Paraboloids and The Building which Set Things on Fire 

"When life gives you lemons, scorch them."

*bursts into flame "yes!" *slower burst "yyeess!!" *slowerer burst "YEEEEEEEEEEEEEEEEEE-"

Someone made combustible lemons. Cave Johnson would be proud.

To me, a Norwegian, the fact that satellite dishes are paraboloids is quite intuitive. It might have to do with the fact that our word for _sattelite dish_ is _parabol_. Just thought you'd like to know (:

Love these laid back proofs, and an assumption of basic calc was a pleasant surprise for youtube!

Biggest problem I've had in any math class is lack of interest by the instructor. NO SUCH ISSUE HERE. got to love it

"You're in London. You're out taking your lemon for a walk." That sounds like an opening to a great interactive text adventure webcomic. XD

Pfft this is so fake - we don't have sun in Britain

I was experimenting with parabola and may have accidentally blown up a light bulb. The fun part was how my face was about 5 inches away. A real parker square on my part

"Loss of generality" nice :)

11:03 "To get that d" Everyone, take notes.

I watched until the end, think I need to subscribe

11:03 - > Keep that in mind ladies. If you want the d, start with the gradient of the tangent.

"accidentally curved in a certain way" How do you know it's accidental? What if it's an evil alien who came to Earth to sabatoge all of our lemons?

13:40 Chalk on a blackboard is a fantastic sound! It was a very sad day when my Maths department replaced them with fancy whiteboards and projectors, they were the only thing that persuaded me to offer solutions in lectures.

Combustible lemons. Portal anyone?

who doesn't like chalk board?? much more fun.

Hey Matt I showed this in my science class and my teacher was really impressed and my classmates laughed a lot at the lemon part. Keep up the amazing videos!

Ha, jokes on you Matt. I watched the entire thing and didn't subscribe!

he should be next doctor who

I was just about to demand a proof

The windows were aligned to the parabaloidal architecture, but can be detuned to actually be flat wrt the street. It's a tweak engineers have had to invent to save architects for decades.

In Sweden, a satellite dish is actually called a "parabol".

It wasn't until this year that I appreciated that "trigonometry" is literally "the study of trigons" or, as we know them now, "triangles".

this was fun, I feel like I don't get to watch people work out slightly complicated math problems anymore.

Having been told, when I was younger, that this kind of stuff is supposed to be boring, I'm grateful to have found this!

The sound chalk makes is satisfying! I have no idea what you're talking about.

Where did the lemon go at 1:12?

"To get that D..." Beautiful quote

That curvy action kept me focused all the way to the end.

"I highly recommend deriving the formula. It's good fun" said Matt. I'm writing my secondary education exam the next month. I can assure you I hate proving LHS trigonometry = RHS, because there are many formulae to choose from and there are dead ends.

Life is like riding a bicycle which is on fire, and you're on fire, and everything is on fire and you're in hell.

Perhaps do a video about retroreflectors.

"to get that D, we need to start with the gradient of our tangent"... said no one ever... ;)

Nice video. Maybe if you had been my Math101 lecturer I might not have ended up as a lawyer.

In the US they have a similar building and it's even worse, it actually murdered all the plants in the local park.

"to get that D we have to start with the gradient of our tangent"

Thanks Matt Parker. YOU ARE THE BEST. YOU MAKE MATH LOOK EASY.

Mathematics: the art of doing nothing and still getting it done.

Just a note the term for a no longer manufactured care or badly designed car is "LEMON."

To be honest, I love chalkboards more than whiteboards. the sound of the chalk (when used correctly) is so satisfying.

5:18 "YYYYYYYEEEEEEEEEEEEE-"

COMBUSTIBLE LEMONS!!! GODS MAN CAVE JOHNSON ACTUALLY DID IT!!!!

Bike lights are often made with paraboloid shape, so the light source shines light more straight towards the front, letting the light reach further.

hahah yup, already subscribed.

Ok bois, let's settle this once and for all, put your satellite dish on the table...

I'm not sure how I feel about this. ._.

It is super easy to find the focus for x^2. Where would the tangent line be exactly 1? Well that is one! We didn't move the parabola so the x is 0, then the y would be 1.

I don't care about the maths, but how the hell did he vanish that lemon at 1:12?

The architect probably didn't expect there would be enough Sun in London for something like this to happen

Already there in sixty symbol poor Matt Brady always beats you

I used this video to teach my 9 year olds about the usefulness of paraboloids! (only the first half, the Math is too complex). I love how you introduce these concepts! Please tell me how to finance more of your videos!!!

WHY ARE THERE 4 ARROWS IN 7:30 INSTEAD OF TWO YOU CAN'T SAY WHAT'S THE POSITIVE DIRECTION THAT WAY AHAHAHAHAH

The worst possible shape would have been an elliptical dish, not a paraboloid. A paraboloid assumes that the light source (sun) is an infinite distance away. A ellipse, however has 2 focal points such that any light source from point A is reflected once and is pointed perfectly at focal point B.

There was (is) a solar oven in southern France using exactly this concept.

You're APPROXIMATELY one third if the comedy group? Who's the slightly more or less than one that causes that, or do you have a 1/8th member as well? ;-P

Mmm, pyromania.

"I'm gonna start with a standard vertical y-axis" **draws curved line**

Every mathematics teacher should be this enthusiastic. I was lucky enough to have a pretty good math teacher, but it surprises me not one bit that so many people not only struggle with it, but then failing to get help and see this level enthusiasm, write it off from their list of things they want to have in their brain. Keep up the enthusiasm/

When he mentioned scorched lemons, I immediately scrolled down to see how many Portal references were in the comment section.

I can't believe the guy that gets annoyed at 'incorrect' snowflakes is making videos so regularly

If you cut a lemon in half and remove the fleshy pulp, the internal skin would be a parabaloid. If you put the empty lemon back together and shine a REALLY REALLY bright light on it so it penetrates the skin, would it then scorch itself internally just because?

Whiteboards > Blackboards.

The Olympic Flame is lit using paraboloid mirror right?

man, I couldn't get any sleep because I couldn't get to this conclusion. I'm really thankful, t's way funnier to look at you on a black board than reading for it in a sober well-documented piece of paper

What is the practical application of the paraboloid? What is the derivative of x^2? What is the tangent of 20(2 theta)? What is the gradient of the beam? they questions that i have clue and it is for math class plz help

I love your videos I'm a total fan after your amazing lecture, you even signed my calculator in binary! I'm choosing maths at your uni :D p.s. please reply to me

Boom..... YES! Boooooooooooom...... YYYEEEEESSSS....! Boooooooooooooooooooooooooooooooooooom..... YYYYYYYYYYYYEEEEEEEEESSSSSSSSSS........!

Love the sound of chalk.

6:44 - It took me several minutes of turning this sentence around in my head and playing with that simulator before I understood what you meant. Partly because I didn't know that you meant "the same distance from another point _as from_ a line"; and partly because I didn't know which line and which point you meant. Then suddenly, it finally clicked. XD So basically, you can make a parabola by selecting a point, drawing two lines perpendicular to each other (one fixed and one not), drawing a line from the first point to the point where the two lines meet, drawing the perpendicular bisector to _that_ line, marking the point where it meets one of your lines, then move the unfixed line one position over, and lather, rinse, repeat?! That's so cool!

put..put this building in Dubai.

This is so awesome! :D I love weird architecture & mathematics & history. Thank you for making this video!

"To get that D, you need the gradient of the tangent." - Matt Parker 2016

I almost didn't watch the proof. You're quite the trickster.

16:05 thank you matt, this simple and yet powerful act of recognition and appreciation, and that feeling of belonging the arises from it. Belonging to the same species of math nerds. You make me want to embrace and accept fully that part of me that was always there, and make me want to express that nerdiness shamelessly - I have always felt compelled to hide rather to fully accept who I am - You are an inspiration, And being able to talk about maths, making it accessible and even an attractive subject, is quite an achievement.

it is such a major flaw bt still how is it that a lot of buildings still are the shape of paraboloids ??

"scorching your lemon" sounds nasty xD

You can't focus sunlight to a point. You can focus it to a circle and the size of that circle is proportional to the distance to the reflector. For a collector the size of a large building the light can't be focused onto a circle smaller than a couple feet wide. Worse, while the building is curved, I suspect the individual panes are flat, they would not focus light to an area smaller than themselves plus about one degree.

That’s a hefty title

"(...) more fun!" hahaHAhaha... So, how many boxes of anti anxiety pills should I bring?... Seriously, by minute three, I was spacing out into internal screaming... 😅 #IHaveProblems

I like your charisma, instructions are clear... Video 10/10 audio 10/10 please never stop making these. You and that other numberphile guy... Wow

Getting math proofs is so satisfying and always let me smile. It's better than ....................! [fill in your preferred activity]

I found the generalized focal point for ax^2+bx+c. It's (-b/(2a), (1-b^2)/(4a)+c). The working out was pretty long. Here's a visualization: www.desmos.com/calculator/k6vib3w0nv

Did you specifically create the song for the channel? Is there a link to it anywhere?

I love the fact that since you're not _from_ London, your mockery of London isn't self-deprecating; it's sincere. XD 4:01 - "Just for Graphs". I love that! 5:39 - "Full-Frontal Nerdity"… You guys… I can't even handle you guys. XD

Nobody is going to make a paraboloid shaped structure? Take a trip from Westminster England to Westminster Colorado: goo.gl/maps/kMqaZC2WkvoYARgK9

Because of you and Numberphile, I am now watching videos on RU-vid about my most hated subject in school. For FUN. And I'm LEARNING.

Combustible lemons that BURN YOUR HOUSE DOWN! Cave Johnson approves.

"if you're concerned that that is a ridiculously big satellite dish, of course I'm kidding, that's not my satellite dish." *turns around showing an even larger satellite dish* "THAT IS MY SATELLITE DISH!"

...just caught the "LOSS OF GENERALITY". Now I need to go hunt down somebody else who'll get the joke so I can show them in person. This could get tricky.

'If you made it all the way through this, you must already be a subscriber.' That effective marketing, though. Aaand...subscribe.

Nice proof. We can also quickly derive the length d by using the law of sines: we get a right triangle with sides x and d, and 2θ and 90-2θ as the angles (clearly visible at e.g. 13:23, 2θ is the angle between d and the hypotenuse since the y-axis is parallel to the vertical line at x). From this, we can quickly say that x/sin(2θ) = d/sin(90-2θ) = d/cos(2θ), or simply d = x/tan(2θ) = x*(4x^2-1)/4x = x^2-1/4. Therefore, h = x^2-d = x^2-x^2+1/4 = 1/4 (writing it with LaTeX would have been easier :-P ).

You got me Matt. I watched until the end and so, feeling compelled, I subscribed. BTW, I don't need a proof, I WANT a proof!

we can prove this for y^2=4ax.....using the same steps.....and then u have proved it for any parabola......obviously the focus is going to be a/4

In Sweden "Satellite Dishes" are called "Parabol Antenner", which translates to "Parabol Antennae" (I think, not completely sure)

Transcendental "functions" aside, you can do "angle" addition with complex numbers. The expression (4x^2-1)/(4x) is effectively the same as the square of 1+2xi.

I have one question about the proof: wouldn't you need to take the angle between the ray and the normal of the 'surface' (i.e. the normal to the tangent line)? Because the line hitting the point (0,0) (i.e. x = 0) would make an angle of pi/2 radians, and tan(pi/2) = sin(pi/2)/cos(pi/2) = 1/0 ... When using the normal, however, there can never be an angle of pi/2, since that would mean the ray would be parallel to the tangent line, so it wouldn't reflect anyway.

You didnt mention that rocket engines are paraboloids! They vector the thrust like flashlights for maximum efficiency... Like a flashlight)

It is true I require no further convincing to subscribe, as I already have... Now if only people I know wouldn't think I am weird for thinking math is fun...

I would love to see a video on buildings warming things up about the Vdara Hotel & Spa in Las Vegas, NV, USA. www.nbcnews.com/id/39403349/ns/travel-news/t/death-ray-vegas-hotel-pool-heats-guests/