A while 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.
I don't bother with all this math, I simply take a waist tape measure and measure the ellipse. 😎. I began watching many educational videos of ellipses when I wanted to know the minor or major axis with just knowing the perimeter.
@@ProfJeffreyChasnov Pi is aproximated by 3.14... and that allows us to calculate numeric. The ellipse perimeter also has an infinite expansion, that allows for calculation to any desired approximation.
@@johnnisshansen I agree. What I want to say is that there is no simple formula for the perimeter in terms of a and b comparable to 2 pi r for the circle. We can't just introduce a new constant.
Hey Jeff, I loved you video on calculating the perimeter of an ellipse. I believe I have discovered a new way. Can I share it with you? If so, can I get your email? Kevin
I'm impressed how well you can write right-to-left behind the glass so that we see things normally left-to-right!
No, he just flips the video horizontally in post-production :)
@@Corcoancaoc lmao
I remember when teachers would write backwards on the early, mirrored overhead projectors. Pretty wild.
My man, you deserve the WORLD. You saved me from my calculus test today. You got a sub man and I'm here to stay
A while 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.
In the derivation at 6:22 time mark there is a floating open parenthesis without a matching close parenthesis.
Thanks! I can fix it on Coursera. RUclips cannot.
@@ProfJeffreyChasnovcould you please show me how to integrate P = integral sqrt((1-(e^2)*cos^2(theta)*d(theta) at the end of video? Thanks a lot 😊
@@Jihad_Bankai You can integrate that by applying the taylor expansion for root(1-x^2)
Thank You Professor
I actually followed along really well here surprisingly! Nice explanation and creative techniques!
It's awesome thank you.
Why are the parameters from 0 to π/2?
You only have to compute a quarter of the way around due to symmetry, as the ellipse has four segments of equal length.
2:07
Thanks a lot professor
2 pi r is not a closed Form. Pi is defined as U/d
Nonsense!
I don't bother with all this math, I simply take a waist tape measure and measure the ellipse. 😎.
I began watching many educational videos of ellipses when I wanted to know the minor or major axis with just knowing the perimeter.
*math intensifies*
You did not show how to calculate the P of an ellipse. Just how the basic machinery stalled.
That's it! The rest is approximations or numerics.
@@ProfJeffreyChasnov Pi is aproximated by 3.14... and that allows us to calculate numeric.
The ellipse perimeter also has an infinite expansion, that allows for calculation to any desired approximation.
@@johnnisshansen I agree. What I want to say is that there is no simple formula for the perimeter in terms of a and b comparable to 2 pi r for the circle. We can't just introduce a new constant.
@@ProfJeffreyChasnov we could find Taylor series for a function pi(x) 0
@@johnnisshansen The constant depends on the eccentricity of the ellipse?
I saw you on breaking bad
yeah, his middle name is Heisenberg.
Weathermen of the 80s got NOTHING on you.
Let's take a minute to appreciate how this man pushed himself out of his comfort zone and learned to write right to left for only teaching purposes 🙏
lmfao he inverted it horizontally
@@GammaFZ he did the entire equation horizontally backwards? absolutely stunning mathsmetician
Hey Jeff, I loved you video on calculating the perimeter of an ellipse. I believe I have discovered a new way. Can I share it with you? If so, can I get your email? Kevin