Ellipses Mega Review: ua-cam.com/video/_BuUMQAFWmI/v-deo.html Hyperbolas Full Review: ua-cam.com/video/aBednvA7rSY/v-deo.html Parabolas Full Review: ua-cam.com/video/7dH24WsuGsM/v-deo.html Conic Sections Quiz: ua-cam.com/video/vqZO_CrEdPs/v-deo.html Next Video: ua-cam.com/video/Iu-4-fizlD4/v-deo.html
Professor Organic Chemistry Tutor, thank you for a powerful analysis of the Circumference of an Ellipse in Calculus Two. The integrals in this video are difficult to evaluate in closed form. These integrals are known as Elliptic Integrals. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
here is another integral to calculate the circumference of an ellipse i found using the arc length formula: 2(integral from -a to a of sqrt(1+(b^2x^2)/(a^4-a^2x^2))dx) an alternate form is 4 times the same integral but from 0 to a
A few years back I figured out an easy calculation to use in a pinch that is about 98-99% accurate. Assume "a" is the longer axis, "b" is the shorter axis. Axis being the radius distance from the center. For ellipses with an a/b ratio up to around 5/1, use Perimeter = [(3.7a/b)+2.4]b. If you get into more extreme ellipses, for an a/b ratio up to 10/1, use P = [(3.84a/b)+2]b. For a/b ratio up to 15/1, use P = [(3.9a/b)+1.7]b. For up to 20/1, P = [(3.93a/b)+1.55]b. You can also use a polynomial function (for whatever crazy reason). For a/b ratios up to around 5/1 try, P = [(0.072a/b)^2 + 3.26a/b + 2.93]b. For a/b ratios up to 20/1, try P = [(0.007a/b)^2 + 3.78a/b + 2.1]b.
a better form of the ellipse equation is: f(x)=y=b*sqrt(1-x^2), where b is the ratio b:a when a=1, a=b=1 when circle, so you get to substitute the circle (1/4) perimeter when b=1, which is (1/2)*pi (times r), which implies that the general 2d ellipse perimeter is 2*pi*r*b
_This is a Cross-Post._ I actually discovered *4(a + b) - ln(4a + 1)* at ~10AM on 08/04/2021 as my own Approximation! It only ever reaches 1.6813% (-When b = 1) error and eventually approaches 0.0297% error.
@@chickencyanide9964: It actually approaches 0% (correction 1 year later). I took the derivative of an ellipse function. An approximation of that happened to contain an x⁻¹ term.
23:32 how should i integrate that function? Can you please help me with that!! None of the online integral calculators seem to give me the result of integral :(
16:43 ... Hey, I just found a minor mistake. For ellipses, x should be acosθ, y should be bsinθ. You actually used x=asinθ to calculate the limits of the integration for θ.
23:27 "So this..." - then you extend the square root right over d(theta). So wrong on many levels. Also, you may confuse some with your double use of c, one being a^2-b^2, the other being the circumference. But then, your video is so nerdy that mainly only nerds and geeks will watch it, and they will know exactly what you meant.
Ellipses Mega Review: ua-cam.com/video/_BuUMQAFWmI/v-deo.html
Hyperbolas Full Review: ua-cam.com/video/aBednvA7rSY/v-deo.html
Parabolas Full Review: ua-cam.com/video/7dH24WsuGsM/v-deo.html
Conic Sections Quiz: ua-cam.com/video/vqZO_CrEdPs/v-deo.html
Next Video: ua-cam.com/video/Iu-4-fizlD4/v-deo.html
Professor Organic Chemistry Tutor, thank you for a powerful analysis of the Circumference of an Ellipse in Calculus Two. The integrals in this video are difficult to evaluate in closed form. These integrals are known as Elliptic Integrals. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
here is another integral to calculate the circumference of an ellipse i found using the arc length formula:
2(integral from -a to a of sqrt(1+(b^2x^2)/(a^4-a^2x^2))dx)
an alternate form is 4 times the same integral but from 0 to a
Can you give a short explanation of why the shortcuts work in approximations please?
A few years back I figured out an easy calculation to use in a pinch that is about 98-99% accurate. Assume "a" is the longer axis, "b" is the shorter axis. Axis being the radius distance from the center. For ellipses with an a/b ratio up to around 5/1, use Perimeter = [(3.7a/b)+2.4]b.
If you get into more extreme ellipses, for an a/b ratio up to 10/1, use P = [(3.84a/b)+2]b. For a/b ratio up to 15/1, use P = [(3.9a/b)+1.7]b. For up to 20/1, P = [(3.93a/b)+1.55]b.
You can also use a polynomial function (for whatever crazy reason). For a/b ratios up to around 5/1 try, P = [(0.072a/b)^2 + 3.26a/b + 2.93]b. For a/b ratios up to 20/1, try P = [(0.007a/b)^2 + 3.78a/b + 2.1]b.
Thank you very much for your awesome instruction, prof. I appreciate it.
a better form of the ellipse equation is: f(x)=y=b*sqrt(1-x^2), where b is the ratio b:a when a=1, a=b=1 when circle, so you get to substitute the circle (1/4) perimeter when b=1, which is (1/2)*pi (times r), which implies that the general 2d ellipse perimeter is 2*pi*r*b
this approach relies on the line integral from 0-1 of sqrt(1-x^2) being (1/2)*pi, or (1/4) of perimeter of the circle
_This is a Cross-Post._
I actually discovered *4(a + b) - ln(4a + 1)* at ~10AM on 08/04/2021 as my own Approximation! It only ever reaches 1.6813% (-When b = 1) error and eventually approaches 0.0297% error.
I found a more general Approximation of *4(a + b) - ln(4a/b + 1)b.* It always maxes at only 1.6813% error.
what was ur method?
@@chickencyanide9964: It actually approaches 0% (correction 1 year later). I took the derivative of an ellipse function. An approximation of that happened to contain an x⁻¹ term.
can you please do a video on series for calculus?
23:32 how should i integrate that function?
Can you please help me with that!! None of the online integral calculators seem to give me the result of integral :(
It is not possible to integrate it with elementary functions as far as i know
@@bjarkehammerbakpaluszewski6219 ye you need non elementary funnctions, that is the elliptic integral.
unless e=1, in which case you get a circle, there is no closed form for that integral.
@@natevanderw e=1 is a parabola
@@natevanderw but ya got ur point
16:43 ... Hey, I just found a minor mistake. For ellipses, x should be acosθ, y should be bsinθ. You actually used x=asinθ to calculate the limits of the integration for θ.
you're right but it will still work because of symmetry
What if you have a quarter of the ellipse?
whats the d(theta) for?
Thank u so much..may allah bless you😊
Curvature and circumference relationship in oval shaped
i imputed in an online calculator and it said it cant be solved :(
try Wolfram Alpha
2:04 ... and ya lost me. Someday it’ll make sense 😞
That days is the next day after you have finished a calculus course. Which part confused you?
He is using first parametrizing and then using arc length formula. It is not explained well at all. I would not feel bad.
Can you finish the integral ?
you can't do it with elementary functions
Circumference of an ellipse is very very hard...
23:27 "So this..." - then you extend the square root right over d(theta). So wrong on many levels.
Also, you may confuse some with your double use of c, one being a^2-b^2, the other being the circumference.
But then, your video is so nerdy that mainly only nerds and geeks will watch it, and they will know exactly what you meant.
What a JOKE!... You FAILED to solve for the definite integral!
it's not possible to evaluate that integral with elementary functions
Homie see an integral symbol and assumes it’s incomplete 🤡
Try to do it!
Are you 13 years old?