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).
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.
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.
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.
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.
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.
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.
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.
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?”
“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.
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.
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.
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!”
You literally do it subconsciously all the time. Written math is just a representation of it, just like language is also a representation of your thoughts.
It’s no wonder you all are still flipping burgers at McDonald’s and bitching about not having a living wage. It’s because you never try to use anything you learned in school to do anything.
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.
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
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