(Long-time followers will remember that I previously covered this topic. I have prepared a new video with a slightly different presentation and a different historical perspective. Thanks to Elto for sending me a similar problem that was posted in a restaurant in Canada.)
In 2018, students in China at the Nanjing University of Aeronautics and Astronautics, saw an unusual sign in a dining hall. They had to solve the following integral in order to connect to the WiFi:
In 2018, students in China at the Nanjing University of Aeronautics and Astronautics, saw an unusual sign in a dining hall. They had to solve the following integral in order to connect to the WiFi:
You can’t use the internet (as you are trying to figure out the WiFi password), and I think the spirit of the problem is to solve only using pencil and paper without a calculator.
The first 8 digits of the answer are the WiFi password. Can you figure it out? Watch the video for a solution.
Solve a Math Problem For WiFi!
0:00 problem 1:22 solution 6:36 history
Or keep reading.
Fun fact!
Around 480, Zu Chongzhi calculated pi was approximately 355/113, which is accurate to 6 decimal places. And he also calculate pi accurately to 7 decimal places using an area method of inscribed and circumscribed polygons (the method was developed by Liu Hui, and is in contrast to Archimedes who used the perimeter of the polygons). Zu’s calculation was the world’s most accurate value for pi for over 1000 years. . .
“All will be well if you use your mind for your decisions, and mind only your decisions.” It costs thousands of dollars to run a website and your support matters. If you like the posts and videos, please consider a monthly pledge on Patreon. You may also consider a one-time donation to support my work. . .
. . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Students In China: Solve This Integral For The WiFi Password
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
The problem is readily solvable with a few tricks. First, distribute the terms in parentheses, and then focus on the integral of x3 cos (x/2) √(4 – x2). We can show this entire integral is equal to 0.
This is because
x3 is an odd function cos (x/2) is an even function √(4 – x2) is an even function
The product of an odd function and an even function is an odd function, so the product of these three functions is an odd function. Furthermore, the integral of an odd function over a symmetric interval [-a, a] is equal to 0. Hence, this integral is equal to 0.
Now we focus on the integral of (1/2) √(4 – x2) from -2 to 2.
The integral of √(4 – x2) from -2 to 2 is the area of a semi-circle, and we want half of that. So the integral evaluates to:
(1/2)(1/2)π(2)2 = π
So the entire integral evaluates to π. But now how can we remember the first 8 digits of π?
One trick is to remember a sentence where the number of letters in each word gives the digits of pi. One such sentence is:
How I wish I could calculate pi easily today
The number of letters in each word is
3 Can 1 I 4 have 1 a 5 large 9 container 2 of 6 coffee
The password is the first 8 digits, which is 31415926.
It’s a pretty neat problem to encourage students to practice math even while they are in the dining hall!
Sources
Beijing News (Chinese) http://tech.ifeng.com/a/20180907/45156013_0.shtml
CNET https://www.cnet.com/news/wi-fi-access-only-granted-to-students-in-china-after-they-solve-a-puzzle/
Chronology of computation of π https://en.wikipedia.org/wiki/Chronology_of_computation_of_%CF%80 https://en.wikipedia.org/wiki/Zu_Chongzhi
Pi wordplay https://mathworld.wolfram.com/PiWordplay.html
PRESH TALWALKAR
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