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.
That guy in that place with the thing that time.
Oh, Lord Nikon.
Crash, and…
FMstrat
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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If only I had more hypothenanuses and less avocado toast… :(
I don’t know who hurt this guy, but it sounds like we’re only a couple more low-effort math jokes away from hearing a rant about the Jews, and how the woke mindvirus is destroying America.
4 hours later… yep :(
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If only you had spell check and the motivation to fix your broken society instead of complaining about having to learn shit.
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Tell us what you think of triggernometry?
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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.
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.
We had that in my local park. There was a huge field that everyone walked through because it was much quicker than going around. So they finally made a sidewalk there (not with tarmac though, more like gravel and sand mix). Just a couple of weeks later there was a new path just parallel to this one. My guess is the problem was that the field was a bit hole shaped (sorry I don’t know a better term in English) and this, as well just the nature of the sidewalk, led to it accumulating water puddles, and also it just turned into sandy/stoney mud when it rained. For bikes it was also just more comfortable to ride over the grass than over gravel. But it still felt like an asshole move.
“Concave?”
For bikes it was also just more comfortable to ride over the grass than over gravel.
True. Personal experience.
Because that’s exactly what has happened multiple times at the community college I go to.
Just pave the entire thing at that point (sarcasm) (pls don’t do this)
Sadly this seems to be exactly their plan, just as soon as the government gives them another $10*10^6 to lose
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.
I don’t see it that way. Most “word problems” are just poorly posed, lack important information, or are ambiguous. Often, they are mostly fairly unrealistic.
It would be better to describe usage scenarios, talk about examples in class, and give exercises which have a clear, discernible pattern. Like, actual physics problems.
Part of what makes all the hatred for Common Core math so hilarious to me is that when I finally saw what they were teaching, it was a moment of “holy shit, this is exactly how I use and do math in real life.” It’s full of contextualizing with a focus on teaching mental shortcuts that allow you to quickly land on ballpark answers. I think it’s absolutely wonderful.
But it’s so foreign to the rote manner that a lot of parents were taught that many of them have a hard time grasping it, and get angry as a result.
Nah, the word problems suck because they’re intended to teach you how to convert word problems into math problems. They did absolutely nothing to show how math is used in real world scenarios.
There are three problems I had with word problems in school. Not every problem applied to every word problem.
-
“This is way too vague.”
-
“Why would someone buy 35 apples and 23 oranges?”
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“Why would the person in the problem want to try to figure this problem out? It’s completely unrelated to what they were doing.”
I get the point was for us to be able to convert information given in a text format into something we can actually solve, but the word problems were usually situations you’d never realistically find yourself in in real life.
I think 2 and 3 are the same problem.
No, 2 is more “why are they buying this many”, and 3 is more “why would this person want to figure out some random thing that popped into their head about this”.
Okay, concerning 2 I thought you meant, why count and buy exactly this number. But it’s actually realistic, for a big family, or for desserts for a party, etc.
-
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.
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.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^2No 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’d like to teach math to anyone who’s interested, but I lack infrastructure to do so, unfortunately.
Zoom+laptop webcam pointed at a sheet of paper?
That doesn’t feel viable.
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.
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
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”
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 itThis is actually a case of the Cauchy-Scwartz inequality: https://en.m.wikipedia.org/wiki/Cauchy–Schwarz_inequality
c<=a+b🤓
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.
I said a thriving community. There hasn’t been a post there in three months.
Be the change you want to see in the world.
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!
