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
Couldn’t have said it the way he said it better if I said what he said myself.
FMstrat
That guy in that place with the thing that time.
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.
Ah yes some euclidean space
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
This has happened at a LOT of colleges. Penn State's quad is crisscrossed with paths that they paved.
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 used them in computer graphics and game programming. As a regular software dev, not so much.
They're used for manipulating vectors.
Just like how in
a×v
the a makes the vector v longer or shorter, in
M×v
M can change the vector, for example rotate it.
Just like vectors and other mathematical objects, matrices are purely theoretical concepts. There is no direct real-life meaning to them.
However, there are a bunch of real-world problems where matrices can be put to use to calculate something meaningful.
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
If you're not opposed to stealing from Reddit, desire paths was one of my favorite subs before the shitification
Thank you!!
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...
That footpath looks like a brachistochrone curve. Interesting.
all the student needs to know is c<a+b, not the actual formula or theory behind it
This is actually a case of the Cauchy-Scwartz inequality: https://en.m.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality
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).
Now, I'm wondering if we have a thriving Desire Paths (that's what these paths are called) community somewhere on here.
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