A Truly Crazy "Right" Triangle

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In today's video, I'm tackling the fascinating equation "π^4 + π^5 ≈ e^6" and bringing it to life through geometry. I'll show you how I turn this abstract mathematical statement into a tangible geometric figure - almost a right triangle with sides of π^2, π^(2.5), and a hypotenuse eerily close to e^3. Using Pythagoras' theorem as my guide, I dive into the relationship between π and e, dissecting how these transcendental numbers interact in a geometric setting. We'll walk through the algebra needed to morph our initial equation into this geometric wonder, all the while understanding the precision and boundaries of such an approximation. It's a journey from the realm of algebra into the visual world of geometry, shedding light on the intriguing dance between π and e. With great thanks to John Cook who first introduced me to this approximation. You can find more of his work here: www.johndcook.....
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Опубликовано:

7 сен 2024

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Комментарии : 740

@ReformationRamblings 7 месяцев назад

The betrayal when you said it was just an approximation.

@polymathematic 7 месяцев назад

😬😬😬

@liambohl 7 месяцев назад

I will sleep better tonight knowing that it's only an approximation and that e and pi aren't really related in such an inexplicable way

@karpholmes6942 7 месяцев назад

@@liambohlEuler would like to wake up up e^(ipi)=-1

@sophiophile 7 месяцев назад

@@karpholmes6942 Euler's Identity is not inexplicable at all, though. It is literally the most basic statement that allows a first glimpse into the very rudimentary facts of the complex plane as a basic case of Euler's formula. The inexplicable stuff is all the other crazy ways you can derive e and pi, (especially all the weird kinds of nested self-similar relationships for e)- at least to my feeble brain.

@janisir4529 7 месяцев назад

It should have been obvious.

@petrsvetnicka7620 6 месяцев назад

Cool aproximation! I personally use this one: π = e = 3

@mathijskraan3606 6 месяцев назад

Finally, someone! 🎉

@taijmohabeer4515 6 месяцев назад

fundamental theorem of engineering

@hydroarx 6 месяцев назад

I prefer 3=π=e=2

@pandabearguy1 6 месяцев назад

In a based system of units they are all equal to one.

@lirich0 6 месяцев назад

@@hydroarxI prefer pi = e = 3 = 1

@sophiophile 7 месяцев назад

You had me excited that there would be some beautiful underlying relationship that made the relationship exact.

@polymathematic 7 месяцев назад

Just a weird coincidence as far as I know!

@Chewy427 7 месяцев назад

how do we know it's NOT analytically true? deamos doesnt have infinite precision

@polymathematic 7 месяцев назад

@@Chewy427 that's true, but it has enough precision that we can use law of cosines to solve for the angle and see that, although it's very very close to 90º, it's off by roughly 0.000003 degrees. more precision in π and e wouldn't recover that value.

@Chewy427 7 месяцев назад

@@polymathematic perhaps, but honestly using the law of cosines doesnt seem to do anything except introduce more chaos? 180*arcos((pi^4 + pi^5 - e^6) / (2pi^4.5) ) / pi

@Chewy427 7 месяцев назад

@@polymathematic To prove they are not equal we would need to use different levels of precision and show that they diverge instead of converge, law of cosines does not help at all

@mrildsilva9885 7 месяцев назад

Finally, the wrong triangle

@MattMcIrvin 6 месяцев назад

a Parker triangle, if you will

@joaowiciuk 6 месяцев назад

Underrated comment 😂

@KindlyKalen 6 месяцев назад

A left triangle.

@Bhuvan_MS 6 месяцев назад

Lol

@_Aniket. 6 месяцев назад

Haha 🎉

@KaramAlayan 7 месяцев назад

My teacher : "prove that this is a right triangle" Me : "its obvious look at it " Teacher : "no its 90.000003 degrees"

@ismo11 7 месяцев назад

Engineer: This is closer than right angles in this 100 story building I built.

@SynoPTL 6 месяцев назад

Correct number of zeros, guau

@GustavSvard 6 месяцев назад

The earth isn't flat. So the curvature of the earth make it a right triangle (if you make the units of length fit this idea - and I will leave figuring that out to you dear readers)

@pyglik2296 6 месяцев назад

@@GustavSvardI know this is a joke, but the angle is slightly bigger than 90 degrees, so to make it a right angle we would need a hyperbolic (negative curvature) surface and a sphere has positive curvature and would make the angle bigger. Of course the Earth isn't a perfect sphere and has some negative curvature in places and it's such a small difference that only a small bend would be enough and the global shape of the Earth doesn't matter and why am I overthinking this?

@michaelwicker9538 6 месяцев назад

@@ismo11 That's why mathematicians are a breed ask their own.

@Jar.in.a.Bottle 6 месяцев назад

Yes!, we are getting closer and closer to the true 'Pi' and 'e' relationship, which we already know would be very straight forwardly named "Pie" if it is ever found.

@polymathematic 6 месяцев назад

Lol

@deltalima6703 5 месяцев назад

Need to fit the speed of light in there too, then it will be epic

@ky7299 5 месяцев назад

I believe Leonard Euler named the equation e^iπ + 1 = 0 "Kuchen". 😶

@kaibalonek2916 5 месяцев назад

@@deltalima6703And alpha, the fine-structure constant, which is painfully close to 137 without actually being 137.

@paulgoddard7385 5 месяцев назад

exp(i*pi)+1=0

@GregBetz2010 7 месяцев назад

“I am not a sane person, I am a math teacher” is the most accurate thing I’ve heard

@wyattstevens8574 7 месяцев назад

Me: *hears this statement* My brain: *Exactly*

@snared_ 7 месяцев назад

if you can't comprehend any amount of basic math you might not be sane.

@snared_ 7 месяцев назад

and you don't wanna know what I consider "basic"

@tacotuttle 6 месяцев назад

@@snared_..what? how is this replying to the comment?

@yajurraghavan4193 6 месяцев назад

@@snared_ I consider anything RIGHT UP UNTIL calculus as basic. introduction to calculus with class 11 and 12 are just moderate. advanced come with competitive entrance exams.

@randys2669 7 месяцев назад

"I'd rather multiply my final answer by 180/π than sully a calculator by switching from radians to degrees" is a mood

@polymathematic 7 месяцев назад

lol, exactly

@jlindo9326 7 месяцев назад

lol what does this even mean

@ilikememes1402 7 месяцев назад

Degrees and radians. We have 2 measurements for angles. @@jlindo9326

@Shtikface 7 месяцев назад

@@jlindo9326in a calculator there are different modes for calculating angles. Most commonly used are degrees and radians, to switch to either one you simply tap a few buttons but that could be troublesome at times or if you're just lazy. Inputting 180/pi to convert your answer in radian to degrees or pi/180 from degrees to radian is so much faster if it's only for a couple of calculations. However if your entire problem requires you to use radians, it's better to just switch the modes as its more time consuming to not do so.

@xaniyat9491 7 месяцев назад

@@jlindo9326probably talking about everyone multiplying by 180/π to convert radian into degree Instead of just pressing a button on the calculator which does it automatically , and more quickly

@pastaplatoon6184 7 месяцев назад

Bro, that approximation broke my lil heart.

@polymathematic 7 месяцев назад

sorry 😬😬

@nguyenvu8262 2 месяца назад

If you know irrational, that should never been believable to begin with. But so damn close.

@aritrabiswas752 7 месяцев назад

"I am not a sane person. I am a math teacher." And I sent it to my math teacher.

@polymathematic 7 месяцев назад

ha!

@samparkins6268 6 месяцев назад

To clarify to anyone wondering, this triangle has no relationship with e^i*pi = -1 and is a complete coincidence.

@Walczyk 4 месяца назад

what are you talking about? that relationship wasn’t implied anywhere.

@Walczyk 4 месяца назад

and no i doubt this is just a coincidence, but a deep near perfect number like ramanujan’s sqrt(163)

@davidgillies620 7 месяцев назад

This is just a coincidence, of course. However, the fact that exp(pi sqrt(163)) is within about 1 part in 10^29 of being an integer is not a coincidence, but a rather deep result in number theory.

@cubing7276 6 месяцев назад

any links for further reading?

@davidgillies620 6 месяцев назад

@@cubing7276 That depends on how deep you want to dive. The number 163 arises because it satisfies a certain condition in the theory of modular forms, which are analytic functions defined in the top half of the complex plane. Specifically the condition is that the _j_ invariant of (1 + sqrt(-163))/2 is an integer. This is postgraduate-level number theory, I'm afraid. You could start with group theory, representation theory and complex analysis before moving on to modular forms, which is where this result lives.

@btf_flotsam478 6 месяцев назад

@@cubing7276 Look up Heenger numbers, it's a start.

@camilogallardo1003 6 месяцев назад

@@cubing7276 look up Heegner number in wikipedia. It's very neatly explained there and quite accessible

@camilogallardo1003 6 месяцев назад

@@davidgillies620bro youre just flexing now, dude asked for some info dont scare him away from this amazing result, even if its deep (its true though that you need all that to further your understanding)

@SpaceOutlaww 7 месяцев назад

I paused the video, took the natural log of both sides then realized i have nothing and let the video finish

@alphazero339 6 месяцев назад

_💀_ good job bro

@M42-Orion-Nebula 3 месяца назад

You did more than me 💀

@peterwiphle1860 6 месяцев назад

Never betray us like that again.

@AB-zk4mk 5 месяцев назад

Him: if you saw this, what would you do with it? Me: cry

@wilurbean 6 месяцев назад

As a physicist, tell the mathematicians to go outside and be quiet until they're needed

@DonkoXI 5 месяцев назад

As a mathematician... fair enough.

@mrildsilva9885 7 месяцев назад

Finally, the approximately right angle triangle

@wyattstevens8574 7 месяцев назад

I think the term you're searching for is "Parker right triangle."

@bilingualistic8514 5 месяцев назад

The left triangle

@robertstack2144 5 месяцев назад

Yes, engineers use these approximations. It was used in the Tacoma Narrows bridge design

@tisajokt7676 3 месяца назад

Thought I was losing my mind, no way two transcendental constants would be related in such a way, was so relieved that it was only an approximation!

@madisonlink7141 7 месяцев назад

The first thing *I* did was look at it suspiciously and throw it into my calculator to determine that it was 1.7674E-5 off, which is well within the precision limits of my calculator.

@BooBaddyBig 7 месяцев назад

Your calculator should be more accurate than that.

@STEAMerBear 6 месяцев назад

This is why I DESPISE numerical approximations when dealing with irrationals. The fact is that even a billion digits of precision merely increases the probability of something that either is or is not true. We have exact definitions of both pi and e which will give us digits for ad long as we’d like. Just to make that point, WolframAlpha just gave me a difference of -1.9847129977756085212932242665220179954 × 10^-8 from e when I bumped up the precision once. I wonder what it is if the computation is precise to a million places!

@BooBaddyBig 6 месяцев назад

@@STEAMerBear I mean, yeah in theory, but in this case that number is probably almost right. Calculators generally work in floating point and are correct to up to 12 significant digits of accuracy. I think about 5 of those digits should be correct in this case.

@STEAMerBear 6 месяцев назад

@@BooBaddyBig interesting point. I’d still like to solve it abstractly or maybe toss it into a CAS to see if it can be solved exactly. Is it actually close, or is it exactly what it seems to be?

@jeromesnail 3 месяца назад

A Parker right triangle

@JoeyCakes2008 2 месяца назад

lmao

@JoeyCakes2008 2 месяца назад

Lmao

@tay-lore 6 месяцев назад

Thank goodness! I thought these numbers were about to do something rational!!

@polymathematic 6 месяцев назад

Lol

@Kaepsele337 6 месяцев назад

It's clearly not exact. I can prove it by the "If this was real I would have heard of it" Lemma.

@isaacdeutsch2538 6 месяцев назад

I was gonna say "that can't be true because then π and e would be algebraically dependent, with π being a root of a polynomial over Q(e), but that's an open problem" and then I finished watching

@maelhostettler1004 7 месяцев назад

Ive actually dug into it by representing f(x) = (4 arctan(x))^4 + (4 arctan(x))^5 - e^(6x) as a power serie...it's stupid but shows that it's an approximation

@MrMelvinSchlock 3 месяца назад

If it’s close it’s a conference.

@Lord_Baphomet_ 6 месяцев назад

“What do you mean that’s not a right triangle Terry?…. What… do… you… mean…” “Don’t be obtuse David” “I bet you think you’re being acute” “David… don’t make me go over 180 degrees…” “BLASPHEMY! YOU WOULDN’T DARE ANGER THE GREAT ISOSCELES!” “Maybe we should take a break” “A squiggle?” “…David…” “Sorry, yeah let’s go”

@polymathematic 6 месяцев назад

lol

@Rio-zh2wb 6 месяцев назад

lmao

@Real_Beaky 7 месяцев назад

One of those cute little oddity equations

@HeyKevinYT 7 месяцев назад

yeah just like π = e

@Real_Beaky 7 месяцев назад

@@HeyKevinYT I meant more like the "3, 4, 5 perfect right triangle." Pi is 3.14... and e is 2.71... those are not equal.

@PotassiumLover33 7 месяцев назад

@@Real_Beaky approximately equal 👍

@Real_Beaky 7 месяцев назад

@@PotassiumLover33 not really close... you can use 22/7 and pi to approximate each other, but not e.

@RigoVids 7 месяцев назад

Not an equation tho 🥲

@servetyildiz4318 3 месяца назад

This is a triangle that I discovered before this video and I can prove it.

@user-su3qr6zc6q 4 месяца назад

this teacher is great

@davidtitanium22 6 месяцев назад

Transcendental numbers are so mysterious i almost just believed that the equation is exact

@Tletna 5 месяцев назад

Something felt wrong on the equals, but when I tried it on my dumb default calculator it looked equal, so I was thinking to myself "huh?" and then you showed it's just close and I thought, wow, that's close.

@reinymichel 4 месяца назад

Ahhh, the "Approximately Right-Angle-Triangle Theorem" !!

@tejasbr5455 3 месяца назад

now thats a wrong triangle

@zerocat888 3 месяца назад

Introducing the wrong angled triangle

@carultch 18 дней назад

Sorry I'm late. I took the rhombus.

@jameshogge 7 месяцев назад

"You being a sane person would probably do nothing" No, I had just cracked out Leibniz formula for pi and equivalent series for e to try and verify this. Glad I didn't pause the video at that point

@ethanbottomley-mason8447 7 месяцев назад

Conjecturally, there is no polynomial in pi and e which will ever give 0, i.e. pi and e are algebraically independent. So there is no way this would be true.

@btf_flotsam478 6 месяцев назад

@@ethanbottomley-mason8447 The conjecture isn't necessarily true.

@ethanbottomley-mason8447 6 месяцев назад

@@btf_flotsam478 I agree, but I would be absolutely shocked if they are not algebraically independent.

@revimfadli4666 6 месяцев назад

Petition to call this wrong triangle

@Nought_8 5 месяцев назад

"I am not a sane person I'm a math teacher " -Polymathematic A quote applicable to math teachers everywhere.

@Awkwerp 7 месяцев назад

"what would you do" idk, theres not really an unknown so Id just plug it into a calculator to see if its true, then if so try to find why (and end up seeing its not, just coincidentally close, which is the expected result from comparing those two irrationals)

@priyanshugoel3030 7 дней назад

Okay so here goes my understanding of it. Slope is dy/dx Hence if slope is < 1, Let k=0 While(x1 {K-=1 Y++}

@priyanshugoel3030 7 дней назад

Like a cup and a bucket,where the bucket's volume is not an integer multiple of the cup,without spilling a simple drop of water you can fill the bucket, after say n cups, with a bit left in the cup then you empty the bucket then start over.

@dmitrygerenrot9765 3 месяца назад

And you put the equals sign instead of "approximately equals" because...

@maxallen218 3 месяца назад

Because that equation would loose audience retention

@alogentforbin7190 3 месяца назад

... it puts butts in seats.

@somsackvongsa7077 3 месяца назад

Made up math.

@CliffSedge-nu5fv 3 месяца назад

Because clickbait baits clicks.

@mtaur4113 6 месяцев назад

Like I know they're transcendental, but that doesn't automatically preclude P(e,pi)=0 for some non-zero polynomial P. I suspect that P doesn't exist though.

@JuanGarcia-qd8ig Месяц назад

Listen, I'm just happy because I understood.

@artix315 6 месяцев назад

I am not a math teacher, nor a sane person, I am AN INSANE STUDENT!

@theatheistpaladin 6 месяцев назад

Ha! That means a goat can still climb up on that wall.

@pipgoodman2164 3 месяца назад

Is there known to be a good reason why these numbers are so close? I'm thinking something equally satisfying as to why e^(pi *sqrt{163}) is almost an integer.

@polymathematic 3 месяца назад

there is sometimes, but in this case, i think it's genuinely just a coincidence.

@user-cg7gd5pw5b 7 месяцев назад

I FEEL like I must ask. If the end process is to send it into a calculator anyway, what is the point of the first part of the video??

@polymathematic 7 месяцев назад

knowing that something is very nearly a right triangle is different from knowing just how "very nearly" we're talking. the calculator demonstrates how truly close the relationship is.

@vaderires 7 месяцев назад

@polymathematic I think the point of the question was: if we can throw the original equation at a calculator and see that it is very close, what new information do we get from mixing in the Pythagoras theorem? Is the point just visualize an equation that has nothing to do with Pythagoras or triangles as a triangle? If so, I can think of better visualizations...

@ignantxxxninja 7 месяцев назад

@@vaderiresthere’s no proof here. It’s just a relationship and I think the whole point was to look at something that was discovered that’s interesting. The approximation is nearly equal, and maybe some mathematician might find a way to utilize it.

@JaceGameplay 6 месяцев назад

@@ignantxxxninjawell, to be fair it's a counterexample that proofs that the conjecture is false. Could be more rigorous but it's enough as a curiosity.

@Fire_Axus 6 месяцев назад

your feelings are irrational

@Sen-ki- 4 месяца назад

"I am not a sane person, I am a math teacher" Truer words have never been uttered

@cufflink44 6 месяцев назад

Wow. A math short that is actually interesting . . . in fact, astonishing. I'll never forget that approximation.

@JohnRandomness105 5 месяцев назад

The first thing I did was to check it. Yes, the two expressions are equal to about eight significant figures. If you want a shape that approximates a square, but has exact integers for both sides and the hypotenuse, use 20x21. 20² + 21² = 29².

@h2ogun26 Месяц назад

kinda relieved when i get to find out it is eventually approximation

@ChristopherKing288 5 месяцев назад

It's conjectured that pi and e are algebraically independent, in which case all such equations are false. Finding an equation like this that is exactly true would resolve the conjecture!

@herambsharma7408 6 месяцев назад

THE BETRAYAL AT THE END !!!

@polymathematic 6 месяцев назад

😬😁

@TranquilSeaOfMath 7 месяцев назад

I might not be seen as normal; I'm a mathematician. I would want a proof, or possibly try to produce one. Possibly look into the expression and its background. This reminds me of the Simpson's where they show a counterexample to Fermat's Last Theorem. You did a nice job presenting this.

@Lybinyx 6 месяцев назад

I am so happy you changed that equals sign to an approximately equals sign at the end because I was about to throw hands when I saw that equation

@Rev3rse_PL 4 месяца назад

"Im not a sane person, im a math teacher" Best quote from a teacher i heard in a while😂

@Ciofey 3 месяца назад

Have you tried to evaluate the McLaurin series for each term and see at which polynomial degree it begins to deviate from equality?

@polymathematic 3 месяца назад

i have not! sounds like a fun exercise though

@colinjava8447 6 месяцев назад

I knew instantly that was wrong, but cool how close it is.

@nmg1909 4 месяца назад

I would have jumped the question😂. Thank you, prof.

@ALeafOnTheWind42 6 месяцев назад

I spent the entire first half thinking "show me the proof of this identity, cause I'm suspicious". Glad my intuition wasn't wrong

@Notthatkindofdr 4 месяца назад

This is so cool! I have never seen this coincidence before. Both sides are equal to 403.4287...and have a relative error of about 1 part in 23 million.

@lightyagami1752 6 месяцев назад

It's a nice approximate identity. The algebraic independence of e and pi has not actually been proven though, so it is an open question whether a polynomial identity involving the two can actually be constructed.

@huawafabe 5 месяцев назад

That's a great approximation :) What about e^pi - pi = 20? Can we do something similar there?

@polymathematic 5 месяцев назад

that's another killer! though i think that one has been shown not to actually be a coincidence, but to come from an infinite series.

@huawafabe 5 месяцев назад

@@polymathematic oh really, I didn't know that! Can you make a video about it?

@1nfius948 7 месяцев назад

A moment of silence to the people who thought they had to solve for e

@logic_nuke4034 5 месяцев назад

I briefly tried to figure out if this could be exactly true somehow and then I realized if it were it would disprove Schanuel's conjecture and I would have definitely heard about it if that had happened.

@kevinlago1619 7 месяцев назад

“I’m not a sane person, I’m a math teacher.” - A math teacher

@gabrielbarrantes6946 4 месяца назад

As a mathematician I immediately knew it wasn't an "="...

@carultch 18 дней назад

As an engineer, I immediately knew it wasn't equal as well. It smelled like a near miss to me.

@gabrielbarrantes6946 10 дней назад

@@carultch you have good math foundations.

@DLTyrus 5 месяцев назад

I'm just gonna take your word for it bro.

@polymathematic 5 месяцев назад

fair enough :)

@Ameya837 5 месяцев назад

Technically, any three positive real numbers inn the form x + y = z can be shown as pythogorean triplets.

@polymathematic 5 месяцев назад

yes!

@ciangrant3042 5 месяцев назад

The amateur Galois theorist in me was so excited for a very short time...

@astroorbis 7 месяцев назад

Animation vs math prepared me well

@CybernetonPL 21 день назад

Me drawing the almost right triangle on a math test. And calling it right angled. My math teache: you failed

@IlTjaylI 7 месяцев назад

Love your content! I watch this stuff in my free time (before I go to bed). 💀🙏🏽🔥

@polymathematic 7 месяцев назад

awesome! i hope i help put you to sleep, but not too fast :)

@raphaelguerin2691 7 месяцев назад

I have one for you that might not be as cool as this but I find interesting : the sum of the arithmetic sequence Un = 2n -1 from n=1 to n=k equals k^2 for any k >= 1

@andreasxfjd4141 4 часа назад

I didn‘t expect that it is so close: π^4+π^5-e^6= -0.00001767…

@adenwellsmith6908 3 месяца назад

I'd get the calculator out. I'm a comp sci bloke

@dmitrygerenrot9765 3 месяца назад

That's the thing to do with a video like this. By a math teacher's standard, this is a catchy headline, which gets you to watch the video, only to find an admission that it isn't, strictly speaking, exactly true. By mathematician's standards, that means false, nonsense, BS.

@dmitrygerenrot9765 3 месяца назад

And with a calculator, you would still need to exercise a little care to make sure that the discrepancy you are seeing is real, and not a piece of round-off nonsense.

@gustavoaroeira7329 6 месяцев назад

Thank God it's just an approximation... I wouldn't be able to live thinking that exact tradition was just a coincidence

@milehighslacker4196 5 месяцев назад

now, when I am laying a string grid for the foundation on a construction site, I will measure down one string pi^2, down the other string pi^2.5, then verify the strings are square by measuring diagonal to the points and checking for e^3 !!!

@Daniel_Ping 7 месяцев назад

"I am not a sane person, i'm a math teacher"

@wwl1952 6 месяцев назад

the ratio is 0.999999956, as an engineer, i agree they are equal

@xinpingdonohoe3978 3 месяца назад

So many people here don't know π and e are algebraically independent. We could have some fun with this on the street.

@carultch 18 дней назад

It is still unknown whether simple arithmetic combinations of pi and e are even rational numbers. We know that at least one of pi*e and pi+e must be irrational, but for all we know, we don't know which one is, or whether both are irrational. Likewise, we don't know whether either pi - e or pi/e is irrational, or if both are irrational. Occam's Razor would lead us to strongly suspect that all four of these combinations of pi and e are all irrational and transcendental, since there's seemingly no reason why any of them should be either rational or algebraic.

@algorithminc.8850 3 месяца назад

Fun one. Thanks. I look forward to scoping your channel. Subscribed. Cheers

@polymathematic 3 месяца назад

thank you!

@tomctutor 5 месяцев назад

Proof: Divide through by pi^4 and rearrange 1 = e^6/pi^4 - pi^2 LHS= rational, RHS = irrational.

@integrantedavidanoturna 7 месяцев назад

Engineers be like: I don't see a difference

@onradioactivewaves 7 месяцев назад

π⁴=100

@AlphaAnirban 2 месяца назад

*THE AMOUNT OF SHEER DISAPPOINTMENT WHEN HE SAID "APPROXIMATELY"*

@aivydenniselegaspi4435 3 месяца назад

"If you saw this what would you do with it" Nothing

@DoubleBob 7 месяцев назад

And then he went crazy by asking "but why?"

@ekeebobs7520 6 месяцев назад

You had me in the first half not gonna lie.

@qqqquito 5 месяцев назад

It is amazing that it is so close to equality. Who discovered this relation?

@polymathematic 5 месяцев назад

i don't know! i saw it in a social media post, and i think it's also listed in the wikipedia page for mathematical coincidences.

@qqqquito 5 месяцев назад

@@polymathematic Many thanks for the information!

@ralfbauerfeind8236 25 дней назад

Which precission of π and e did you use to calculate the resulting "90 degress angle"?

@sarandip 4 месяца назад

So, sane ≠ mathematicians

@MichaelRothwell1 6 месяцев назад

Nice video! Just in case anyone is wondering, it is not yet known whether there is a polynomial relationship (with rational coefficients) between π and e. For example, it is not even known if π+e is irrational. I expect most mathematicians would expect π and e to be algebraically independent (i.e. for there to be no polynomial relationship between them with rational coefficients). It is just really hard to prove these kinds of things. See en.m.wikipedia.org/wiki/Algebraic_independence#Algebraic_independence_of_known_constants or do a search on: Are pi and e algebraically independent

@johnbofarullguix1499 5 месяцев назад

and this is a good example why I got an engineering degree .. because it takes so so much time for theoretical people to get to the point, that humanity would still be wondering how to start a fire.

@polymathematic 5 месяцев назад

you're talking about a video that lasted one minute long. maybe recalibrate.

@plant3341 7 месяцев назад

I genuinely dont think id been able to cope if it was a true equality

@math_Nerd-nt2gb 6 месяцев назад

I saw this and went "that's most definitely not true, its just an approximation"

@-ShootTheGlass- 3 месяца назад

….”and THAT is how the pyramids were built.”

@BaptistPiano 3 месяца назад

I’m offended by the insinuation that I am a sane person

@mattnicholson6362 Месяц назад

The exponent in the denominator should be 9. You used Law of Cosines to solve this, and A*B should be pi^4 * pi^5 = pi^(4+5) = pi ^9 Correct me if I am wrong

@joshuachan6317 6 месяцев назад

Would the error be caused by some floating point error, and it is actually a right triangle?

@thatchrisguy188 7 месяцев назад

"I am not a sane person, I'm a math teacher." Fellow math teacher here. I felt that.

@brandonpurvis3878 7 месяцев назад

Soooooo…. It’s a lie?

@Im.Yer.Huckleberry 7 месяцев назад

That depends on how nitpicking you're attempting to be. Purely objectively, as in its inaccuracy needing to be measured in millionths is enough to disturb your obsessive need for perfection? Still no. Inaccurate, but not a lie. Very, very few agencies operate past the 5th decimal. For all intents and purposes, it's accepted as true.

@fahrenheit2101 7 месяцев назад

@@Im.Yer.Huckleberrythere are no intents and purposes anybody's using this tho. Trying to apply a practical mindset to a very niche impractical problem isn't extremely convincing. Personally I'd say the only folk even remotely interested in things like this would be more pure mathematicians, and to them the distinction is everything.

@user-jn4sw3iw4h 7 месяцев назад

@@Im.Yer.Huckleberry A non-engineering math problem Explicitly presented as a "no practical use, just pretty"-thing. on a math-channel. That turns out to be *not* as pretty *as presented* where the actually accurate statement can be obtained by changing a single character, refused *explicitly* for the purpose of drawing in mathematicians, with a mathematical falsehood. Which when called out, gets defended by ripping it completely out of context..... So yes: a lie.