*Still looking for a way to store your millions of Pure Maths Major $ ? :^D* Big thanks to Ridge for sending me this wallet and supporting the channel! Here’s the site if you want to check them out! www.ridge.com/PAPAFLAMMY Or use the code PAPAFLAMMY at checkout
I immediately thought about the theorem you mentioned but I then thought of another pretty way to see it: going from a line to its perpendicular is a symmetry. We’re exchanging the roles of x and y here (actually, not quite, the y axis is exchanged with a line parallel to the x axis at height (b1+b2)/2) which is why the slope gets inverted (since the slope is (Delta y)/(Delta x), it becomes (Delta x)/(Delta y)). The axis of symmetry then goes through the middle (b1+b2)/2 and the intersection point. As a changes, you get an axis of symmetry for every possible direction. The only shape which is symmetrical with respect to every direction is a circle. QED
In India, the equivalent of this Thales' Theorem which you explained at 17:03 is stated as follows: ' The angle in a semicircle is a right angle.' Quite interesting how one theorem has different names in different places.
Another nice thing about perpendicular lines: Start with the graph of x^2. To multiply a*b, go to A(-a|f(-a)) and connect it to B(b|f(b)). The crossing point of AB with the y-axis is at y=a*b (You have to find the perpendicular lines yourself:)
Thales Theorem's proof using Analytical Geometry is quite teduous compared to it's proof using Classical Geometry.If you use classical Geometry, it's an absurdly small proof xD It's as simple as this:- Angle at the circumference is subtended by the diameter And the angle subtended by any arc at the centre of the circle is double the angle subtended at the circumference. Angle subtended at the centre by the arc=180° Angle subtended at circumference =180÷2=90 Done
Yes but line 2: " the angle subtended by any arc at the centre of the circle is double the angle subtended at the circumference." is just as unintuitive as the initial theorem to prove. So to be fair you need to prove this too, making the proof significantly longer. But Wikipedia is your friend here.
@@richardbloemenkamp8532 i dont think it's intuitive at all... actually it's quite intuitive, and it has a pretty small proof too. But why should I prove it? I mean if you see this video, Flammable maths has used pre-defined theorems as well. So I took the privilege to do that too. Please do reply and tell me where I'm going wrong bud, I would love to correct myself
@@johubify The proof of every theorem is simple if your start from one or a few other pre-defined theorems or equations close the end of the proof. Simplicity depends on the knowledge you start from. To me the derivation by Flammable maths is at least as simple as your geometric analysis. His calculus is straightforward to me requiring no special insight/thought.
@@richardbloemenkamp8532 you do have a point, and I'm more of an Analytical Geometry person myself. But still, someone new to Analytical Geometry might question that why is the equation of the circle taken to be (x-h)^2+(y-k)^2=r^2 . There are always prerequisites to proofs, so I wrote the proof assuming the person has a certain background in classical Geometry. Do tell me where I'm going wrong
@@richardbloemenkamp8532 but yes I do agree with you It's always better to stumble upon the proof by intuition and simplicity, than using pre-defined theorems and formulas
9:55 "Foci": You are literally the first youtuber actually using the right plural of "focus", even though you are german. So you could say that you are better in english grammar than actual english people. lmao
its not about english, literally the same thing applies in latin, which is commonly used in many european languages. most words that end in -us are -i in plural, but technically you'd have to use other cases es well, which english doesn't support
Mmm always gotta love the Dark Cloud 2 soundtrack; a rather fitting track for the video as well. I just recently finished (most of) a 100% playthrough too, first time I've played in years, to introduce my gf to the game - she only played the first growing up, but we had a fun time with this one.
1:40 this is a video that hid deep within my watch-later list but i'm going to predict the proof: for all pairs of lines passing through the same two opposite points on a circle's curcumference, if they intersect at a right angle then they intersect on the circumference. Therefore if you take all pairs of lines passing through the same two unnamed points in a plane, they will trace out a circle centered at the midpoint.
nevermind i'm a cheater, it took me a while but i found my older comment, so it turns out i've seen this video before and that's how i knew the solution probably
The variance equation for linear combinations of random variables applies to dot products. Oh, neural network researchers🙈🙉🙊 The Walsh Hadamard transform is a fixed system of dot products. You can make an inside-out neural layer using fixed dot products followed by adjustable parametric activation functions. Eg. Fast Transform fixed filter bank neural networks.
@@Housecat333 I was just saying that all these fancy AI neural network researchers on a million dollars a year literally haven't done the basic math. The basic science was never done just assumed to have been done. So you are getting all these practical results from super inefficient AI code and they even admit they don't know what it is doing. Well, of course they don't know. How could you know if you didn't do the basic math. ReLU is a switch by the way, connect is f(x)=x, disconnect is f(x)=0.
going to get a major in comp sci and a minor in math but you really makes me doubt this decision. I feel like I think so much like a mathematician and love math but comp sci is so much fun and very profitable...
20 minutes of straight faced trolling ... BTW, the result you quote at 16:38 is called the abc conjecture in France (on account of the 3 sides of the triangle). Funnily enough this result still seems to be open over here ...
I was taught thales theorem in france. I think you confused it, because the abc conjecture is a very famous unsolved problem in number theory about primes. While thales theoreme is an ancient theorem from the antiquity (NEVERMIND) I looked at the video and what he calls thales theoreme is different. I learnt thales theoreme to be the fact that similar triangle have a coefficient of proportionality between them
Btw why do you think he's trolling? Is it because the whole video could be summarized by the principle that a right triangle inscribed in a circle has a diameter for hypothenus?
Nope, the abc conjecture is about number theory. The theorem here is also called Thalès’ theorem, but this name is rarely used because of the possible confusion with its namesake.
@@alexismiller2349 Well it doesn’t really have a proper name, most of the time we call it the inscribed triangle theorem or something, but that might be even more confusing. The thing is that’s not something you typically use everyday, so nobody really cares about the name, especially given that it takes a couple of seconds to specify what you’re talking about.
@@johubify that makes sense but why does eliminating a tell you anything about what the intersection points do? He comes up with an equation for a circle but why does that equation coorespond to what the intersection points do?
@@joshualinsky9859 he assumed the intersection points to be x,y at the start so he was solving for x,y Multipling the functions eliminated a, hence simplifying solving for the intersection points x,y
@@johubify oooohh I see. He solved the system of linear equations for x and y and those values always take the form of the equation of a circle. Thanks for the clarification
![A Rope Sliding Down a Table [Lagrangian Formalism Approach]](http://i.ytimg.com/vi/qBeywEsVePg/mqdefault.jpg)
![A Rope Sliding Down a Table [Lagrangian Formalism Approach]](/img/tr.png)
*Still looking for a way to store your millions of Pure Maths Major $ ? :^D* Big thanks to Ridge for sending me this wallet and supporting the channel! Here’s the site if you want to check them out! www.ridge.com/PAPAFLAMMY
Or use the code PAPAFLAMMY at checkout
*Don't forget to check out the video mentioned in the video! =) **ua-cam.com/video/4j4bVGa-jP8/v-deo.html*
@@PapaFlammy69 ridge wallet giveaway
There's nothing more funny, that can make me happy, than that meme in the beginning.
Reddit moment
Does anyone notice he looked more fresher and fresher each video? Also he is very passionate and radiant. This channel is growing
I immediately thought about the theorem you mentioned but I then thought of another pretty way to see it: going from a line to its perpendicular is a symmetry. We’re exchanging the roles of x and y here (actually, not quite, the y axis is exchanged with a line parallel to the x axis at height (b1+b2)/2) which is why the slope gets inverted (since the slope is (Delta y)/(Delta x), it becomes (Delta x)/(Delta y)). The axis of symmetry then goes through the middle (b1+b2)/2 and the intersection point. As a changes, you get an axis of symmetry for every possible direction. The only shape which is symmetrical with respect to every direction is a circle. QED
8:05
Calls b2 "b-squared"
So relatable😂
:'D
My perfectionist ears got triggered
Nice. We also use this concept to derive the diametrical form of the equation of a circle!
In India, the equivalent of this Thales' Theorem which you explained at 17:03 is stated as follows: ' The angle in a semicircle is a right angle.' Quite interesting how one theorem has different names in different places.
Yeah exactly. Also the integral by parts is stated differently.
@@Abhishek-hy8xe true.
What is you field btw?
@@Abhishek-hy8xe tenth grader.
Ah. Okay. Best of luck for your future.
Be curious.
So cool! Also love your shirt!
Thanks! :D You can get all the merch oevr on stemerch.com :3
I find it interesting that the radius is the difference between the square of the arithmatic mean and the square of the geometric mean.
That would be true for all numbers wouldn't it?
Now that you're sponsored by The Ridge I expect a collab with Anthony Fantano coming down the pipe any day now
This is the best video I’ve ever seen! Papa flexing 😘😍💪🏼
ah, who hasn't heard of
"y-luigi"
Never heard this pronunciation 😄
Johann Lehmann yt = what
Another nice thing about perpendicular lines: Start with the graph of x^2. To multiply a*b, go to A(-a|f(-a)) and connect it to B(b|f(b)). The crossing point of AB with the y-axis is at y=a*b
(You have to find the perpendicular lines yourself:)
Papa flammy is the one true Father Christmas. Always bringing us the gift of knowledge! Arigato gosaimasu flammy-sama
Its only 2 months cant wait! Btw my birthday is dec. 30
Wha is the music in the desmos part though?
Dark Cloud 2 Soundtrack, Rush Theme :3
I appreciate the humor but I don't want to hide my appreciation for this math content. I don't understand it, but I want to.
Thales Theorem's proof using Analytical Geometry is quite teduous compared to it's proof using Classical Geometry.If you use classical Geometry, it's an absurdly small proof xD
It's as simple as this:-
Angle at the circumference is subtended by the diameter
And the angle subtended by any arc at the centre of the circle is double the angle subtended at the circumference.
Angle subtended at the centre by the arc=180°
Angle subtended at circumference =180÷2=90
Done
Yes but line 2: " the angle subtended by any arc at the centre of the circle is double the angle subtended at the circumference." is just as unintuitive as the initial theorem to prove. So to be fair you need to prove this too, making the proof significantly longer. But Wikipedia is your friend here.
@@richardbloemenkamp8532 i dont think it's intuitive at all... actually it's quite intuitive, and it has a pretty small proof too.
But why should I prove it? I mean if you see this video, Flammable maths has used pre-defined theorems as well. So I took the privilege to do that too.
Please do reply and tell me where I'm going wrong bud, I would love to correct myself
@@johubify The proof of every theorem is simple if your start from one or a few other pre-defined theorems or equations close the end of the proof. Simplicity depends on the knowledge you start from. To me the derivation by Flammable maths is at least as simple as your geometric analysis. His calculus is straightforward to me requiring no special insight/thought.
@@richardbloemenkamp8532 you do have a point, and I'm more of an Analytical Geometry person myself.
But still, someone new to Analytical Geometry might question that why is the equation of the circle taken to be (x-h)^2+(y-k)^2=r^2 .
There are always prerequisites to proofs, so I wrote the proof assuming the person has a certain background in classical Geometry.
Do tell me where I'm going wrong
@@richardbloemenkamp8532 but yes I do agree with you
It's always better to stumble upon the proof by intuition and simplicity, than using pre-defined theorems and formulas
9:55 "Foci":
You are literally the first youtuber actually using the right plural of "focus",
even though you are german.
So you could say that you are better in english grammar than actual english people.
lmao
From Merriam-Webster:
fo·cus | \ ˈfō-kəs \ plural foci\ ˈfō-ˌsī also -ˌkī \ also focuses.
Apparently both "foci" and "focuses" are acceptable.
@@lukeng6404 Also: focusses is possible. But I think foci just sounds nicer. But thx for your correction. :)
its not about english, literally the same thing applies in latin, which is commonly used in many european languages. most words that end in -us are -i in plural, but technically you'd have to use other cases es well, which english doesn't support
@@Ocklepod Can you give a few example of words that end with -us? English is not my first language and I couldn't find any example.
@@farukkaya4396 Hippopotamus, Cactus, Walrus, Abacus are a few.
They become Hippopotami, Cacti, Walruses and Abacuses in the plural form
Is it possible to generalize that for the geometry in the non-Euclidean space, on a sphere for example? 8)
You should start a series where you do your hardest to solve a navier stokes or something of equal difficulty
Mmm always gotta love the Dark Cloud 2 soundtrack; a rather fitting track for the video as well. I just recently finished (most of) a 100% playthrough too, first time I've played in years, to introduce my gf to the game - she only played the first growing up, but we had a fun time with this one.
Brilliant video!, Analytical Geometry is T H E S T U F F
flammable boy comming back again. YES
17:30 or just do what 3b1b said and flip the triangle over and prove that it's a rectangle?
1:40 this is a video that hid deep within my watch-later list but i'm going to predict the proof: for all pairs of lines passing through the same two opposite points on a circle's curcumference, if they intersect at a right angle then they intersect on the circumference. Therefore if you take all pairs of lines passing through the same two unnamed points in a plane, they will trace out a circle centered at the midpoint.
nevermind i'm a cheater, it took me a while but i found my older comment, so it turns out i've seen this video before and that's how i knew the solution probably
This is just inverse of Thales theorem
and how is that different to what he's said?
What shape does it make when g(x) slope is at a fixed, different angle with f(x)?
Most smartest youtuber ever!!!
Whoah I love the plot twist here🌞💪
Papa just proved that Thales had a computer!!!!!!!
Much more interesting than I thought :p this proves that right angle circle thingy oh yeah Thales
What happens for special values for the b’s?
The variance equation for linear combinations of random variables applies to dot products. Oh, neural network researchers🙈🙉🙊 The Walsh Hadamard transform is a fixed system of dot products. You can make an inside-out neural layer using fixed dot products followed by adjustable parametric activation functions. Eg. Fast Transform fixed filter bank neural networks.
@@Housecat333 I was just saying that all these fancy AI neural network researchers on a million dollars a year literally haven't done the basic math. The basic science was never done just assumed to have been done. So you are getting all these practical results from super inefficient AI code and they even admit they don't know what it is doing. Well, of course they don't know. How could you know if you didn't do the basic math.
ReLU is a switch by the way, connect is f(x)=x, disconnect is f(x)=0.
this was really cool
Most people don't think it be like that, but it do
Super cool !!
Thanks !
= )
Bruh, if we use k*x instead of x we have an elipse (same for y).
Make a small batch of Hanukuh merch it will sell out. Trust me.
Yoooo papa’s got GUNS 💪
I multiplied the two equations without solving for x first and the shifted circle was obvious since the factor of a disappeared
Appreciated!
The advert ends when the next advert starts :/
What’s your pfp? Looks cool
How’s this interesting in any qay bruh the median of a right triangle is half the ipotenuse so it’s a circle
Any way*
going to get a major in comp sci and a minor in math but you really makes me doubt this decision. I feel like I think so much like a mathematician and love math but comp sci is so much fun and very profitable...
Nice one
The ebst way to advertuse a durable wallet is clearly to throw it at the wall
good vid
Nice!
8:04 b squared minus waah HAHAHA
Can someone make a compilation of Papi promoting wallets? Would sound like one of this compilations with Trump
13:40 it's the average xd
xD
xD
@4:00 weird flex, but ok
20 minutes of straight faced trolling ...
BTW, the result you quote at 16:38 is called the abc conjecture in France (on account of the 3 sides of the triangle). Funnily enough this result still seems to be open over here ...
I was taught thales theorem in france. I think you confused it, because the abc conjecture is a very famous unsolved problem in number theory about primes. While thales theoreme is an ancient theorem from the antiquity
(NEVERMIND) I looked at the video and what he calls thales theoreme is different. I learnt thales theoreme to be the fact that similar triangle have a coefficient of proportionality between them
Btw why do you think he's trolling? Is it because the whole video could be summarized by the principle that a right triangle inscribed in a circle has a diameter for hypothenus?
Nope, the abc conjecture is about number theory. The theorem here is also called Thalès’ theorem, but this name is rarely used because of the possible confusion with its namesake.
@@onemadscientist7305 thanks for the repetition. Otherwise what's the name for it if you dont use thales theoreme
@@alexismiller2349 Well it doesn’t really have a proper name, most of the time we call it the inscribed triangle theorem or something, but that might be even more confusing. The thing is that’s not something you typically use everyday, so nobody really cares about the name, especially given that it takes a couple of seconds to specify what you’re talking about.
Why does multiplying the functions together tell you anything about what their intersection points do?
Multiplying the functions was done to eliminate a(one function had a in it's denominator, and the other at it's numerator)
@@johubify that makes sense but why does eliminating a tell you anything about what the intersection points do? He comes up with an equation for a circle but why does that equation coorespond to what the intersection points do?
@@joshualinsky9859 he assumed the intersection points to be x,y at the start so he was solving for x,y
Multipling the functions eliminated a, hence simplifying solving for the intersection points x,y
@@johubify oooohh I see. He solved the system of linear equations for x and y and those values always take the form of the equation of a circle. Thanks for the clarification
@@joshualinsky9859 welcome:)
WAH
😎😎😎😎
I feel like you said "spare money",,,,,,
Is the way you pronounce 'y' because of your accent, or because of a wario meme? 😅
Super interesting video though, big fan!
He said it in another video that it's a reference to a series he's watching, I don't remember what thou'..
Wah?
690th like. Nice.
"Das gleiches spiel"?
is the answer 42?
Okay. I don't understand this.
My highest class is multivaribke calculus. Wut other classes do I need to take to understand dis sht.
Waa=y. Google Translate.
3rd
Nice!