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Thread: Completely pointless math facts

20190331, 01:41 AM (ISO 8601)
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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.
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20190331, 02:41 AM (ISO 8601)
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Re: Completely pointless math facts
Um, what is FF here?

20190331, 02:44 AM (ISO 8601)
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20190331, 07:56 AM (ISO 8601)
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Re: Completely pointless math facts

20190331, 11:34 AM (ISO 8601)
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Re: Completely pointless math facts
I have a LOT of Homebrew!
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20190331, 04:00 PM (ISO 8601)
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Re: Completely pointless math facts
e^{𝜋}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.
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20190331, 07:12 PM (ISO 8601)
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Re: Completely pointless math facts
i to the power of i is a real number.
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20190331, 08:37 PM (ISO 8601)
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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.If you need me to address something as a moderator, please include a link.
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20190331, 08:48 PM (ISO 8601)
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Re: Completely pointless math facts
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20190331, 09:05 PM (ISO 8601)
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20190331, 09:12 PM (ISO 8601)
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Re: Completely pointless math facts
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20190331, 10:08 PM (ISO 8601)
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20190331, 10:33 PM (ISO 8601)
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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 threedigit 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.Last edited by Peelee; 20190331 at 10:34 PM.
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20190401, 01:22 AM (ISO 8601)
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20190401, 03:17 AM (ISO 8601)
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Re: Completely pointless math facts

20190401, 06:36 AM (ISO 8601)
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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(10y27a)
851 = 37(5027) = 37*23
So for this to work y must be greater (or equal to) 3 times a. (edit3 : since 10y27a => 0 <=>y => 27/10 *a)
EDIT:
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.Last edited by Fyraltari; 20190401 at 06:59 AM.
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20190401, 07:58 AM (ISO 8601)
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Re: Completely pointless math facts
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20190401, 08:49 AM (ISO 8601)
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Re: Completely pointless math facts
"Any technology distinguishable from magic is insufficiently advanced."
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20190401, 11:14 AM (ISO 8601)
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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!

20190401, 11:41 AM (ISO 8601)
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Re: Completely pointless math facts
Thank you! substituting 10b+c isn't actually needed as the important part is realizing that moving the first digit around means y = 10(x100a) + 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).
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.
I probably will too.Last edited by Fyraltari; 20190401 at 11:41 AM.
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20190401, 12:09 PM (ISO 8601)
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20190401, 02:05 PM (ISO 8601)
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20190401, 02:52 PM (ISO 8601)
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Re: Completely pointless math facts
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20190401, 03:09 PM (ISO 8601)
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Re: Completely pointless math facts
The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

20190401, 03:19 PM (ISO 8601)
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Re: Completely pointless math facts
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.The Mod on the Silver Mountain avatars by the wonderfully talented Cuthalion!
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20190401, 03:40 PM (ISO 8601)
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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."Any technology distinguishable from magic is insufficiently advanced."
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20190401, 03:47 PM (ISO 8601)
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Re: Completely pointless math facts
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.

20190401, 03:55 PM (ISO 8601)
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20190401, 06:09 PM (ISO 8601)
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Re: Completely pointless math facts
Also the proof was actually (and explicitly) for all nonmultiples of 2 and 3. But that would be boring and give away the trick.
And from X being coprime with 2 and coprime 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. 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 oddprime, and of course odd, non three prime.gives away the pleading.Spoiler: at 100 it's 23 primes to 7 compositesby 1000 there are 166 primes out of 333 and by 5000 it's 667 out of 1666
Anyhow for my fact
60*60*24*365 is within 1% of pi*10^{7} or sqrt(10)*10^{7}. Allowing a moderate compromise between order of magnitude and accurate numbers for anything involving years.

20190402, 01:20 AM (ISO 8601)
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