I love those path

Student: "Hey, a shortcut! Let me first just walk around the long way so I can measure the length of the other two sides, multiply those lengths by themselves, add them together, and find out how much extra walking I've saved myself by taking the shortcut. Boy, this shortcut sure is saving me a lot of effort. Hooray Pythagoras!"

Just because you do something so crazy fast in your head it seems obvious, doesn't mean you didn't do the thing you did with the thing.
- That’s beautiful who said that
The hypotnuse is shorter than the other two sides combined. That is the usage here though
- "the shortest distance between two points is a straight line" is what is being used here. It forming a triangle is incidental.

There's a college in Chicago, i think it's IIT maybe, that used aerial photography to map out the student cow paths, then they redid all the sidewalks to incorporate those paths.

Edit: they ended up adding a building in a grassy area and maintained all the hall/walkways of the building in line with the sidewalks/cowpaths. Kinda neat.

Ohio State University
- Brilliant!
- My old college looked a lot like that! I wouldn't be surprised if they were copying their idea
- The grass is hot lava.
This has happened at a LOT of colleges. Penn State's quad is crisscrossed with paths that they paved.
I'd be surprised if students didn't immediately make new paths off the new sidewalks
- why would they, desire paths happen because the initial pavements aren't designed well.
I love this type of urbanism. Some cities also study how cars behave in winter by looking at the tracks in the street, and they realized cars actually needed much less room on street corners than they thought.
- Every winter I see same corner filled with snow and nothing changed. They for sure need to cut some corners.

I wish I was taught about the usefulness of maths growing up. When I did A-level with differentition and integration I quickly forgot as I didn't see a point in it.

At about 35 someone mentioned diff and int are useful for loan repayment calculations, savings and mortgages.

Blew my fucking mind cos those are useful!

That's one of the big problems with maths teaching in the UK, it's almost actively hostile to giving any sort of context.

When a subject is reduced to a chore done for its own sake it's no wonder most students don't develop a passion or interest in it.
- In the US it's common to give students "word problems" that describe a scenario and ask them to answer a question that requires applying whatever math they're studying at the time. Students hate them and criticize the problems for being unrealistic, but I think they really just hate word problems because because they find them difficult. To me that means they need more word problems so they can actually get used to thinking about how math relates to the real world.
Hated Algebra in high school. Then years later got into programming. It's all algebra. Variables, variables everywhere.
- Ehh I wouldn't say variables in programming are all that similar to variables in algebra. In a programming language, variables typically are just a name for some data. Whereas in algebra, they are placeholders for unknown values.
The other use is as a door-opener; Learning these maths fundamentals enables you to pursue a stem degree
- as a door-opener
  
  You say that but they still need to teach you the "why". For example I did A-level maths which was a door to learning discrete maths in uni. Matrices, graphs, etc.
  
  In 20yrs as a software dev I never used any of it. Only needed basic arithmetic.
  
  To this day I've got no bloody clue what the point of matrices are.
I do some 8-bit coding and only last month realized logarithms allow dirt-cheap multiplication and division. I had never used them in a context where floating-point wasn't readily available. Took a function I'd painstakingly optimized in 6502 assembly, requiring only two hundred cycles, and instantly replaced it with sixty cycles of sloppy C. More assembly got it down to about thirty-five... and more accurate than before. All from doing exp[ log[ n ] - log[ d ] ].

Still pull my hair out doing anything with tangents. I understand it conceptually. I know how it goddamn well ought to work. But it is somehow the fiddliest goddamn thing to handle, despite being basically friggin' linear for the first forty-five degrees. Which is why my code also now cheats by doing a (dirt cheap!) division and pretending that's an octant angle.

One of my favourite names for anything is these being called 'desire lines'. It's so whimsical.

Indeed! “Desire paths” is the name I heard. There’s a community, too: !desire_paths@sh.itjust.works
- Unfortunately theres no posts for 4 months.
  
  Time to go get myself so photos
- thats a lovely community - thanks!
- Now my migration to Lemmy feels complete.
Around here we call them "bootleg trails"

Idk, this really doesn't have to do anything with Pythagora's Theorem

Beyond the general "hehe funny meme" Some seem to think there's some kind of math going on in people's heads other than "shortcut"

The knowledge of Pythagoras or math doesn't factor in here at all. Toddlers do this.

Having the knowledge just gives you fancy words for the resulting coincidental shape.
- Having the knowledge just gives you fancy words for the resulting coincidental shape.
  
  Isn't that basically all of physics? Just an abstract concept to describe something that sort of fits the rules we extrapolated from observations so far.
- Yeah, somebody once explained this to me like
  
  "even stupid animals go directly at where they want to go"
The way is sqr(2)=1.4 instead of 2.
- It's also a straight line between points, so nobody really cares just how much shorter it is.
Yeah, it's just the triangle inequality.
Yeah, true. No Euclidean distances implicit to this problem. Oh, wait...
Yeah... this is just "the shortest distance between two points is a straight line"
yea i get the intent but it doesn't really make sense

That footpath looks like a brachistochrone curve. Interesting.

It is.
- Here is an alternative Piped link(s):
  
  It is.
  
  Piped is a privacy-respecting open-source alternative frontend to YouTube.
  
  I'm open-source; check me out at GitHub.

all the student needs to know is c<a+b, not the actual formula or theory behind it

I think this is more a case of the triangle inequality in metric spaces, as you don't have to calculate any particular edge to see the shortcut, as well as that it applies to any even non-rectangular triangle.

But if you want to know your saving, you will need to dust off the old formula. And if you do, you find the maximum saving to be around 41% (in the case of isosceles right triangle where the hypotenuse is a factor of sqrt 2 shorter).
- That's true (y)

Triangle Inequality also!

Now, I'm wondering if we have a thriving Desire Paths (that's what these paths are called) community somewhere on here.

!desire_paths@sh.itjust.works
- I said a thriving community. There hasn't been a post there in three months.
Don't know but that sounds like a great idea of one. LOL

this is actually the one thing i am glad to have learned in math class. saves me a lot of guesswork sometimes.

SOHCAHTOA and a calculator have been real useful for that too
I can't think of when I've actually used it.

I've seen comments about how 3, 4, 5 allows you to make a square corner with a tape measure, but I've never had an opportunity to use that trick.

I find myself trying to guess the area of things a lot more.
- I guess your not a carpenter and you don't build things? It's super useful. I don't use it all that often but it's an excellent tool to have. Even just laying out a square garden, say. It also works with any multiple to make bigger perpendiculars, 6, 8, 10 or 15, 20, 25

I have literally done this calculation in my head while walking before to see if it was faster to cut the corner or walk around. Nice!