I was surprised to see how such an idea could strike one's mind! An absolutely elegant connection between trigonometry and cubic equations. Thanks to your method I was able to solve the other part of this problem! That one required a little bit of clever trig manipulation, but coming up to the end result was as fruitful :) Excited to pose some problems using this concept! Thankss again!
@@davidfinance Got it. I moved the minus sign inside the cube root. Hopefully I did so correctly. In retrospect, I could have been clearer on this point.
I like your method, but it is quite a “special” case because the polinomial yield a low degree and the polinomial itself can be easily solved. I actually more curious the other way around because it seems a lot harder, how to come up with that kind of trigonometric question that has a “beautiful” answer?
I usually don't leave comments, but this video deserves it. Awesome explanation and short history lessons! To the algorithm!
Ramanujan was brilliant! Also, great video; I'm happy to have learned this technique of finding polynomials with relations between the roots.
I was surprised to see how such an idea could strike one's mind! An absolutely elegant connection between trigonometry and cubic equations. Thanks to your method I was able to solve the other part of this problem! That one required a little bit of clever trig manipulation, but coming up to the end result was as fruitful :)
Excited to pose some problems using this concept! Thankss again!
Thank you! I'm glad to hear that you solved the other part of Ramanujan's problem!
Muito interessante. Congratulations for the solve this trigonometric expression. From the Brazil
Amazing. Good job and thanks.
How wonderful, congratulations
Wonderful video! This was very fun to follow along and watch. Please make more content like this. Learned something new :)
Good!
Awesome video, as usual. What happened to the minus sign at 16:39?
Thanks, David! Can you give the time code again? The one you gave seems to be at the last second of the video.
@@BoppanaMathsorry it was 15:31.
@@davidfinance Got it. I moved the minus sign inside the cube root. Hopefully I did so correctly. In retrospect, I could have been clearer on this point.
@@BoppanaMathohhhh got it. Cool. Thanks for explaining!
I like your method, but it is quite a “special” case because the polinomial yield a low degree and the polinomial itself can be easily solved. I actually more curious the other way around because it seems a lot harder, how to come up with that kind of trigonometric question that has a “beautiful” answer?
That man is from another dimention
it's spelt as dimension
PRONUNCIATION ROMANUGIN 💀
what is the answer of the last problem?2/7pi is really unfriendly.
how to prove?
Hint: can you evaluate cos(2 pi/7) + cos(4 pi/7) + cos(6 pi/7)?
@@BoppanaMath Haha,I forgot actually 8pi/7=6pi/7.But why this expression=-1/2?
@@波神cr Second hint: What do the seven 7th roots of unity add up to?