtons law of gravity and Einsteins theory of gravity actually.
no simply square the number of miles times 8inchs
What are you talking about?
EXAMPLE. watch a boat sail away. 6 miles away your standing at the beach. 6x6=36x8 inches=288 inches down .Dived by 12 in. in ft =24feet below the horizon. CAN you see it ?.yes even 60 miles away,why are they lying to us. ok the miles away are squared x8 inches =curvature of earth.
"simply square the number of miles times 8inchs" Wrong.
@kenneth caron That expression comes from a very old book and it's a very rough approximation, it's outdated lol.
@@kennethcaron572 Earth is not a parabola ok
I'm imagining π moving
Hahahaha curvature yeahhhh
Just multiply 0.31830988618377 * the distance you drove and that will give you your curvature. So, if you drive 4 miles, your curvature will be 1.27323954473508 miles of curvature. In fact, to get the radius of any circle just multiple 0.31830988618377 * C and dived by 2.
Engineering student?
are you ok?
Why are you over complicating it?
Uvuvuevuevue Onyetwenuevue Ugwemugbem Osas
I prefer the normal guy for this tbh
this is wrong...if im at point A looking at point B one mile away, there is 8 inches of drop (roughly)..Now if someone else is at point B looking at point C another mile away, thats also 8 inches (roughly) for the 2nd person...So why is everybody multiply squared for every mile? If there is 8 inches of drop between me and point B and 8 inches of drop between point B and point C, that means there is only 16 inches of drop between A and C and so on...You just add 8 inches for every mile...Why would you multiply anything? The purpose of the "squared" in that theorom is simply to account for all directions or to give you the curvature in one mile...It never sais keep multiplying expodentially lol...you'd hit infinity pretty fast almost lol...all flat earthers wrong including me
..........BECAUSE YOU USE MULTIPLICATION INSTEAD OF ADDING MULTIPLE NUMBERS OVER AND OVER! INSTEAD OF DOING 8 +8+8+8+8+8+8+8+8+8+8+8 or 8x12!
This is actually an approximation that’s convenient because coincidentally simple to do in your head. It’s an approximation that yields very close to the actual results when using the correct trigonometry of TD=R sinθ and OT=R(1-cosθ ), where theta equals the subtended angle between the two points separated by AL miles where θ=360R(AL/2π)
Now back to the approximation. 8 inches per miles squared does not mean that two miles would be 16 inches or that 1/8 of a mile would be 1 inch. 2 miles needs to be squared, so that 8”x2x2=32 (not 16). 1/8 mile would be 8” x 1/8 x 1/8, which is 1/8”, not 1”. And none of this has anything to do with how far you should see. That equation, to determine obstructed distance, “y”, is y=R/cos⌊ch/R-sin^(-1)(√(H(2R+H))/(R+H)) ⌋ -R
but 8” per mile squared results in a parabola that fits very snuggly onto the graph of a sphere of radius 3959 miles and understates this amount by an insignificant amount for short distances, and gets closer, and then crosses over and begins to overstate the actual result by the time you get to 500 miles…(by 0.11% at 500 miles) So that implies there’s an arc distance between two points where this approximation is dead on. This can be solved by the equation 8/〖AL〗^2 =R(1-cosθ ) and restated as
8/〖AL〗^2 =R(1-cos〖360R(AL/2π) 〗 )…solve for AL (arc length) and the answer is it’s a perfect match at about 217.95 miles.
The percentage of error between the 8” approximation and the actual theoretical results with accurate one first and 8” method in the third column and the error in the fourth. First col is arc length distance.
1 mile 0.6668 feet 0.666… -0.03%
5 16.6708 16.666 -0.03%
10 66.6834 66.666.. -0.03%
50 1667.065 1666.66… -0.02%
100 6667.99 6666.666 -0.02%
500 166487 166666 +0.11%
1000 663297 666666 +0.51%
see how hard bullshit is ! whats wrong with simply miles times 8 in squared?
kenneth caron This is curvature defiend for any random shape not the Earth itself
It's called 8 inch per mile squared and it doesn't work for spheres, since it's an equation for parabolas