I was watching this video, which was describing the intution behind the second derivative. I understand how the 1-dimmensional result was found, but I am quite at a loss for how to arrive at the n-dimmensional result, where the second derivative is the laplacian (the video provides the 3-dimmensional result, i.e. $f(x,y,z)$, at 00:08:08). The specific part that I'm having trouble with is finding the average of the multivariable function so that it fits the equation stated in the video, which, even more confusingly, has a single variable in it.

• Update (2024-05-08T06:31Z): I found this document, which provides a lot more detail.

Posting this from lemmy.world because I wasn't able to from lemmings.world. I also wasn't able to upvote comments, and thumbnails of newer posts are appearing blank.

Are there any known right triangles that have integer side lengths and rational angles? If not, has it been proven that none exist?

Source: https://www.artstation.com/artwork/YBxoew

cross-posted from: https://dormi.zone/post/1806889

Source: https://en.wikipedia.org/wiki/Dancing_Fairies

I have had pretty bad pain all week in my stomach. And today I started to actually feel sick.

It seems like my ibs/gastritis ridden stomach feels all of this happening miles before anything even happens. Anyone else have similar exp?

Source: https://www.artstation.com/artwork/Ry604e

This is what the bot posted:

This is the best summary I could come up with:

The Reuters Daily Briefing newsletter provides all the news you need to start your day.

Sign up here.

The original article contains 18 words, the summary contains 18 words. Saved 0%. I'm a bot and I'm open source!

Daily bunny no.2437 bestows magic upon thee

Source: https://bsky.app/profile/willquinnart.bsky.social/post/3kofymqu6oa22

There are certain things whose number is unknown. If we count them by threes, we have two left over; by fives, we have three left over; and by sevens, two are left over. How many things are there?

Source: https://www.artstation.com/artwork/9EwKEL