Mathematician Answers Geometry Questions From Twitter | Tech Support | WIRED

[@AustinJohnPlays]

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.

[@chesterotontop]

The only true use of the Pythagorean theorem

[@RunstarHomer]

@@chesterotontop unless you're an engineer, architect, scientist, mathematician, programmer, city planner, game developer, digital artist, etc etc etc.

[@estebanalcantara616]

Didn't expect to see AustinJohnPlays here but cool to see!

[@trinitrotoluene3D]

@@RunstarHomer He’s being sarcastic

[@darkfoxfurre]

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.

[@klausoshaunacey8429]

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.

[@Mark-wd5zb]

OMG THANK YOU SO MUCH FOR THIS RECOMMENDATION....One page in and I absolutely love this premise. It's so perfect.

[@nessamillikan6247]

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.

[@beckmsha]

Same goes for language and literature tbh. People tried to make language more interesting to learn by including pop culture and popular fiction, but it still doesnt capture the incredible nuance and thought/philosophy that goes into writing, speaking, and communication in general.

[@dotuvoidsynth]

​@@nessamillikan6247do you perhaps remember the name of said teacher? I'd love to check out more about her

[@rmg480]

I loved math and science, I hate my psrents for hitting me for not answering correctly, but I always knew it was them, I've always loved math.

[@Vaenivo]

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.

[@riesvanwijngaarden3417]

To be fair, he did miss the opportunity to proclaim that hexagons are the bestagons

[@thatrandomharpguy7564]

thats my uncle lmao

[@lucasm4299]

Why did you use “but” as though you were going to say something bad?

[@alan_davis]

​@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).

[@ElusiveTy]

@@lucasm4299 'But' is used to contrast or add something. I have to agree with Alan, they used the word because they have a better understanding of English. 'But' is very commonly used to mean 'as an aside', 'also', or 'additionally'. 'This was a wonderful meal, but I have to say the chicken was particularly excellent!'

[@robertalexander-bk5zj]

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.

[@SpitfiretheCat16]

actually, triangles are the divine shape

[@robertalexander-bk5zj]

Don't make me call RCE. lol

[@yxx_chris_xxy]

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.

[@PauloSousa86]

I think is simpler than that, you can really only put around 6 circles of the same diameter as the central one. In any circle diameter that happens. And what happens when you smash those sides equally together? You create an hexagon. Just check a box of straws and you will see that happen. Alas you can create a honeycomb filter for a light (that focus light) with straws inside a tube

[@hw7003]

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

[@3snoW_]

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.

[@colinwood9717]

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"

[@ima.ekenes]

I came here to say I use the Pythagorean theorem for sewing too! For me it's to make zero waste flaired skirts. 💃🏻

[@BrainBlaster11]

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

[@CraigKostelecky]

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.

[@rol1in0n20s]

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.

[@kaseyrolow]

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.

[@randallpetersen9164]

For sure. I was a bit disappointed at his glib and not particularly knowledgeable or intuitive answer. Makes me wonder about some of his other answers.

[@cankoklu]

Hexagons are bestagons

[@Majwt]

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).

[@ClonedGamer001]

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.

[@jw4985]

Wittgenstein says hello!

[@eric8764]

I mean, more of a topology question than geometry.

[@johnnythunders968]

I feel the same way about the question of “are we living in a simulation?”

[@hugomondoloni9808]

Y it s a question of définition In maths (topology) the straw has one hole cause it s fondamental group is isomorphic to Z

[@Zomgnomnom1]

​@@hugomondoloni9808Because literally everything you just said uses language. It's a language game. Every single person has different definitions of when it is 2 or 1 hole. Math is still predicated on language.

[@yaekmon]

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.

[@FHL-Devils]

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...

[@kingchickadee8694]

​​@@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

[@lourainevillalon3852]

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

[@kered13]

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.

[@matthewhale1572]

I qm an engineer and i use it all the time

[@TeEstoyMirandoDeCerca]

I feel that now I have a greater respect for straws. Thank you Mr. Jordan Ellenberg, it is incredible how you manage so much information to filter it into something simple, direct and with great humor

[@JoshBelville]

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. 🤣

[@MagatsuNimura]

This is precisely the only way I've used the theorem in the last 25 years hahahahaha. And quite often, I must say.

[@ccorvid]

saaame lol. til the dm reminds me that diagonals technically don't exist in dnd lol

[@obiwanpez]

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.

[@plazma5343]

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.

[@jensraab2902]

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.

[@brianjackson2733]

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.

[@mm9773]

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.

[@some-math-nerd6805]

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! 😊

[@redredred8408]

3.7111111111111111111111111111111

[@ilangated]

Pythagorean theorem is really handy for figuring out distances in D&D where all battles are on a grid

[@anonymousaxolotl]

Nice one lol I'll be using that now

[@stonedmountainunicorn9532]

This is like the sixth comment about D&D i'm reading, amazing

[@riotpaladin9764]

I just watched a 17 minute video about math of all things, and was entirely entertained by the presenter. Incredible.

[@EugeneEff]

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!

[@jpacklick]

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.

[@ccorvid]

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!

[@yxx_chris_xxy]

Agree. And this wasn't the only suboptimal description in this video.

[@fieryweasel]

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.

[@stevegonzalesjr6007]

I’ve never liked math but I love this man’s enthusiasm.

[@safariguy]

Love his enthusiasm for math and geometry!

[@14768]

This dude needs his own KZbin channel where he teaches math. So much more charismatic than any teacher I ever had.

[@iamspeare]

As an Army Sniper I used to do a brief/lecture called "How the Pythagorean Theorem Saved My Life." We use it in ballistics.

[@TheNaturalGamer1]

Send me the power point cuh

[@SARUMEOW]

Yea aight

[@davidm2.johnston684]

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.

[@friendlybello]

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.

[@cariboubearmalachy1174]

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.

[@nomadicyears3978]

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..

[@stephenmdalton]

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.

[@NandrewNordrew]

Thats exactly what the normal theorem is

[@kalentober-hammell1896]

@@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.

[@the_koschi]

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.

[@k-hersey]

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.

[@cleverclover7]

wait you might be right

[@averynicebean]

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.

[@bayleev7494]

​@@k-herseyperhaps 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.

[@the_koschi]

@@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!"

[@marshallc6215]

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.

[@theastuteangler]

is a bottle a bowl?

[@marshallc6215]

@@theastuteangler sure, seems a reasonable grouping

[@fulanoide718]

A balloon doesn't have a hole either?

[@marshallc6215]

@@fulanoide718 correct, it does not. A balloon that is not tied is a deformed disc. Holes cannot be created nor destroyed merely by stretching a shape. Balloons are just bowls with small necks.

[@JJean64]

​@@marshallc6215 You should definitely look into topology, it's basically the study of these "groupings"

[@rohinkartik-narayan7535]

"[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)

[@d4rkgriff1n3]

I'm pretty sure that proofs are common in exercises and tests for any undergrad level math courses lol

[@stephengreenberg1806]

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!

[@RomanNumural9]

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.

[@hughjazz4936]

Took me almost 10min to realise I own on of this guys' books. "How not to be wrong". Great read.

[@arothmanmusic]

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!

[@KittenOverlord]

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.

[@BobKimball]

That was the most clear and succinct explanation of gerrymandering I have ever heard. Incredible

[@afonsoferreira5835]

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)

[@xraygamer9895]

What is the fundamental group of the straw?

[@someguy1ification]

if you bend a straw too much, then it will have more holes and you won't be able to use it.

[@redshift0230]

​@@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.

[@RCG3.]

That's a lie it still has one hole in the top. A hole doesn't have to go completely through an object, if you have a hole punched into your car door on the outside, but not the inside you still have a hole in your car door

[@afonsoferreira5835]

@@RCG3. I'm not sure if I understood, but the car door has many layers and if you count each layer as an object you can have a hole that doesn't go through the whole door. The equivalent to the straw example would be a dent on the car.

[@Ninjaeule97]

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.

[@redredred8408]

3.6444444444444444444444444444444

[@JustGetitDoneQuilts]

I'm a quilter. I use the Pythagorean theorem almost every day

[@yxx_chris_xxy]

You also are an expert on knot theory, which is much deeper math than the Pythagorean Theorem.

[@dethbucketghostparanormalg5042]

5:24 the straw theory makes my brain short circuit!!

[@BeardedNerdSE]

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.

[@95rav]

A straw with one end closed, or a bottle, is just a disc with bent up sides, and NO holes.

[@goldkomodo26]

"Imagine someone with no sense of purpose." Me: Of course I know him, he's me

[@salislazy]

wired messed up not giving this poor mathematician his chalk and board 😭 on a serious note, what delightful communication skills this guy has

[@Sunflowersarepretty]

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.

[@travelsandbooks]

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.

[@laksitowp]

@@travelsandbooks I still don't understand it :(

[@yinjohn23]

How I think about shapes in 4 dimensions is by thinking about shapes in 3 dimensions, and hoping that similar reasoning carry over.

[@Fitzrovialitter]

5:52 You are changing the goalposts. If you pinch the bottom of the straw, it is no longer the straw as we understand it to be in your question, or what we commonly recognize to be a straw.

[@redredred8408]

3.3333333333333333333333333333333

[@victormanjarinsala2253]

Why hexagons? Why hexagons??? Well, because hexagon is the bestagon!

[@yeahitsscott]

The other ones just go on and on and onagon.

[@nexisle7508]

7:50 Because hexagons are the bestagons

[@drew3399]

This was really good he made geometry sound pretty dope

[@K_FI_L_Y_P_S_O]

Such a great episode. You should film a few more with this guy!

[@aqwaa3057]

Pretty sure he is the first non-german Person, that i've ever heard to pronounce the name "Einstein" 100% correctly. Neat!

[@rebeccamcnutt5142]

"Ein-shtein"?

[@yxx_chris_xxy]

@@rebeccamcnutt5142 Yes.

[@tarmo4435]

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.

[@vminhope3040]

When he said “imagine a person with no sense of purpose” I felt that

[@ANunes06]

Arithmetic - Here's a number line Algebra - The formal logical rules and language of math Geometry - Can you draw it in some logical way and then deconstruct that drawing into an algebraic expression? Trigonometry - Geometry is cool, but we're going to spend a year talking about just Triangles but secretly it's about Circles. Calculus - Turns out rates of change are related to measured values are related to total accumulation is related to rates of change. Hope you really learned that Trig stuff. Linear Algebra - Box of Numbers Means Everything Differential Equations - How well did you understand Calculus? Statistics - Look at this bell curve for a full semester Set Theory - You will understand Set Theory so well that it will hinder your understanding of everything else forever. Real Analysis - Nobody really knows

[@Dasyati]

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

[@vincevvn]

No you didn’t. You just walked across the street. You didn’t use any theorem at all.

[@ttmfndng201]

not really. you're just using the fact that the shortest distance between two points is a straight line (in euclidean space)

[@Dasyati]

@@ttmfndng201 phblttbtt Euclidean who? You'll never catch me using THAT daily :P

[@Flintstoned223]

bro is onto nothing😭

[@Monika-hw7ey]

no, you used the triangle inequality theorem if you walked diagonally for less walking distance. you would use the pythagorean theorem if you wanna know how much distance you walked and would have walked

[@Zzyzzyzzs]

Pythagoras's theorem manifests most simply in how we navigate. You can see it in action when you have a block that's an open field and most people, rather than walking two sides of the block, cut diagonally across it to meet the other side, because we intuitively know that is a shorter distance. And if you extrapolate that in wider space, what you realise is that we intuitively recognise that walking a series of hypotenuses (i.e. radial lines plotted against imaginary right angles) is actually the most efficient way to navigate, which is why, as much as rectangular city blocks seem like the most efficient use of space for building, neat squares and right angles are actually very unnatural to us and a radial city plan is the most efficient for travel.

[@rossbooth4635]

I absolutely love the "how many holes are there in a straw" question. As someone who routinely does CAD as a design engineer, my perspective is in the way I'd create it (two steps): 1) Create a cylinder. 2) Cut extrude a hole through the entire body. Done. One hole.

[@LoveFreak18]

3:06 "oh man the wife threw me out again" a few calculations later: a squared plus b squared, carry the one "oh shoot I forgot our anniversary again"

[@jersh69alex]

Topologically a straw has one hole and a bottle has 0 with the cap off and one when the cap is on your answer to the number of holes depends on how you define a hole if an open bottle has a hole because of empty space then a straw has 0 or 2 holes but if you define a hole as a complete hole all the way through a straw has one hole, an open bottle has 0, and a closed bottle has a different kind of hole

[@zoltanlukacs5059]

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

[@TorQueMoD]

I loved your straw answer! It shows that there are multiple ways to look at anything.

[@Pershath08]

I actually used the pythagorean theorem in real life! We built a shed in my backyard. Did this for each corner paver to make sure they were straight.

[@GatherYeRosebudsWhileYeMay]

3:29 the absolute mathematician sheldonesque sarcasm makes it for me ❤

[@acustomer7216]

Yay geometry!! The only math class that made sense to me!!

[@m.moonsie]

How about differential equations???

[@ericrosen6626]

RE: diameter / circumference always equals pi. Of course it isn't any different than any other regular shapes. An equilateral triangle's perimeter will always be exactly 3x it's width at it's widest point. A square's perimeter will always be exactly 4x it's width A regular hexagon's perimeter will always be exactly 3x it's width at it's widest point. A regular octagon's perimeter will always be exactly 8/(sqrt(4+2*sqrt(2))) of it's width at it's widest point. maybe that last one doesn't have a clever name like 3 or 4 or pi, but it is still a fixed value.

[@lptotheskull]

6:35 I find it pretty funny that we call it the golden "ratio" despite the fact that it is, almost by definition, *irrational*.

[@idlesquadron7283]

pi is also said as a ratio too (unless im missing something)

[@KuroroSama42]

2:50 How to use the Pythagorean theorem to solve a problem in your life? Simple: Build something. A shed maybe. Then put a corner beam as support. How long does that corner beam need to be? sqrt(a^2+b^2), where a and b are the 2 side it's connecting to. If your problem isn't solved by a shed, maybe you can build something else that might be able to use some kind of corner bracing.

[@BenjamintheTortoise]

This was a good one!! He's an excellent communicator and super engaging! Loved this ❤️😊

[@redredred8408]

3.4111111111111111111111111111111

[@yxx_chris_xxy]

@@redredred8408 pi-ish?

[@TheZanzaroni]

I am an engineer, and yes I use the pythagorean theroem to make the odd calculation but I use it qute more often in a much simpler form: If want to reach the other corner on a block and you may have 2 options: 1. Walk the sides of the square (block), or if possible 2. Walk straight diagonally If you call the sides of the square a, b and the diagonal c you can do some pretty simple math to prove that (a+b)^2 > a^2+b^2, or (a+b)^2 > c^2, or that if you have the chance to take the diagonal, you can walk less, saving time.

[@Kazutoification]

One hole, two openings.

[@Gimmickvr]

A donut has 2 openings?

[@obiwanpez]

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.

[@savitatawade2403]

binomial theore-

[@MartyD]

hated doing geometry proofs in high school 😅😢😂

[@ferryvantichelen6521]

When you pinch one end of the straw it has 0 holes. A hole is only when you go in one end and come out of another. Otherwise it's a dent. So a(n unpinched) straw has one hole, like a bagle, but unlike a water bottle that's not broken, that has a dent out of which you can drink. You also wouldn't say a bowl has a hole (although it sounds good).

[@NFITC1]

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.

[@RikFTK]

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?

[@BigOttomatic]

New application for Pascal's triangle learned. Cool. Only one I knew was coefficients for binomial exponential expansion

[@kingarth0r]

Jordan is type of guy to make easy exams and hard homeworks

[@JaxMerrick]

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.

[@MessinAbout80]

I’ve never heard anyone describe Euclid as “a guy who lived in North Africa” …

[@MartinHermans-dw3is]

maybe Greece was part of north africa?

[@v.heywood]

He was born in Egypt

[@JordonPatrickMears11211988]

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.

[@xliquidflames]

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?"

[@kvonation8852]

60° but I’m not understanding the joke or the ppint

[@duckymomo7935]

@@kvonation8852the triangle cannot exist in Euclidean geometry (flat surface)

[@metallsnubben]

@@duckymomo7935 I mean it's just an equilateral triangle?

[@sillyjellyfish2421]

To answer the pytaghorean theorem question - all the time if you are creating physical objects of any sort. The length of plants in furniture, the size, lenght and angles of big poles and thick planks while building a house. The length of fashion trim needed for finishing sewing a skirt. The geometry and math is used in seemingly mundane blue collar jobs and houseworks like calculating the amound of wall surface of a room so you know how many cans of paint you need to paint it, aproximating the amound of fabric tou need to cover a sofa of some particular shape, ordering the correct amound of concrete to pour into your driveway. Stuff like that all uses geometry and angles and equations for surfaces and volumes and plenty of people use those every day

[@cappuchino_creations]

Hexagons are the Bestagons and Bees know that

[@dmscholl4]

Just rewatched that video the other day

[@bradypostma3708]

The discovery of the hat and the specter - the aperiodic monotile (and its reflection) - is a great example of a newly discovered shape.

[@arablues4142]

A straw has 0 holes, its just a warped plane

[@internetcutie]

a warped plane that formed a hole by definition

[@Bangin0utWest]

The dictionary says a hole is a small and unpleasant place 😂😂

[@arablues4142]

@@Bangin0utWest 🤣🤣🤣

[@Bangin0utWest]

@@arablues4142 so a straw IS a hole 😂😂

[@elemenopi55]

@@Bangin0utWest so donut holes are a lie and a donut is actually already a donut hole?

[@RaDeus87]

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 😅

[@BobSmith-fx9sz]

5:09 The straw thing just depends on your definition of a hole. If you define it as an opening through something, like a hole in your shirt, then a straw has only one hole. If it doesn't need to perforate, if a pit in the ground is a hole, then a straw has two holes. This probably rifts off the word 'hole' having confusingly similar but strictly different meanings in language and in maths.

[@septictopix4797]

I disagree. According to the dictionary, a hole is 'an opening through something" or "an area where something is missing". Since a straw is simply a tube (a bent plane whose edges meet), the continuous surface of it has no openings or areas where anything is missing. If it did, you wouldn't be able to create a vacuum. Therefore it has zero holes.

[@MrBLAAHHHHHHHHHHH]

The Arithmetic of Holes sounds like something Lisa Ann would star in.

[@davedavem]

Breaking 5700-year-old news: the first answer is wrong. Archeologists have just translated (December 2023) a Babylonian tablet and it turns out it's a trigonometry table. About 3000 years before Euclid and Pythagoras.

[@12thDecember]

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.

[@johns1625]

7:17 AHH I hate when people do this! The shell is not the same shape at all and you can tell by looking at it lol. The ratio only has two curls and the shell has like five. Even with succulents people try to show that nature produces this "golden ratio" and all of them are just a swirl pattern.

[@christopherjaya342]

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.

[@sho3782]

I swear this guy sounds like Khan Academy

[@volbla]

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.

[@BruceCinema1337]

6:00 How many holes in a bottle? Topologically speaking there are 0 holes.

[@RitzBitz13]

So Pythagorean Theorem i used to say the exact same...where am i gonna use this ever, but being an electrician, when i was running pipe if i had an offset to make and i was making 45 degree bends, i could get the length between bends and it would fit every time perfectly

[@violetsparklez1191]

Why do bees use hexagons? Because hexagons are bestagons

[@RecklessFables]

He really dodged that question but probably because it is a physics question, not a geometry question.

[@RonJohn63]

2:53 Use the Pythagorean Theorem (and the angle-side-angle geometry theorem) to determine the height of a tree. That's very useful if you want to know if it'll fall on your house. 5:05 There's one hole, and *two circles.* 15:57 Asked by a Flat Earther?

[@Tesh2Geeked]

12:50 I deadass stopped the video to play some Tetris lmao

[@SteveBakerIsHere]

Hypercubes are used "for real" in many applications. In computer graphics we have chips that connect to four other chips...so if you connect up a lot of these chips to get more and more performance - you place them at the vertices of a hypercube.

[@PatrizzaEatsApizza]

6:17 top hole and bottom hole ( ͡° ͜ʖ ͡°)