Mathematician Answers Geometry Questions From Twitter | Tech Support | WIRED
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- čas přidán 13. 05. 2024
- Mathematician Jordan Ellenberg answers the internet's burning questions about geometry. How are new shapes still being discovered? Where are we using Pythagorean theorem in real life? How many holes are in a...straw? Ellenberg answers all these questions and much, much more!
Jordan Ellenberg's book Shape is available on Amazon or Penguin Random House
www.amazon.com/gp/product/198...
www.amazon.com/gp/product/198...
Director: Lisandro Perez-Rey
Director of Photography: Constantine Economides
Editor: Richard Trammell
Expert: Jordan Ellenberg
Line Producer: Joseph Buscemi
Associate Producer: Brandon White
Production Manager: D. Eric Martinez
Production Coordinator: Fernando Davila
Casting Producer: Nick Sawyer
Camera Operator: Christopher Eustache
Gaffer: Rebecca Van Der Meulen
Sound Mixer: Michael Guggino
Production Assistant: Sonia Butt
Post Production Supervisor: Alexa Deutsch
Post Production Coordinator: Ian Bryant
Supervising Editor: Doug Larsen
Additional Editor: Paul Tael
Assistant Editor: Billy Ward
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I'm a fan of this series, but Jordan was a particularly strong communicator. Thank you for bringing him on, and thank you to Jordan for being a fantastic ambassador for geometry and math writ large.
To be fair, he did miss the opportunity to proclaim that hexagons are the bestagons
thats my uncle lmao
Why did you use “but” as though you were going to say something bad?
@lucasm4299 because they understand language better than you 😊.
"But" can be used to contrast with (e.g. I'm a fan, but this was trash), or to add to (I'm a fan, but this was excellent).
I have a use for the pythagorean theorem in real life application. I’m told a TV’s screen size always as side C and I know it is a 16:9 aspect ratio. I can find the height and width of that screen when the site doesn’t list the dimensions.
The only true use of the Pythagorean theorem
@@chesterotontop unless you're an engineer, architect, scientist, mathematician, programmer, city planner, game developer, digital artist, etc etc etc.
Didn't expect to see AustinJohnPlays here but cool to see!
@@runstarhomer2754 He’s being sarcastic
Well, you'll be able to find out the height and width of the LCD panel; but that screen size doesn't include the plastic frame around the LCD panel. So it can be useful for comparing monitors to one another, but not for knowing exactly whether or not the monitor/tv can fit in a given area. It wouldn't be a bad ballpark for it, though.
As a quilter I use the Pythagorean theorem to figure out how many triangles I can get out of my fabric and how big to measure them. Once I had a pattern for a skirt that wanted right triangles of a certain length on the "c" side so I used it to calculate the "a" and "b" sides
As someone who's played around trying to program a pool game, balls in the game have known X and Y coordinates, I've used the Pythagorean theorem to find the distance between balls to check when the balls hit each other.
I once had to use the Pythagorean theorem as a web developer to calculate the size of a resizable widget when you clicked and dragged the corner! I was like "huh I guess knowing that actually was useful after all"
I came here to say I use the Pythagorean theorem for sewing too! For me it's to make zero waste flaired skirts. 💃🏻
I use it for plastic wrap 😂 the wrap is normally always the c, so if you go all the way down to a, it will always be enough wrap
Contractors can also use it to make sure a corner is actually 90 degrees. Measure 3 going one way, 4 going the other, and adjust the corner until the hypotenuse is 5.
As a regular Dungeons & Dragons DM, I have sometimes used the Pythagorean theorem to calculate the distance of flying creatures moving diagonally to the ground to attack players. I'm just glad online calculators exist so I don't have to do the math myself. 🤣
This is precisely the only way I've used the theorem in the last 25 years hahahahaha. And quite often, I must say.
saaame lol. til the dm reminds me that diagonals technically don't exist in dnd lol
I created a Collatz Dungeon for a party that was testing the Constable's patience. They would get dropped in Room 3,505,346, and they would be connected to two others, one double the number, and the other half as much. Eventually, they would hit an odd-numbered room, n, which would connect to Room '3n + 1'.
All numbers, eventually, will connect to Room 1, where the exit would be.
Its very helpfull in vidéo games too ! I use it all the time to calculate distances between two objects in a plane in small personnal game projects :)
Every object has x and y coordonnates, calculating the distance between the two is one of the most important things in a game. For détection, colisions etc... and Pythagore is always used.
I highly recommend the essay “A Mathematician’s Lament” for anyone who wants to go deeply into the way we teach math and how poorly it’s taught that most students find math boring and frustrating in most math classes (I know mine classes were definitely not taught well). Jordan has the energy and love of mathematics that would make him an excellent teacher, and I wish I had someone like him while I was crying over my algebra 2 homework.
OMG THANK YOU SO MUCH FOR THIS RECOMMENDATION....One page in and I absolutely love this premise. It's so perfect.
I hated math in school with the exception of geometry in 10th grade. That was a blast. But algebra was always a nightmare. Then I signed up for an algebra class in college with a specific math teacher everyone recommended. She taught math on colorful handouts and in true layman’s terms to where it all connected and made sense. It was like learning math where every lesson is “explain to me like I’m 5”, and her method of teaching was extremely effective and fun! So many students needed a total refresh of some basic math concepts just because of how poorly they were taught in the public school system, and she helped so many students, including me, to be unafraid of math. I wish there were more teachers like her around.
The Pythagorean theorum has a lot of real world applications in architecture. For example, it's useful for designing staircases, since if you know the height of the upper floor, you can calculate the length of the staircase for any given footprint.
I used it recently to calculate the bill of materials on the roof of a shed I was building. Of all the mathematical / geometrical rules, this one is one of the more applicable ones to the real world... of course, if you google 'Trigonometry calculator', that's even more precise, and takes away the actual need to do the math...
@@FHL-DevilsI did something similar to turn the old, flat, but too short driveway into a new, longer driveway that would have a steep slope. Needed to make sure the rise on the slope wouldn't scrape the car
i was able to use phytagorean theorem on how much we need to extend our roofing for us not to have side-hitting rain hit our wall (which can weaken the concrete overtime due to accumulation of moisture). i was actually surprised when the calculations worked!! i felt like a wizard
TV screens are all measured in the diagonal dimension. So if you have a space on your wall that is X inches wide, you can use the Pythagorean theorem (and the fact that most TVs have a 16:9 aspect ratio) to determine the largest screen size you can put there.
I qm an engineer and i use it all the time
I think the issue with the "Does a straw have one hole or two?" question is that everyone treats it as a geometry problem when it's more of a language problem.
Wittgenstein says hello!
there is no language problem. A straw clearly has one hole which ever way you look at it 😉
I mean, more of a topology question than geometry.
I feel the same way about the question of “are we living in a simulation?”
Y it s a question of définition
In maths (topology) the straw has one hole cause it s fondamental group is isomorphic to Z
6:58 The A paper sizes (A4, A3 etc) have a similar property, but it uses sqrt(2) instead of the golden ratio. When you fold it in half the ratio between the long and short side remains sqrt(2).
I used to use Pythagoras to mark out an accurate filed when laying out our clubs field hockey lines at the start of each season. Mark the baseline and then use a 3,4,5 triangle to make 90 degree corners for each sideline.
That’s the one. The Pythagorean theorem’s most useful real world application is to mark out exact right angles when the biggest square you have is still far too small: you can do it with a tape measure.
Honey combs is 100% a packing efficiency problem. If you take any circular object, beer bottle, golf ball, whatever. Any circle, and more circles of the same size. You can wrap 6 more circles around the original.
That’s wrapping around to make another circle. So yea. But there’s still negative space that’s not being utilized. With strait lines you can take away that negative space. Hence Tetris etc.
As we all know, hexagons are the bestagons, but it was nice to hear an explanation about it being incidental in the case of hive cells. Never heard that before in explanations of the subject.
actually, triangles are the divine shape
Don't make me call RCE. lol
Jordan gave a bad explanation here though. What is special about the regular hexagon is that among all regular polygons (i.e. whose sides are all the same length and the angles between adjacent sides are the same), it's the one with the most sides, such that you can fill a plane with them without gaps. So this uniquely satisfies the goals of maximizing the space for larvae with round cross-section, packing as many compartments into a given space, and minimizing material (wax) cost while having uniform wall strength. No other possible shape is as good as that. You can build a honeycomb out of regular triangles of squares and you'll fill the space with compartments and maintain uniform wall thickness, but it's a bad use of space because you need to make the triangle or squares rather big to fit the round-cross section larvae; if you take regular polygons with 7, 8, 9, or any large number of sides, you will leave unused gaps or waste wax.
I love how unapologetic Jordan is about drawing crappy circles! 😂
On a more serious note, I was impressed by how well you pronounce the German names (Einstein and Möbius) in such a casual manner.
The Pythagorean theorem is used constantly in data science as a measure of similarity between data points, like if you want to know which of your customers are most similar to each other.
yup, just usually in higher dimensions
@@fallen3424 I wonder if they shouldn't teach in school that you can have like a 17-dimensional Pythagorean theorem and it works just fine
Not really, the pythagorean theorem is just a rearrangement of the distance between two points in Euclidean space.
@@tmjz7327 Which part of that do you believe is a contradiction
that seems to be a pretty weird literalization of an abstraction and idk how well that holds up
"[Geometry] is the only part of math where you're asked to prove something..."
Number theorists: "Am I a joke to you?"
*war flashbacks to Abstract Algebra*
(To be clear, it's fun, but hard)
I'm pretty sure that proofs are common in exercises and tests for any undergrad level math courses lol
6:10 if you pinch the bottom, it has zero holes. A bowl or a plate don't have a hole, and an open-topped bottle is the same shape as a bowl or a plate.
is a bottle a bowl?
@@theastuteangler sure, seems a reasonable grouping
Pythagorean theorem is really handy for figuring out distances in D&D where all battles are on a grid
Nice one lol I'll be using that now
This is like the sixth comment about D&D i'm reading, amazing
The straw answer was confusing. Topologically, the straw clearly has ONE hole, like a bagel. And a bottle has NO holes. Think about it: A bottle is basically just a deformed bowl, and a bowl is just a plate with an higher edge. A plate has no holes.
There are people who view a straw, rather than as continuous surface, as a set of two spaces: an inside and an outside. The argument for a straw having two holes is that there are two clear connection points between the spaces, at the top and at the bottom. Depends on if you view the straw as a topographical surface or as a household object.
wait you might be right
If you dig a hole in the ground, you would call it a hole. Does it go through the Earth? No, but we still call it a hole. Maybe we need better definitions of what is a hole that goes through an object vs a hole that is subtracted volume.
@@keetonhersey2245perhaps more precisely, one can view a straw as a 2-manifold-with-boundary, and the boundary consists of two disjoint circles. those two circles constitute the holes of the straw. however, i do agree that it was confusingly worded; in his effort to avoid jargon, he ended up watering down the discussion and making it seem less certain than it is.
@@averynicebean I agree, a clear definition would help. The definition in everyday live is not rigorous. It will heavily depend on the actual shape of the subtracted volume, not the total amount, what we call a hole. No one looks at a valley and says "That's a hole!"
When he mentioned the super hero movie not inventing the tesseract, I angry-scrolled to make sure "A Wrinkle in Time" was mentioned, just as he said it.
I had to give this a watch. I just used the Pythagorean theorem about two minutes ago. Creating miters for a picture frame and I needs to determine what the third side is going to be!
Love his enthusiasm for math and geometry!
5:04 There is one hole on the straw. When you cover the bottom, then the straw has no holes (a water bottle can be deformed into a bowl or a plate, for example)
What is the fundamental group of the straw?
if you bend a straw too much, then it will have more holes and you won't be able to use it.
@@xraygamer9895Z. It's either homeomorphic to a solid torus (if you assume it has width) or a cylinder (assuming no width). Either case the fundamental group is Z. It could still have higher dimensional holes but the homology groups are of course all trivial except for dim 0 and 1.
As a math teacher, this brings back memories of my college geometry and math history courses! Love it! It’s awesome to see somebody love their profession so much! 😊
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As an Army Sniper I used to do a brief/lecture called "How the Pythagorean Theorem Saved My Life." We use it in ballistics.
Send me the power point cuh
Yea aight
I just watched a 17 minute video about math of all things, and was entirely entertained by the presenter. Incredible.
A slight variant of the Pythagorean theorem is very useful in the real world: for a triangle, a^2+b^2=c^2 precisely when the angle opposite c is 90 degrees. This can be used, for example, when pouring house foundations, to ensure the corners are (very close to) right angles. It translates the accuracy of length measurements to accuracy of angle measurement.
Thats exactly what the normal theorem is
@@NandrewNordrew Usually I see Pythagorean Theorem presented as "For a right triangle: a^2 +b^2 = c^2", he seems to be saying "If a^2 + b^2 = c^2 then you know the angle opposite c is 90 degrees", which is a slight variation.
One hole, two openings.
As someone who plays a lot of D&D we use the Pythagorean theorem all the time to figure out spell distances with flying creatures lol..
"Imagine someone with no sense of purpose."
Me: Of course I know him, he's me
Fun fact: the four dimensional tesseract was the central plot feature of Robert Heinlein's short story 'And He Built a Crooked House' published in 1941, twenty one years before 'A Wrinkle in Time' came out. Though I loved a Wrinkle in Time, Heinlein did a far better job describing it.
I just finished Stranger in a Strange Land, and his description of Mike sending things Away was so good! I'll have to check out that short story sometime soon!
Agree. And this wasn't the only suboptimal description in this video.
I’ve never liked math but I love this man’s enthusiasm.
Such a great episode. You should film a few more with this guy!
I'm a quilter. I use the Pythagorean theorem almost every day
You also are an expert on knot theory, which is much deeper math than the Pythagorean Theorem.
This dude needs his own CZcams channel where he teaches math. So much more charismatic than any teacher I ever had.
I always had a much easier time with geometry than algebra. At least with geometry I could get a mental picture of what I was trying to do, whereas algebra was just letters on a piece of paper. Of course, I still didn't do very well in geometry because I wasn't that good with the mathematics portion, but at least I knew when I got the wrong answer even if I wasn't sure why!
For me it was quite the opposite. In algebra I was always top of my class but then we moved on to geometry. I sucked at geometry because I don't have the "mental picture" that all the other kids claimed to have. When doing algebra I just had to look at the equation and I would be able to write the correct answer almost immediately. Geometry wasn't like that though.
6:00 How many holes in a bottle? Topologically speaking there are 0 holes.
I’ve never heard anyone describe Euclid as “a guy who lived in North Africa” …
What's fun about this guy is he's clearly talking to the people in the room, not necessarily to the camera. Looks like they were eating it up.
Why hexagons? Why hexagons??? Well, because hexagon is the bestagon!
On the Pythagorean theorem : when I was a little boy, on my usual path to school, I had to around two sides of a square, as to not walk on a bit of lawn. I wondered how much distance I would spare every day if I just crossed that lawn across a diagonal. Well... One day I learned how to get that answer.
You just have to be curious and you will need math in your everyday life.
Took me almost 10min to realise I own on of this guys' books. "How not to be wrong". Great read.
wired messed up not giving this poor mathematician his chalk and board 😭
on a serious note, what delightful communication skills this guy has
The Pythagorean theorem is good for calculating straight distances on a map with grid lines. You count how many vertical and horizontal lines you're crossing and then use Pythagoras to calculate the distance.
Loved this episode! I didn't take geometry in high school; Ellenberg's knowledge, insight and enthusiasm make me want to take an online course to see what I missed.
If you've ever been walking down the side of an empty street, and you jaywalked diagonally to the other side instead of going straight across and down because it made for less walking overall to your destination... guess what, you used the Pythagorean theorem
No you didn’t. You just walked across the street. You didn’t use any theorem at all.
not really. you're just using the fact that the shortest distance between two points is a straight line (in euclidean space)
@@ttmfndng201 phblttbtt Euclidean who? You'll never catch me using THAT daily :P
This was really good he made geometry sound pretty dope
This was a good one!! He's an excellent communicator and super engaging! Loved this ❤️😊
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@@redredred8408 pi-ish?
Math finance PhD student here, just a comment about the random walk question. The Bachelier model in finance is a terrible model for stock movements and this was known at the time they published their model. A better model nowadays is models of the form e^(X(t)) where X(t) is some stochastic process (see something like geometric Brownian motion, the vasicek model, or more exotic models like the Heston model or general jump diffusion models). I bring up this detail because people get really silly and paranoid with stocks and it's important to note that these modeling problems are remarkably complex and nuanced. They require much more than just a random walk to be useful.
The answer to the straw problem is it is no longer a straw if pinched and a bottle is no longer a bottle with a hole in the bottom.
And thank you for mentioning honeycombs are actually circular when created. They settle into hexagonal shapes because of how tightly the bees pack them in and how flexible the material is initially.
A straw with a pinched bottom has completely lost it's function. Is it still a straw if it can't do what a straw is supposed to do? At this point, it becomes a philosophical question.
Another interesting question regarding this: of you hang up a spinning disk and the shadow of the disk is exactly under it, is the shadow also spinning or is it stationary?
Why do bees use hexagons? Because hexagons are bestagons
He really dodged that question but probably because it is a physics question, not a geometry question.
I've used the Pythagorean theorem when I framed a new deck. Measured off to ensure the layout of the build was square. 3-4-5 method is what's it's called on most jobsites.
i love the arithmetic of holes. always learning something new everyday
The Arithmetic of Holes sounds like something Lisa Ann would star in.
Pretty sure he is the first non-german Person, that i've ever heard to pronounce the name "Einstein" 100% correctly. Neat!
"Ein-shtein"?
@@rebeccamcnutt5142 Yes.
The straw hole one is crazy. My answer was two holes tho. Also I wish I could understand shapes in a 4 dimension. It makes no sense to me.
If you imagine time as the fourth dimension that works to my brain. The cube exists now and in a second and in two seconds. You can kind of imagine it moving through time.
@@travelsandbooks I still don't understand it :(
How I think about shapes in 4 dimensions is by thinking about shapes in 3 dimensions, and hoping that similar reasoning carry over.
We have an outdoor hot tub.
I had to calculate how much cholrine to add. And thus needed its volume in liters (or dm3).
First time I ever had to bust out pi IRL, and I only needed to wait till I turned 40!
6:35 I find it pretty funny that we call it the golden "ratio" despite the fact that it is, almost by definition, *irrational*.
When he said “imagine a person with no sense of purpose” I felt that
I live in eastern Europe, I had a friend over, and he asked how many inches big my new monitor is. I could not remember it, but then I remembered the Pythagorean theorem, and that 1 inch is roughly about 2.5 cm-s.
So I took my measuring tape, measured the sides, did the quick math, and could tell him it's 27".
Could I have just measured the distance across? Yes
Would that have been fun? No
There is one hole at regular straw. If other side is plugged then there are no holes since if you start cut the straw shorter you end up plane. Also you can tie a string throught the hole of regular straw, but not plugged one.
Awesome! He visited topics I have heard of before but named them so elegantly that I’ll never look upon them the same again!
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Yay geometry!! The only math class that made sense to me!!
How about differential equations???
A straw has 0 holes, its just a warped plane
a warped plane that formed a hole by definition
The dictionary says a hole is a small and unpleasant place 😂😂
@@easymoneysniper9013 🤣🤣🤣
@@arablues4142 so a straw IS a hole 😂😂
Literally started reading "How Not to Be Wrong- The Power of Mathematical Thinking" 2 days ago and this is the first thing that popped up when I Googled him. Highly recommend the book!
Awesome video! We need a part two!
hated doing geometry proofs in high school 😅😢😂
Jordan is type of guy to make easy exams and hard homeworks
Pythagoras is very handy for figuring out neat ways to build Lego in an interesting angle and still keep to the required strict dimensons of a piece. The recent Tranquil Garden set uses this to place the supports of a building five studs apart.
i've used pythagorean irl by trying to figure out my monitor size and having a ruler too short to measure the diagonal.
I've used pythagoeran irl to figure out how much i need to move in diagonal to maintain same speed when coding video games.
i've used area of circle/cylinder volume formula to find our the volume of the pots i have in the kitchen to see if they'll accomodate the recipes.
During a debate with a debunker, a flat earther was asked, "If a triangle has sides 1, 1, and 1, what are its angles?" The flat earther said, "One what?"
60° but I’m not understanding the joke or the ppint
@@kvonation8852the triangle cannot exist in Euclidean geometry (flat surface)
@@duckymomo7935 I mean it's just an equilateral triangle?
To be clear, self-similar objects are merely a subset of fractals
New application for Pascal's triangle learned. Cool. Only one I knew was coefficients for binomial exponential expansion
I loved your straw answer! It shows that there are multiple ways to look at anything.
I swear this guy sounds like Khan Academy
Finding 90 using 3,4,5.
Matt marker made a video on the reason why bees make hexagon patterns, it's called "Why Do Bees Make Rhombic Dodecahedrons" it's a good watch.
I'm always ready to learn more about the arithmetic of holes.
You cannot come up with a use of the Pythagorean Theorem? Clearly you are not an Engineer. I use it daily in most of my designs.
Well he isn't an engineer lol, he's a mathematician, we use triangles a lot in nautical engineering and it definitely comes up, but the question was more so for the everyday person.
well yeah mathematicians deal with more complex stuff than just pythagorean theorem, they come up with the formulas you engineers use
@@Astyl_ Still it would be useful if he’s a teacher to provide a practical application to it, I know that as a professor real-world examples are better than abstract ones.
@@ingGS I agree with that for sure.
This guy may know his math. He may be a genius at that. But he is truly awful at being a math communicator. Not only is he heavily biased to a branch of math applications, he is painfully unimaginative. The first question he answered is very euro-Plato-logo centric. It totally misses the richness other cultures, other philosophies, other paradigms and systems, other creative interpretations bring to math.
Do you think the pitagoras theorem is only used to measure distances?! That is like saying that the number 4 was only invented to count apples. My dude, measuring distances may be less than 0.1% of the use of the pitagoras theorem. Vectorial analysis is a an invetion that transformed the world. Newton mechanics would be incredibly impractical without the PT. Electricity cannot be understood without the PT.
Wow
The straw has one hole by definition of topology. There is no wiggle room here.
The bottle example is really interesting and if you used it right it would have proofed the point. The bottle has ZERO holes (when you remove the cap). It is the same if punch a "hole" in a baloon. what you get is a surface with STILL zero holes. The bottle can be put flat with the rim of the opening to become the OUTER edge of a disc. So when you punch a hole in the bottom of the bottle you add ONE hole - and this bottle has ONE hole - as the straw has.
Fun side view: A trouser has TWO holes. If you remove the height of the trousers to "zero" you have the two holes of the legs and the upper part of the trousers become the outer edge of a disc. Topology is precise in these definitions. I recomend checking out Matt Parker on this topic.
"by definition of topology" that's the problem.
Even though when talking about topology a straw undeniably has 1 hole, people aren't usually talking about topology when talking about straws.
for example, if you asked most people how many holes a bottle has, they would probably say one.
Enlightening! Someone recently asked how many holes a T-shirt has, and I said 6. My reasoning was:
1 - neck to waist
2 - neck to left arm
3 - neck to right arm
4 - waist to left arm
5 - waist to right arm
6 - left arm to right arm
Thus, the number of holes would be the number of openings (n):
(n-1) + (n-2) ... + (n-n)
But with your stretching out revelation, I can see that it is openings (n):
n-1. A T-shirt has 3 holes.
5:24 the straw theory makes my brain short circuit!!
Pythagoras' theorem is incredibly useful when you are trying to make right-angle triangles. Since you generally want a house to have walls at right angles to each other, you can achieve that by just building a decently sized triangle that you can place into the corners. Apparently, not every mason knows this considering the ones that built our house screwed up and built the wall of angle to each other.
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I used Pythagoras in the army. It made going through bncoc incredibly easy because i didnt have to manually gind the distance between points. I had it exact everytime.
Hey, I love this wired series! But I got to say this is one really special good one!
That was the most clear and succinct explanation of gerrymandering I have ever heard. Incredible
Matt Parker (yt: Stand-up Maths) explained the honeycombs as simply the result of the bees pushing out all the walls when they build them. Circles don't tile the plane, but if you stack a bunch of circles and then expand them to fill all the empty space you end up with a hexagonal tiling.
I always think of geometry as the study of spaces that have so much structure that they are interesting both analytically and algebraically(in that for instance, they have an inner product)
I just love this series
The discovery of the hat and the specter - the aperiodic monotile (and its reflection) - is a great example of a newly discovered shape.
I've known the pythagorean theorem since I was a small kid in the sixties. my mom made me watch old movies with her. We watched "Merry Andrew', a musical starring Danny Kaye as a school teacher who teaches his boys math, and the Pythagorean Theorem through a musical skit. it's repeated several times in the skit. best into to maths ever!!
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Cool video, happy to see someone else also appreciates how pringles are shaped so cool
I use it daily in HVAC sheet metal duct fabrication, especially for offsets and transitions.
10:56 I have to take issue with your statement that geometry is the only part of math where you're asked to prove things. It's certainly the first time most students are asked to do it, and it might be the only time it's required below an upper-class level college course, but higher algebra courses and even calculus classes have them.
Came here to say this
14:00 - I use Pascal's Triangle (probability), al-Karaji's Triangle (binomial multiplication), and Yang Hui's Triangle (number theory) all the time! (hint: these are the same thing, but better attribution given for the appropriate advancement. We need to think about the full story, and not merely give Pascal all the credit)
My research expands the triangle into more dimensions (an n-Simplex) and the summation of more rows.
binomial theore-
Pythagorean Theorem comes up *constantly* in 3d graphics programming. Although it's usually handled under the covers by the engine you're using, it's required to normalize surface vectors to allow for faster and more accurate matrix transformations of said vectors. In short, you can describe a surface as a vector that is perpendicular to that surface, where the length of the vector tells you the size of the surface. So a rectangular wall may be described by [3,4,0]. You could apply the matrix transformation to that, but it's better if you divide all the components by something that makes the actual length of the vector equal to 1. In this case, sqrt(3^2+4^2+0^2)=5. The new vector is [3/5,4/5,0].
It also comes up in surveying, construction and engineering, at least.
I use pythagorean theorem to determine the pixel density of 24" 1080p monitor and 27" 1440p monitor; the 27" has slightly more pixel per inch than 24", btw.
I've used the Pythagorean theorem often enough, helping people calculate how much cable they need for ham radio antenna guide wires. Very specific, but it helps them know how much or how large a reel they'll need, so they don't buy too much.
3:29 the absolute mathematician sheldonesque sarcasm makes it for me ❤
The Pythagorean therom is what carpenters use to keep your door straight and square, it's what's used to make sure ur walls are straight and square too. I use it alot when building something. Built a planter bed and used it, etc and etc
I'm still proud of the time I used the Pythagoran theorem to drill a hole through a wall, it was for a fiberoptics duct.
My co-worker just said sure go ahead, thinking it was just a waste of time.
So I did my measurements of the wall (thickness and drop to the target), did the math and marked of a point on drill (the drill was the hypotenuse) and then used a ruler to measure the distance of that point to the wall so that I got the right angle.
The triangle that I created with the drill and ruler was a smaller version of the triangle that the desired path was taking through the wall.
I nailed the target exactly, my co-worker just looked at me and said that we'll be using my method going forward 😅
the pythagorean theorem comes in handy in construction all the time! I can use the 3 4 5 rule to see if something is square for example