I figured this out in school and my math teacher was not happy about it since I started drawing only standard parabola with the ruler and then adjusting the coordinates accordingly. After the second homework we were given the system we have to draw it into (also on all the exams). Mathematical creativity is not always appreciated in school.
Before you finished the explanation, I tried to visualize it in my head and it’s fairly simple to understand intuitively. A “fatter” or wider parabola is simply a zoomed in “skinny” parabola. As you zoom into a point of the parabola, it flattens out, thus, getting wider. I’m not 100% certain this assumption is correct, but it feels pretty solid.
Clifford Stoll? I think he's awesome! I just don't think of maths with him so much as learning in general. But thanks to him, I have both a mini Klein bottle and a Curta calculator on my wishlists.
+Thrashiko Well, Dr. Matt Parker is also excited it seems! What I wouldn't give to have had such an enthusiastic educator when I was in school. Actually showing you things with excellent explanations instead of just copying examples out of the book and presenting that. :)
I can explain that, seeing as a parabola is technically a cut through any 2 points on a circle or at least the rest bits left over. He just went from the 2 connecting ends of the parabola, which do not have 2 connecting ends, because if they were connecting it wouldn't be ends. It would be a circle. So he went around in a circle.
+Pablo Arroyo Something interesting to note, over the complex numbers all ellipses and hyperbolas are equivalent, and over the complex projective plane, all conics are equivalent.
standupmaths Maybe that's why TH-cam recommended your channel. I haven't watched numberphile for a long time now tho. Weird. But I like it. I love math even tho I don't do good at it anymore.
Seems to me that you made it look unexpected by not actually picking corresponding points in your graph. y2 = by1/a and x2 = bx1/a, so the rectangle you drew with the axes would be similar.
Very good point. I could have picked a point further down on bx^2 with the same ratio. But I wanted to emphasise the arbitrary nature of the two parabolas.
+standupmaths I've allways seen the flat one as the tip of the skinny one, resized. In the Apollonian Cone, the parabola and the circle have a fixed tilt, while the hyperbola and the ellipse have wide ranges of tilt. Anyway, the cone can be skinny or flat as well. You've given analytical proof, could you make another video giving a geometrical proof?
+standupmaths Sometimes when I have to graph parabolas for homework, I change the scale so it is easier to graph. So I feel like I understand what you mean.
I reckon that an easier way to demonstrate it is by *zoom-ing* any single parabola at its base (or peak, if it's inverted). If you zoom in, the parabola becomes wider as the branches will separate gradually; and if you zoom out, the parabola gets skinnier. *That way, you can map any given parabola onto any other one.* Sorry for my bad english :)
It’s no more a parabola. It will just be a straight line. Don’t you remember quadratic equations? Ax^2 + bx + c where a ISNT ZERO. If A or B in this case is 0 then the equation will be linear
There is a fairly intuitive way of looking at this. If you zoom out on the yellow one, you eventually have a picture of the red one, and zooming out is basically scaling the same in both the x and the y directions. Great video to prove this though.
At first I thought, "but why then do different parabolas give different results? Like, if they're the same parabola, why do they have different derivatives and areas?" Then I checked, and the derivatives and areas are related by the same constant multiple. Awesome.
This is the most Australian video I've ever seen. I really like how Matt builds up the disbelief factor about the possibility of parabolas scaling to each other.
Here is a MUCH simpler way for me to think of it algebraically: In y=x, there is 1 variable to the left and one variable to the right. In order to change the slope, you need to multiply the right side by m: y=mx. To scale, you need to multiply all the x's and y's by m: my=mx (basically y=x).However, y=x^2 is an imbalance in the number of variables! If you multiply every x and y by m, you get: my=mmxx. Which simplifies to... wait what! It's y=mx^2! Scaling is the same as multiplying the right side! This means that parabolas can't possibly change shape ;) Does anyone else find this simpler?
I'd add that similarity of all parabolas is easily seen by looking at the focus-and-directrix definition. But the algebraic argument here is more accessible, thank you for the nice exposition! (and a great video, of course)
I wished you repeated the coin thing with the parabolas: cut a parabola out of paper and bring it really close to the camera to show it can line up with a "different" parabola.
TheMrCarnification A lot of people have asked me this over the years. I'll give you my usual copypasta: When I was 19, I was trying to think up a username for TH-cam (this was before Google got it, I think). At the time, I was living in a shitty, freezing apartment eating store-bought tomato soup and store-bought bread. They both tasted awful, but dip the bread in the soup and it was the best thing I'd tasted in months. I typed in "TomatoBreadOrgasm" and thought it wouldn't matter anyway, it's just a video site. After Google Plus integration, I had the option to use my real name, but I liked the fact that people would be forced to face the fact that they can't judge a book by its cover. I decided to keep it for the sake of the contrast between my username and the things I actually say.
The ending was magnificent.
Alexey Saranchev i died at the end xD
_ MΛrCO28 _
... John?
***** ?
_ MΛrCO28 _
It's a movie, "John dies at the end"
***** oh
It took some time but the acid finally kicked in around the end of the video.
lol
oddly appropriate profile picture for this comment
@Boco Corwin Powerfully Concocted Parabolas
Guess you took it about 30m before it started then
"Triangles come in all shapes and sizes." Um...pretty sure triangles come in just one shape. Triangle.
An acute triangle has a different shape than an obtuse triangle. Otherwise, they'd be similar
@@jacl9976 even 2 right angled triangles need not be similar
@warmCabin then why dont they all satisfy Pythagoras theorem?
@@kingscross4233 fairly sure, that's a joke :)
@@kevinkuryshev6958
Yes, very sure @warmCabin comment was a joke. But not sure about @JACL comment's "Otherwise, they'd..." part.
Thought I was going to learn math about parabolas, ended up joining a cult conspiracy against "Big Math"
xD
The New World Order of operations
Quick Maths
Big maph
I think I’ve just become a believer in ‘X-Squared Anon’
that ending????
that ending.
yes.
+Jacob Shepley Nighmares forever. I'm traumatized for life!
+Jacob Shepley The ending killed me ;D
Play it backwards and you can certainly hear "Praise the ParaboLord!" ]:->
lol
4:17 Proof that Matt lives in a Non-Euclidean plane of existence!
^^
earth is round he just walked around it really fast
@@karamboubou8579, Earth's surface is Non-Euclidian.
*He lives on a torus :D*
*runs around the camera panting
That chalk writes reallly well...
callumissocoollikf better than marker on brown paper?
Bryan Sutphen Much better. (not sorry)
Hagoromo chalk look it up
I bet he has a stock pile of them.
They're an endangered species and mating isn't an option
love that chalk
Outro starts playing
*slowly backs away from monitor*
Elias Nierengarten xD
So much for the separation of church and scale.
Ah, the rare "separation of church and state" joke.
I figured this out in school and my math teacher was not happy about it since I started drawing only standard parabola with the ruler and then adjusting the coordinates accordingly. After the second homework we were given the system we have to draw it into (also on all the exams). Mathematical creativity is not always appreciated in school.
+Alexander N. Benner (Nikodemus) I feel you, I've experienced that too
I had two awesome math teachers who tutored me, and got me to university level math.
i did the same with exponential plots xD
i did the same with exponential plots xD
My math teacher purposefully choose some of the parabolas we had to draw so that adjusting the coordinates was the only option to draw them.
The editing at the end made my week
"A skinny one there [...] and a flatter one there." That's parabola shaming.
All parabola are beautiful in their own way.
*in the same way
"What immortal hand or eye,
Could frame thy fearful symmetry?"
Exactly.
#Parabolalivesmatter
You son of a parabola
Before you finished the explanation, I tried to visualize it in my head and it’s fairly simple to understand intuitively. A “fatter” or wider parabola is simply a zoomed in “skinny” parabola. As you zoom into a point of the parabola, it flattens out, thus, getting wider.
I’m not 100% certain this assumption is correct, but it feels pretty solid.
I am certain, however, and I gladly take any offer to prove me wrong
Theres a graphing program called desmos which has a zoom function. Entering y=x^2 will help. Hope this helps.
I think it is exactly how it works
THERE IS ONLY ONE TRUE PARABOLA
STANDUPMATHS IS THE MESSENGER OF PARABOLA
PARABOLA IS THE GREATEST
*dix thrown out in a parabolar motion for the parabola*
Parabolas confirmed
Can I have a Hallelujah?!
Adonai Parabola Ehad !
Paraballahuakbar!
-> "Are you religious?"
-> "I'd like to introduce you to my religion"
"9:18"
You get a new editing programme or something, Matt? Just trying out some new features, huh?
I love editing. My life is a constant battle to not spend too long in Final Cut.
Do go ham on editing with one video.
+standupmaths Honestly, it's amazing you get any maths done, really...
+Austin O'Rourke Thought Ray William Johnson had come back to do math for a second
+Colin Evans RIP RWJ years of =3 "You will be remembered" Only Carlos can save us now...
Man, I wish I had a maths teacher who was as excited about this stuff as you or Dr. Grimes.
No one is as excited as Dr Grime.
Clifford Stoll? I think he's awesome! I just don't think of maths with him so much as learning in general. But thanks to him, I have both a mini Klein bottle and a Curta calculator on my wishlists.
Shit...I said Grimes again..too much walking dead
+Thrashiko I am a maths tutor and, without shame, I steal some of Dr G's delivery in my lessons. Hey, anything to get the buggers to pay attention!
+Thrashiko Well, Dr. Matt Parker is also excited it seems! What I wouldn't give to have had such an enthusiastic educator when I was in school. Actually showing you things with excellent explanations instead of just copying examples out of the book and presenting that. :)
9:24
9:24
9:24
These are just replay buttons. You’ll need them. XD
+
+
+
This comment needs to be pinned
@@standing_around yh lol
09:25
Best ending I've ever seen ever
"parabolati confirmed" hahahaha
You're a dork!
Medacium Bin Amon He only said that because it was on the board in the video
Hence the purpose of quotation marks
@@faizalrahman6027 please stop
1:32 I guess you could say that it's a Parker circle
Oh, so THAT'S what OTP stands for!
thejuzey ... you down with OTP?
xD xD xD
You can explain translation but what about teleportation at 4:17
It's a phenomina called "Movie Magic"! lol
I can explain that, seeing as a parabola is technically a cut through any 2 points on a circle or at least the rest bits left over. He just went from the 2 connecting ends of the parabola, which do not have 2 connecting ends, because if they were connecting it wouldn't be ends. It would be a circle. So he went around in a circle.
He is filming it in a trancendent classrom
Oh I just noticed that...
._.
MATT TEACH ME YOUR WAYS because I'm too lazy to get up and walk all the way to those cookies in Japan
It must be a cylindrical classroom.
Gloria in X-Squaris
I'm pretty sure i had a calc lecture end that way before.
"These can't be similar, I'm sorry I've misled you. But hey, let's give it a go anyways" Ah yes, the parker square philosophy
This guy knows exactly how the internet wants to gain knowledge
+Verlisify This isn't a pokemon video, what are you doing here?
wow. internet is a small place.
"we are eternal, all this pain is an illusion"
parabol + parabola
Did not expect to find Tool here XP
aren't all conic sections identical within their own kind
Actually, only the circle and parabola are. You get different ellipses and hyperbolas (as their eccentricity changes).
Thanks
+standupmaths obviously, I mean right. The parablah vlodmi. Hn....Words failing meee...
+Pablo Arroyo Something interesting to note, over the complex numbers all ellipses and hyperbolas are equivalent, and over the complex projective plane, all conics are equivalent.
+standupmaths I'm pretty sure that by "within their own kind" he meant "of same eccentricity". Does the point stand then?
Vector artists like: “yep"
4:17 you must have filmed this on a torus
+đỗ hoàng minh I salute your astute... ness
"Close enough" *parker square flashback*
that ending has scarred me for life i think.
Aren't you on numberphile?
+MoonSaiyan Yes I am!
standupmaths Maybe that's why TH-cam recommended your channel. I haven't watched numberphile for a long time now tho. Weird. But I like it. I love math even tho I don't do good at it anymore.
+MoonSaiyan *well
That's good. You don't have to be good at math to enjoy it :) YAY!
+standupmaths That ending was hillarious! Thank you for brightening my evening :D
+standupmaths Aren't you in Dr. Who?
Seems to me that you made it look unexpected by not actually picking corresponding points in your graph. y2 = by1/a and x2 = bx1/a, so the rectangle you drew with the axes would be similar.
Very good point. I could have picked a point further down on bx^2 with the same ratio. But I wanted to emphasise the arbitrary nature of the two parabolas.
+standupmaths I've allways seen the flat one as the tip of the skinny one, resized. In the Apollonian Cone, the parabola and the circle have a fixed tilt, while the hyperbola and the ellipse have wide ranges of tilt. Anyway, the cone can be skinny or flat as well. You've given analytical proof, could you make another video giving a geometrical proof?
+standupmaths Sometimes when I have to graph parabolas for homework, I change the scale so it is easier to graph. So I feel like I understand what you mean.
+awe lotta
And now you know that all you have to do is draw one parabola and several different sets of axes.
Wait I thought he was drawing with chalk not axes. xp
best.ending.ever
Sometimes I feel down, and when I do I just come back here for this ending.
I've re-watched this every year and it still brings a smile to my face. Your content is delightfully nerdy and very entertaining.
Glorious ending. You have won the internet. Congratulations!
I'm watching this at 2am thanks for the nightmares
Nikki Rennardo Ahahah XD!
A year later.. I read this at 2am O.o... Coincidence? I THINK NOT!
1:18 AM.
2:01
Its 2.12 in the morning. Freaky
At 6:08 it really feels like some flat-earther's mathematical "demonstration"
Holy cows, this has to be the best ending in a science related video I have ever seen, and probably will ever see, in my life.
only if ur hindu
because holy cows
Parabolati Confirmed
Morgan Laco w
Illuminati confirmed
But also, great explanation, hadn't seen it before. Thanks!
Y=X^2 IS THE ONE TRUE PARABOLA AND MATT PARKER IS ITS MESSENGER
+markog1999 I'd thumbs up, but that extraneous apostrophe makes it impossible for me.
+markog1999 allahu akparabola
I understood his main point at 6:00, I remembered zooming out on a parabola in Desmos, and it got more and more pointy
I reckon that an easier way to demonstrate it is by *zoom-ing* any single parabola at its base (or peak, if it's inverted). If you zoom in, the parabola becomes wider as the branches will separate gradually; and if you zoom out, the parabola gets skinnier.
*That way, you can map any given parabola onto any other one.* Sorry for my bad english :)
That's essentially what he did in the proof
ending is spoopy
and funny 😁
Do you mean “spooky”? It’s always good to proof read what you’re going to submit just before you actually submit it.
By far one of my favourite videos, not just on @standupmaths but TH-cam as a whole
In parabola we trust
You need to redo the video post-brexit to account for the smaller pound.
8:40
zero: Am i joke to you?
I was thinking the same thing
But then:
If b = 0
Then there is no parabola
y2 = 0 for all real x2
(considering y2 = b * x2)
You cannot map anything to zero, or map zero to a function, it changes the aspect ratio
It’s no more a parabola. It will just be a straight line. Don’t you remember quadratic equations? Ax^2 + bx + c where a ISNT ZERO. If A or B in this case is 0 then the equation will be linear
Filho do Meepo That is still a parabola. Lines are degenerate parabolas
Teh Yong Lip You can map anything to zero AND map zero to a function. I have no idea of what you are talking about.
Been sniffing the chalk dust again, have we?
There is a fairly intuitive way of looking at this. If you zoom out on the yellow one, you eventually have a picture of the red one, and zooming out is basically scaling the same in both the x and the y directions. Great video to prove this though.
So I'm assuming you took all of the drugs at the end of the video...
I love this video: the mathematical proof is beautiful and the ending is hilarious!
Unacknowledged moments like 4:15 are why this is the best channel on youtube.
This video contains more than one Matt Parker. Are these all similar?
+Benjamin Heasly I'm going to say no.
?
There is only one. true. Matt Parker!
At first I thought, "but why then do different parabolas give different results? Like, if they're the same parabola, why do they have different derivatives and areas?" Then I checked, and the derivatives and areas are related by the same constant multiple. Awesome.
Gloria in x-squaris! One of the best ending ever!!
Absolutely incredible. I always loved math, but never thought a math lesson could be so funny.
lol amazing editing at the end!
This is my first introduction to this channel, and i love it ❤
This is how I imagine the universe ends.
The ending made the video
The first standupmaths video I watched... the good times...
This is the most Australian video I've ever seen. I really like how Matt builds up the disbelief factor about the possibility of parabolas scaling to each other.
almost died laughing at the ending!
That ending hahahaha
Your ability to draw curves is a marvel.
Here is a MUCH simpler way for me to think of it algebraically:
In y=x, there is 1 variable to the left and one variable to the right. In order to change the slope, you need to multiply the right side by m: y=mx. To scale, you need to multiply all the x's and y's by m: my=mx (basically y=x).However, y=x^2 is an imbalance in the number of variables! If you multiply every x and y by m, you get: my=mmxx. Which simplifies to... wait what! It's y=mx^2! Scaling is the same as multiplying the right side! This means that parabolas can't possibly change shape ;)
Does anyone else find this simpler?
I think that's the funniest vid you've ever done. I'm tearing up laughing.
GLORIA IN X-SQUARIS! XD
I'd add that similarity of all parabolas is easily seen by looking at the focus-and-directrix definition. But the algebraic argument here is more accessible, thank you for the nice exposition! (and a great video, of course)
9:36 for a free nightmare tonight
Final sequence was gold
the montage at the end is bliss
Math broke Matt.
I was looking for Parabola by Tool and ended up here. :|
That is some of the smoothest chalk I've ever seen...
4:15 dammit! don't do that! my brain almost explode over the place because of the unexpected left entrance xD
Ariel Vinda parabolatis can not only translate,rotate,and scale but they can also teleport...
hey bill
you have 4 arms and the standupmaths guy at the end also has four arms.
BILLINATI CONFIRMED!
9:36 Dafuq did I just see?
+Tareck Dalco illuminati confirmed?
+Likkan Chung No, Parabinati confirmed!
I probably re-watch this about once a year. The ending gag still gets me.
PARABOLA CONFIRMED
thats fine, i didnt want to sleep today anyway.
That ending though...
The ending really caught me off guard 😂
*pauses at **9:37* Welp, I'm subscribing.
the idea that there are more parabola is just something created by big math to sell more parabolas
I wished you repeated the coin thing with the parabolas: cut a parabola out of paper and bring it really close to the camera to show it can line up with a "different" parabola.
You can also turn a Parabola to make an other. I made a small video about it. It's called: There is only One True Parabola Turning
That wouldn't work, with this method you could turn a square into a rectangle and vice versa. This is against the whole point of this
+Alejandro Apellido I did thought about that at the beginning of the video
+swaroop kumar you are already doing that as soon as you get the shape closer to the viewer in order to make it bigger
+swaroop kumar Nope! To move it closer you slide it in an axis perpendicular to X and to Y
+Alejandro Apellido that is the third dimension
It's funny that I got an ad about schizophrenia at the end of the video
Math taught with memes? I'm in!
Still one of my favourite TH-cam videos
And yet you think zero shouldn’t be a square
What
When did he say that?
He is taking about 'difference of squares' video
Now for a challenge. Prove that all conic sections are in fact similar since they just depend on the angle of a plane cutting through two cones.
It's a bit of hyperbole don't you think?
;-)
In other words..
There is a transformation function from every parabola to every parabola
"...is a lie perpetuated by powerful maths teachers with a vested interest"
Hilarious. Subscribed.
TomatoBreadOrgasm?
Yes? Can I help you?
why did you pick such a (eerm) different name?
TheMrCarnification A lot of people have asked me this over the years. I'll give you my usual copypasta:
When I was 19, I was trying to think up a username for TH-cam (this was before Google got it, I think). At the time, I was living in a shitty, freezing apartment eating store-bought tomato soup and store-bought bread. They both tasted awful, but dip the bread in the soup and it was the best thing I'd tasted in months. I typed in "TomatoBreadOrgasm" and thought it wouldn't matter anyway, it's just a video site.
After Google Plus integration, I had the option to use my real name, but I liked the fact that people would be forced to face the fact that they can't judge a book by its cover. I decided to keep it for the sake of the contrast between my username and the things I actually say.
woah, thats a nice story, thank you.
Me: Hey, I’d like to introduce you to my religion.
Friend: What’s your religion?
Me: 1:14
Friend: I’m intrigued.