1 / CosC

[sinhus-is-minus]

My Solution ⬇️

[sinhus-is-minus]

My Solution ⬇️

Sequence of numbers divisible by 5:

5 + 5n

Sequence of numbers divisible by 5 and 2:

10 + 10n

Sum of arithmetic sequence = n/2(2a + (n-1)d)

answer: 50,000

[sinhus-is-minus]

My Solution ⬇️

[oneirotrope-deactivated20231115]

if you own k distinct colors of sock, you can draw k+1 arbitrary socks from your sock drawer and, by the pigeonhole principle, be guaranteed at least one matching pair. this is the only known application of combinatorics to the real world

[sapphic-adjunction-deactivated2]

I have heard rumours that this also works for gloves, but I'm not an engineer so I don't know.

[sinhus-is-minus]

My Solution ⬇️

[sinhus-is-minus]

My Solution ⬇️

[sinhus-is-minus]

My solution ⬇️

[sinhus-is-minus]

My Solution ⬇️

x = a is not a solution.

subbing in x = a = 1 gives 0 = 2, so it must be incorrect

this “fake” solution came from squaring x-4a = 3root(ax), as the result gives 2 solutions.

im the same way root(16) = x is 4, whereas 16 = c^2 gives two solutions, positive and negative 4.

[sinhus-is-minus]

My solution ⬇️

[makialene]

Tumblr, I come to you with a math question

I'm doing a practice ACT and I cannot for the life of me get this question. I've put it in 2 separate calculators AND even done it by hand, but each time I get 24/19. At this point no one I know can figure this out

[sinhus-is-minus]

I also got 24/19. I think the textbook might be wrong!

[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!

[tamberoo]

i need several moments, math like this scares me

[abalidoth]

Not gonna lie, as much as I want to be helpful and comprehensible, I am very proud of provoking that reaction image.

[the-shape-showdown]

submissions are closed but i need everyone to see this cursed triangle

That's a triangle? I hate how you know it's off but you don't know how

[sleepy-bebby]

[sinhus-is-minus]

My solution ⬇️

Area of shaded region = 10 u^2

[sinhus-is-minus]

Puzzle from Mind Your Decisions on youtube:

My solution ⬇️

[a-crow-with-rights-and-anxiety]

Hey so you remember this thing that everyone on mathblr got excited about recently?

This is the hat, and it's what's called an "aperiodic monotile". This means that no matter how you arrange copies of this tile, you can never get an arrangement that will repeat infinitely (think of it like the irrational numbers of tilings). This was big news in mathematics as while sets of more than one tiles have been found that are aperiodic (e.g: The Penrose Tiles), this was the first tile that's aperiodic by itself, hence "monotile". (There are some caveats to this but that's not important for understanding this post)

However.

If you look at images of the hat tiling, you may notice something.

If you look at the tiles labled 1 and 2, you'll see that one's a reflected copy of the other. In fact, any infinite arrangement with hats requires you to you mix unreflected and reflected tiles. Which raises the question: is it possible to have an aperiodic monotile that doesn't need reflections?

Presenting the Spectre, A chiral aperiodic monotile.

Using only translation and rotation, any arrangement of copies of this tile will never repeat.

Mathematically speaking, this is really fucking cool.

The paper on it is still in preprint, but hopefully I won't need to retract this post. A copy of it can be found here and a post going into some more details of how the shape was discovered is here.