Jeremy Vine asked for help with his 14 y/o’s maths homework and the internet exploded
13.
This is a great question; it’s extremely relevant for applications in science, engineering and coding. For example, it shows how slow a particular computer application will run as it gets more information. Or if a calculator will slow down when you give it more digits
— Claire Edmunds (@EdmundsClaire) November 17, 2018
14.
Part of the trick is the “square”. Our brains are very good at “linear thinking”, which means if the number of digits is doubled, we expect the time taken to simply double as well.
Here, time grows quadratically (as a square of the number of digits). This is faster than we intuit— Claire Edmunds (@EdmundsClaire) November 17, 2018
15.
The sort of equation this uses is a parabola, which looks like :
t = a * n^2
where t is the time taken in seconds, n is the number of digits, ^2 means squaring the number (multiply is by itself), and a is just some constant number— Claire Edmunds (@EdmundsClaire) November 17, 2018
16.
You can pick “n” to be anything (e.g. 5000 or 1 million). You usually want to solve want “t” is. The only missing piece is the constant “a”.
“a” will be the same for all values of “n”. It’s an inherent part of how the computer program solves the problem— Claire Edmunds (@EdmundsClaire) November 17, 2018
17.
This means if you find “a” for some value of “n”, it will be true for all “n”. Because you know 5000 digits takes 0.5 sec, you can solve :
0.5 = a * 5000^2
a = 0.00000002
(or 2 * 10^-8)So now you can find the time for any number of digits!
t = 2 * 10^-8 * n^2— Claire Edmunds (@EdmundsClaire) November 17, 2018
18.
I love all the answers of the kind “when would this ever be useful in real life?”. I genuinely love them. My kids said this to me. Once.
Having a brain that’s taught to understand abstract concepts like algebra, to problem solve, to embrace/enjoy a challenge? That’s huge in life!— Jim (@jimbimcok) November 17, 2018
19.
time = constant x number squared, ie
t = k(n^2)
we given that 0.5 = k(5000^2).
Calculate k— Bob Eagle (@BobEagle2) November 17, 2018
20.
A) t = n^2 / 50,000,000. B) 20,000 seconds. C) 173,205 digits pic.twitter.com/i2XcudpJvD
— Stephen Stokes (@S_J_Stokes) November 17, 2018
21.
T = k*n^2
k = T/n^2 = 0.5/5000^2 = 1/50000000
=> T=n^2/50000000
=> n = sqrt(50000000*T)Time for 1 million digits = (1000000)^2/50000000 = 20000s
Digits in 10 minutes = sqrt(50000000*10*60) = 173205 digits— the paceman (@nFoesrnghioeJ) November 17, 2018
If that still doesn’t help, then Countdown’s Rachel Riley had a go.
@theJeremyVine hope this helps 👍 pic.twitter.com/9pK8f0WzsS
— Rachel Riley (@RachelRileyRR) November 17, 2018
We’re off for a lie down.
