# Thread: Completely pointless math facts

1. ## Completely pointless math facts

If you have a timer that, for some reason, can be set for FF:DD:hh:mm:ss with no error checking, you can set it for up to 1368715689 seconds by using only nines. This is somewhere between 43 and 44 years, but I can't convert it to YY:MM:DD:hh:mm:ss time because Wolframalpha insists on rounding prematurely.

2. ## Re: Completely pointless math facts

Um, what is FF here?

3. ## Re: Completely pointless math facts

Originally Posted by factotum
Um, what is FF here?
Fortnight Fortnight

4. ## Re: Completely pointless math facts

Originally Posted by enderlord99
If you have a timer that, for some reason, can be set for FF:DD:hh:mm:ss with no error checking, you can set it for up to 1368715689 seconds by using only nines. This is somewhere between 43 and 44 years, but I can't convert it to YY:MM:DD:hh:mm:ss time because Wolframalpha insists on rounding prematurely.
I don't know what standard you use for dividing out the months, but skipping months I get 43 years, 146 days, 14 hours, 48 minutes, and 9 seconds. That's if I use exactly 365 days per year with no leap days or leap seconds, though.

5. ## Re: Completely pointless math facts

Originally Posted by enderlord99
If you have a timer that, for some reason, can be set for FF:DD:hh:mm:ss with no error checking, you can set it for up to 1368715689 seconds by using only nines. This is somewhere between 43 and 44 years, but I can't convert it to YY:MM:DD:hh:mm:ss time because Wolframalpha insists on rounding prematurely.
I appreciate this utterly useless fact. :P

Unfortunately, I don't have any to share myself.

6. ## Re: Completely pointless math facts

e𝜋-𝜋 is extremely close to 20. So close, in fact, that 6 of its first 7 digits past the decimal point are 9. And the one digit that isn't 9 is actually not at the end of those 7 - it's a 0 right in the middle instead.

19.99909997919...

7. ## Re: Completely pointless math facts

i to the power of i is a real number.

8. ## Re: Completely pointless math facts

There's a great SMBC comic about someone asking his partner to speak 'mathy' to him in a sexy way, that culminates with him declaring she's a "mathy, mathy girl" that's always made me laugh, and would be the perfect compliment to this thread.

But it's JUST explicitly sexual enough that I don't want to link it.

But, suffice it say, you're all mathy, mathy playgrounders.

9. ## Re: Completely pointless math facts

Originally Posted by truemane
There's a great SMBC comic about someone asking his partner to speak 'mathy' to him in a sexy way, that culminates with him declaring she's a "mathy, mathy girl" that's always made me laugh, and would be the perfect compliment to this thread.

But it's JUST explicitly sexual enough that I don't want to link it.

But, suffice it say, you're all mathy, mathy playgrounders.
Funny, my first thought was the SMBC comic about math transactions that ended with the harmonic sequence.

10. ## Re: Completely pointless math facts

Originally Posted by enderlord99
If you have a timer that, for some reason, can be set for FF:DD:hh:mm:ss with no error checking, you can set it for up to 1368715689 seconds by using only nines. This is somewhere between 43 and 44 years, but I can't convert it to YY:MM:DD:hh:mm:ss time because Wolframalpha insists on rounding prematurely.
To be fair, no one likes a premature rounder.

12. ## Re: Completely pointless math facts

Originally Posted by Grey_Wolf_c
Except 2 and 3.

13. ## Re: Completely pointless math facts

Oh, I'd forgotten about the 37 tricks for a long time.

A.) any single digit number multiplied by 3, then by 37, will give a product of the original number three times. Eg (5)(3)(37)=555, or (9)(3)(37)=999. The double digits also kinda work this way but you dont want to read me describe it.

2.) if you multiply by anything that gives a three-digit product, then move the first digit of the product to the back of the product, the resulting number is evenly divisible by 37. Eg (5)(37) = 185. 851/37 = 23, or (11)(37) = 407. 74/37 = 2. Or (15)(37) = 555. 555/37 = 15. If you want to be cheeky about it.

14. ## Re: Completely pointless math facts

Originally Posted by Peelee
A.) any single digit number multiplied by 3, then by 37, will give a product of the original number three times. Eg (5)(3)(37)=555, or (9)(3)(37)=999.
Er, yes, because multiplying by 3 and then 37 is the same as multiplying by 111? It would be rather more obvious if you just said any single digit number multiplied by 111 gives three times the original number.

15. ## Re: Completely pointless math facts

Originally Posted by Peelee
Oh, I'd forgotten about the 37 tricks for a long time.

A.) any single digit number multiplied by 3, then by 37, will give a product of the original number three times. Eg (5)(3)(37)=555, or (9)(3)(37)=999. The double digits also kinda work this way but you dont want to read me describe it.

2.) if you multiply by anything that gives a three-digit product, then move the first digit of the product to the back of the product, the resulting number is evenly divisible by 37. Eg (5)(37) = 185. 851/37 = 23, or (11)(37) = 407. 74/37 = 2. Or (15)(37) = 555. 555/37 = 15. If you want to be cheeky about it.
The first factotum already debunked (explained) but the second is a neater trick. I'm curious if there is a way to prove it.. And why it only works for three digits but I can't answer off the top of my head.

16. ## Re: Completely pointless math facts

I've got it.

So we have x = 37y where x is a three digit number, that means x = 100a + 10b + c where a, b and c are single digits (between 0 and 9 included).
(in Peelee's first example, y = 5, x = 185, a = 1, b = 8 and c = 5)
Moving the first digit to third position means creating a number z (851) where
z = 100b + 10c + a = 10(x - 100a) + a (eliminating the hundreds, moving the dozens and units up and adding the new units)
z = 10x - 1000a + a
z = 10x - 999a (is 999 a multiple of 37? Yes 27*37 = 999)
z = 10*37y - 27*37a
z = 37(10y-27a)
851 = 37(50-27) = 37*23

So for this to work y must be greater (or equal to) 3 times a. (edit3 : since 10y-27a => 0 <=>y => 27/10 *a)

EDIT:
Originally Posted by Grey_Wolf_c
Oooh, that's a nice one.

EDIT the return:
37*2 = 74, not a three digit number, 37*3 = 111 a three digit number, so for x to have three digits y must be between 3 and 27.

EDIT the trilogy:
37y = 100a + 10b + c
y = (100/37)a + (10/37)b + (1/37)c
100/37 = 2,7027... > 2 so in order for x to have three digits, y must be greater than 3 times a (3 included).

There. Proved.

I now await the easier, more beautiful proof.

17. ## Re: Completely pointless math facts

Originally Posted by factotum
Er, yes, because multiplying by 3 and then 37 is the same as multiplying by 111? It would be rather more obvious if you just said any single digit number multiplied by 111 gives three times the original number.
I am not a smart man. Also, I haven't looked at that since grade school, so blah.
Originally Posted by Fyraltari
I now await the easier, more beautiful proof.

18. ## Re: Completely pointless math facts

Originally Posted by Peelee
Spoiler: My years in math Classes Préparatoires in a nutshell

19. ## Re: Completely pointless math facts

Ah, nicely done! I didn't think of substituting the 10b+c which is really stupid in hindsight.

So the trick boils down to... 37 being a divisor of 999? Which means it should also work for only 3 (obviously), 9 (also) and 27 (less boring).
I think I'll remember that trick, thanks!

20. ## Re: Completely pointless math facts

Originally Posted by Kato
Ah, nicely done! I didn't think of substituting the 10b+c which is really stupid in hindsight.
Thank you! substituting 10b+c isn't actually needed as the important part is realizing that moving the first digit around means y = 10(x-100a) + a. I didn't streamline my reasoning before posting (as is evident by my multiple edits ) and I started with decomposing the numbers into multiples of ten which is always a good idea when there's digit manipulation (in base ten).

Originally Posted by Kato
So the trick boils down to... 37 being a divisor of 999? Which means it should also work for only 3 (obviously), 9 (also) and 27 (less boring).
In order for it to work with 27, y needs to be greater than (or equal to) 3.7 times a (37/10 = 3.7) for every x in the hundreds.
27y = 100a + u <=> y = (100/27)a + u/27
100/27 = 3.70370... so it should work. Not sure about 9 and 3, though.

Originally Posted by Kato
I think I'll remember that trick, thanks!
I probably will too.

21. ## Re: Completely pointless math facts

Originally Posted by Fyraltari
i to the power of i is a real number.
... is it? The complex number is eiπ/2. So ii = ei^2π/2 = e-π/2.

Okay, so it is.

22. ## Re: Completely pointless math facts

Originally Posted by Douglas
Except 2 and 3.
Yes. These are primes. A pattern that doesn't include them is not a pattern for all primes.

23. ## Re: Completely pointless math facts

Originally Posted by halfeye
Yes. These are primes. A pattern that doesn't include them is not a pattern for all primes.
The actual mathematician in the video calls them subprimes. I'll take their word over yours, random internet person.

Grey Wolf

24. ## Re: Completely pointless math facts

Originally Posted by Grey_Wolf_c
The actual mathematician in the video calls them subprimes. I'll take their word over yours, random internet person.

Grey Wolf
Yeah, I'm a random internet person, so is the person in the video. The definition of prime numbers is what it is, look it up sometime.

25. ## Re: Completely pointless math facts

Originally Posted by Grey_Wolf_c
The actual mathematician in the video calls them subprimes. I'll take their word over yours, random internet person.

Grey Wolf
Counterpoint: it seems the mathematician in the video is defining primes based on the them having a value of one more than a multiple of 24 after being squared in addition to the other requirements. Which, after a few quick and dirty Google searches, does not seem to be a standardized definition at all.

That said, I'm not a mathematician, and dude could be using a known definition I didn't uncover.

26. ## Re: Completely pointless math facts

A prime number by definition is an integer that is multiple of only two* integers 1 and itself. By that definition 2 and 3 are primes.

1 has been excluded from the primes because it doesn't share the most useful properties of the other primes, most importantly that every integer can be written as a unique product of primes. So it was either getting 1 off the list or adding "except 1" to the primes' properties. I don't know of any reason not to consider 2 and 3 primes and I would like to hear that person's argument for it.

27. ## Re: Completely pointless math facts

Originally Posted by Grey_Wolf_c
The actual mathematician in the video calls them subprimes. I'll take their word over yours, random internet person.

Grey Wolf
I mean, it was a joke. Cause, like, subprime mortgages or whatever. The thing being proved was just that primes over three have this quality. Mathematicians do things like that sometimes, proving claims only with regard to almost all elements of a set, rather than all of them. The people in the video know that two and three are not prime.

28. ## Re: Completely pointless math facts

Originally Posted by eggynack
The people in the video know that two and three are not prime.

29. ## Re: Completely pointless math facts

Originally Posted by eggynack
I mean, it was a joke. Cause, like, subprime mortgages or whatever. The thing being proved was just that primes over three have this quality. Mathematicians do things like that sometimes, proving claims only with regard to almost all elements of a set, rather than all of them. The people in the video know that two and three are not prime.
Also the proof was actually (and explicitly) for all non-multiples of 2 and 3. But that would be boring and give away the trick.
And from X being co-prime with 2 and co-prime with 3 to generally prime seems a nice way of doing it. You've only lost composites of higher primes, so 25, 35, 49... so for a region it nearly works both ways
Spoiler: at 100 it's 23 primes to 7 composites
by 1000 there are 166 primes out of 333 and by 5000 it's 667 out of 1666
. But now you need weasel words for excluding 2&3) IIRC correctly 2 kind of gets this a fair bit, but it's so easy to say odd-prime, and of course odd, non three prime.gives away the pleading.

Anyhow for my fact
60*60*24*365 is within 1% of pi*107 or sqrt(10)*107. Allowing a moderate compromise between order of magnitude and accurate numbers for anything involving years.

30. ## Re: Completely pointless math facts

Originally Posted by Rockphed
... is it? The complex number is eiπ/2. So ii = ei^2π/2 = e-π/2.

Okay, so it is.
But all real numbers are just a sub-set of complex numbers anyway...

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