At the 23:40 mark the term on the RHS is pi²/8 not pi²/2, reason for the mess up being that I forgot the factor of 4 at the 21:07 mark. Though I'm quite surprised that it took over 12 hours for anyone to point this out proving that mathematicians are terrible with numbers other than pi, e, 1, 0, 69 and 420
I pooped my pants thinking this double integral will take half an hour of evaluation, thankfullly I don't have to retake calculus 3 now lol (honestly, calc 3 is the funnest of all cacli). This was one of the greatest integrals I ever seen btw. we should do a series were math peeps comment on football games, apply math to football strategies and stuff (smelling some graph theory up in here).
@ 23:30 I believe you meant to say that the sum of the reciprocals of the squares is pi^2/6. However, you are correct that subtracting the sum of the reciprocals of the even squares from the sum of the reciprocals of all the squares gives the sum of the reciprocals of the odd squares. Furthermore, the sum of the reciprocals of all the squares minus the sum of the reciprocals of the even squares is equal to (1-1/4)*pi^2/6=pi^2/8, making the final answer to our problem pi^2/2.
Really cool result! What are your thoughts on the Champion's League final on Saturday? My money is on City, because they are an unstoppable juggernaut (has science gone too far?). I will root for Inter tho
3:09 Why when we do these kinds of substitution as we solve integrals, we disregard the fact that the square root of x^2 is not x, but absolute value of x?
Hello @maths505 ...... I like your content a lot. I wish you all the best..... I have a few suggestions for u as a sincere viewer that you should improve the handwriting a little bit, and be little more enthusiastic about the content. You will be happy to know that I am also a maths teacher. So I have few questions that I want you to make a video on those questions...... I will be very thankful to hear from you. Thank you.
I'm afraid it's too late to improve my handwriting 😂😂😂 And honestly this is as enthusiastic as I can possibly be🤣🤣🤣 Nd sure you can DM me on Instagram (just fixed the link)
At the 23:40 mark the term on the RHS is pi²/8 not pi²/2, reason for the mess up being that I forgot the factor of 4 at the 21:07 mark.
Though I'm quite surprised that it took over 12 hours for anyone to point this out proving that mathematicians are terrible with numbers other than pi, e, 1, 0, 69 and 420
Math and Football ⚽ are beautiful.
Ok this has to be my favorite solution of the Basel problem
I pooped my pants thinking this double integral will take half an hour of evaluation, thankfullly I don't have to retake calculus 3 now lol (honestly, calc 3 is the funnest of all cacli).
This was one of the greatest integrals I ever seen btw.
we should do a series were math peeps comment on football games, apply math to football strategies and stuff (smelling some graph theory up in here).
Something something topologically, bowling and football are equivalent
@ 23:30 I believe you meant to say that the sum of the reciprocals of the squares is pi^2/6. However, you are correct that subtracting the sum of the reciprocals of the even squares from the sum of the reciprocals of all the squares gives the sum of the reciprocals of the odd squares. Furthermore, the sum of the reciprocals of all the squares minus the sum of the reciprocals of the even squares is equal to (1-1/4)*pi^2/6=pi^2/8, making the final answer to our problem pi^2/2.
the sum of the reciprocals of the odd squares is pi²/8. And by the way your handwriting is fine.
We can compute I_{x} with one substitution
sqrt(1-x^2)=xu - 1
but if we want to get back original interval we should use second substitution u=1/w
At 23:40 when multiplying both side of 4/3
R.H=(2 π^2) /3
not π^2 /6
Yeah that was actually a pi/8 multiplied by 4/3
@@maths_505 Yeah i think you forgot about the -4 when you switched the integration and the sigma operator
Really cool result! What are your thoughts on the Champion's League final on Saturday? My money is on City, because they are an unstoppable juggernaut (has science gone too far?). I will root for Inter tho
I'm a sucker for an underdog story so inter
3:09 Why when we do these kinds of substitution as we solve integrals, we disregard the fact that the square root of x^2 is not x, but absolute value of x?
That equals x when x lies between zero and 1 which is the case we have
@@maths_505 Right, but people disregard the absolute value even when doing indefinite integrals!
@@Mephisto707 well I don't so I'm gonna have to interrogate people about this 😂
The end result is a famous formula of Euler by a different method - the Basel problem!
nice question
Damn amazing
yellow is ok
Hello @maths505 ...... I like your content a lot. I wish you all the best..... I have a few suggestions for u as a sincere viewer that you should improve the handwriting a little bit, and be little more enthusiastic about the content. You will be happy to know that I am also a maths teacher. So I have few questions that I want you to make a video on those questions...... I will be very thankful to hear from you. Thank you.
I'm afraid it's too late to improve my handwriting 😂😂😂
And honestly this is as enthusiastic as I can possibly be🤣🤣🤣
Nd sure you can DM me on Instagram (just fixed the link)