Triangle Inequality also!
this post was submitted on 23 Jan 2024
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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.
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.
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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.
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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.
Machine Learning is basically a lot of linear algebra, which is mathematically equivalent to solving simultaneous equations.
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.
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.
I fucking loved maths mechanics which is like applied maths/physics. So you'd calculate the distance a ball is thrown or a cannon ball dropped from a cliff. Don't think we ever did matrices in it though. I enjoyed it so much I'd do excersizes in the book for fun!! That and politics were the only courses I was passionate about.
But I became a software dev that didn't use maths or politics. :/
So from age 5-17 I hated maths cos I saw no point in it. Until I hit 17 and someone said I can work out how fast a fucking cannon ball travels on impact?! I mean holy dog shit! If someone told me that in primary school I'd have loved maths!
It was very much taught as a means to answer questions though rather than application. So as an adult I'd have to be shown how a number could be found using algebra. But because it wasn't in an algebra question format it went over my head. It literally required someone taking numbers I'd been given and putting them in a line with letters before my brain engaged to "Oh shit - algebra! I know this!".
Another example is differentiation. I recently looked up my notes and remembered it was told to us very mechanically: f(x) = 4x^3 => f'(x) = 4(3x^2) = 12x^2
No idea why that's the case - it just is.
It's a shame cos I learnt I love maths at 17 but by that point I'd lost years of potential.
P.S. any advice on where I can re-learn real-world maths? I'd love to redo my teens maths learning for fun.
I used them in computer graphics and game programming. As a regular software dev, not so much.
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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.
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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
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Idk, this really doesn't have to do anything with Pythagora's Theorem
Yeah, true. No Euclidean distances implicit to this problem. Oh, wait...
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.
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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.
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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: [email protected]
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!!
this is actually the one thing i am glad to have learned in math class. saves me a lot of guesswork sometimes.
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