(Lengthy-time followers will keep in mind that I beforehand lined this matter. I’ve ready a brand new video with a barely totally different presentation and a distinct historic perspective. Because of Elto for sending me the same drawback that was posted in a restaurant in Canada.)
In 2018, college students in China on the Nanjing College of Aeronautics and Astronautics, noticed an uncommon sign up a eating corridor. They needed to resolve the next integral to be able to hook up with the WiFi:
You’ll be able to’t use the web (as you are attempting to determine the WiFi password), and I believe the spirit of the issue is to resolve solely utilizing pencil and paper with out a calculator.
The primary 8 digits of the reply are the WiFi password. Can you work it out? Watch the video for an answer.
Clear up a Math Drawback For WiFi!
0:00 drawback
1:22 resolution
6:36 historical past
Or preserve studying.
Enjoyable truth!
Round 480, Zu Chongzhi calculated pi was roughly 355/113, which is correct to six decimal locations. And he additionally calculate pi precisely to 7 decimal locations utilizing an space methodology of inscribed and circumscribed polygons (the tactic was developed by Liu Hui, and is in distinction to Archimedes who used the perimeter of the polygons). Zu’s calculation was the world’s most correct worth for pi for over 1000 years.
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Reply To College students In China: Clear up This Integral For The WiFi Password
(Just about all posts are transcribed rapidly after I make the movies for them–please let me know if there are any typos/errors and I’ll right them, thanks).
The issue is instantly solvable with a number of methods. First, distribute the phrases in parentheses, after which deal with the integral of x3 cos (x/2) √(4 – x2). We are able to present this complete integral is the same as 0.
It’s because
x3 is an odd operate
cos (x/2) is a good operate
√(4 – x2) is a good operate
The product of an odd operate and a good operate is an odd operate, so the product of those three features is an odd operate. Moreover, the integral of an odd operate over a symmetric interval [-a, a] is the same as 0. Therefore, this integral is the same as 0.
Now we deal with the integral of (1/2) √(4 – x2) from -2 to 2.
The integral of √(4 – x2) from -2 to 2 is the world of a semi-circle, and we would like half of that. So the integral evaluates to:
(1/2)(1/2)π(2)2 = π
So your complete integral evaluates to π. However now how can we keep in mind the primary 8 digits of π?
One trick is to recollect a sentence the place the variety of letters in every phrase offers the digits of pi. One such sentence is:
How I want I might calculate pi simply at this time
The variety of letters in every phrase is
3 Can
1 I
4 have
1 a
5 giant
9 container
2 of
6 espresso
The password is the primary 8 digits, which is 31415926.
It’s a fairly neat drawback to encourage college students to observe math even whereas they’re within the eating corridor!
Sources
Beijing Information (Chinese language)
http://tech.ifeng.com/a/20180907/45156013_0.shtml
Chronology of computation of π
https://en.wikipedia.org/wiki/Chronology_of_computation_of_percentCFpercent80
https://en.wikipedia.org/wiki/Zu_Chongzhi
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