#math stuff

[knotty-et-al]

Visualization of the Rubik's cube

[abalidoth]

Fun little math trick I find really helpful: the ratio of a mile to a kilometer is within 1% of the Golden Ratio. That means that if you have a good memory for Fibonacci numbers (1 2 3 5 8 13 21 34 55 89) you can convert pretty accurately by taking consecutive Fibonacci numbers.

For example, 89 kilometers is really close to 55 miles (55.3). Or, say you need to convert 26 miles to kilometers: 26 can be written as 21 plus 5, so taking the next Fibonacci number up gives 34 and 8, meaning it should be around 42 kilometers. Sure enough, it's 41.8 km!

[chaucers]

☆fornight of exams 1/14

~trying desperately to romanticise the most stressful time of the the season

~9 hours straight of a module i still don't quite understand

~measure theory exam tomorrow; just looking forward more to a celebratory bubble tea afterwards more than anything

[izara08]

A number generator. A random number generator. That sends out a random number. A number. From one. To infinity. But that description wouldn't be correct, as this utter mockery of the universe's laws can only spit out finite numbers. How many finite numbers? All of them. This monstrosity of a metal box can only be used once. It has never been used.

The sheer idea of this horrifying beast completely and utterly baffles me. The year is 2088. We have solved the Riemann Hypothesis. We have three odd perfect numbers. There are three numbers that don't succumb to the "unavoidable" 4-2-1 chain when faced with the Collatz Conjecture. They were the same. Three. Numbers. All of these monumental discoveries, few of many. Discovered by the most intelligent mathematician that ever lived. Me.

And despite my mental prowess, the sheer idea of this. Thing. Eludes me. This kind of machine shouldn't even be possible. Not only does it break the laws of mathematics, it breaks the laws of physics. And yet it sits in my hands. My feeble, significantly intelligent, yet mortal hands. I am holding the heart of a god. The skull of the devil. The core of the universe. The Big Bang. The Theory of Everything. And it feels. Like a dense, rusty metal cube.

What would the number spit out even be? The chance of any number at all would be that number out of. Infinity? So all and every single number would have an absolute zero chance to be chosen. Yet a number must be chosen. A number will be chosen by this unfathomable entity. Despite every singular rule from every singular law of the universe screaming and begging at the top of its brobdingnagian unfathomable ethereal cosmic lungs.

I take what is likely the most quenching breath of all of humanity. I slowly position my index finger on the obnoxious rectangular shaped button. "GENERATE". It's red. The warning signal of nature. Not the warning signal of the universe, as the universe heeds no warning, the universe is what's heeded. I squeeze my eyes shut as tight as possible, hope for the best, and press down. I slowly, but surely, open my eyes. Would the feeble, unworthy human eye even be able to comprehend the sheer scale and impossibility of the outcome?

The number is four.

[coffeezoii]

they’re watching while i do math stuff + another doodle ↓

[chongoblog]

Have you heard of the Sum and Product Puzzle, aka the "Impossible Puzzle" because it initially seems like there isn't enough information to go on? I think I have the answer, and I'm mad about it.

I hadn't so I looked it up and here's Wikipedia's summary of it

There's also an explanation, but I didn't look. I wanna figure this out myself.

So let's break it down.

"P does not know X and Y" means that X and Y are not both prime. If they WERE both prime, then P would know the two numbers right away. So if S KNOWS FOR CERTAIN that P doesn't know X and Y, that means that the sum of X and Y can't be made up of two prime numbers. So, for example, the sum can't be 20, since if X and Y are 1 and 19, P would get 19 and be able to easily deduce the values of X and Y.

So we have a bound for the sum here, so we just need to find all numbers that can't possibly be the sum of two primes. I tried to get a good list of all numbers that aren't the sum of two primes through trial and error, but I after I found the first few I just let the OEIS do the rest of the work for me

So our possible sums are: 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, and 97.

Now that doesn't narrow it down a TON, but we can probably do something with this. Now that P knows that these are all of the possible sums, they know FOR CERTAIN what X and Y are. Very interesting. That tells me a lot about the product.

So let's say X is 4 and Y is 7. Then P is 28, and S is 11. Now, other factors of 28 include 2 and 14, which add up to 16 (not on the list), so we could just say that and call it a day, but there's something else that perplexes me. What if P is 24? The factors of 24 are 6x4, 8x3 and 12x2, which give us sums of 10, 11, and 14, and 11 is the only one on the list, so we have new X and Y values for S = 11 that could also apply. And since the S mathematician said he knew what X and Y were upon hearing that P knew, we can safely say S isn't 11, since X&Y could have multiple possibilities.

So, simply put, we need a value of S where there's only one possible P that could work for it. On one hand that still sounds like a LOT of guess and check work, but on the other, I feel like there's a way to find this solution without that.

Doesn't matter. I did the guess and check work anyway, granted it was actually easier when I got to the higher numbers, since most possible factors of P went over the sum of 100, which is one of our limitations. Easiest way to find these unique products is to find the largest prime number (lower than the sum) and use that as one of our two values.

So the conversation goes as such.

S sees that their sum is 17. Knowing that 17 can't be reached as a sum of two primes, S says "P does not know X and Y", which tells P that the sum is one of those numbers we saw up there. P's product is 52, he figures and he only knows two numbers whose sum add up to one of those numbers. So he says "NOW I know the value of X and Y". S hears that and figures that it has to be that one EXACT combination.

X and Y add up to 17 and multiply to make 52 which means that X and Y are 4 and-

...

GOD DAMMIT

[takinbreak]

What’s the worst thing about limits?

• Is it always having to amplify by the conjugate to eliminate indeterminate forms? NO.

• Is it having to learn some limits by heart (especially for trig functions)? NO.

• Is it having to sometimes use L’Hôpital-Bernoulli’s rule over and over again? NO.

• Is it having to just write “lim” before each line? YES. FUCKING YES. WHY OH GOD WHY I HATE THE NOTATION.

The most infuriating part of it is that it’s just a notation and it could so easily be changed, BUT NO, we’re stuck with this shit.

[amaniyuuuuuuuuu]

I got a B for my calculus quiz, test corrections don't apply if there's already a B

my overall grade has gone down to an A-,

"well at least its still an A" said the cunt

it brought down my gpa TT