A Strange Map Projection (Euler Spiral) - Numberphile 

Bought the poster and framed it, I love it so much ❤️

I really love this channel. I'm glad that you're all doing this.

Can we see this mapped out properly on a computer model image please? That would be pretty cool!

@@lxdimension Mathematica should be able to handle it.

Earth is flat. Like a dinner plate.

Oh no

There’s probably not a great deal of them watching Numberphile.

My mind went to the team from the marble races instead of poking fun at flat earthers.

Hirudin So globbies can no longer say a sphere cannot be put on a flat surface

Brek Martin I’m a flat earther and a scientist and i watch them

Your joke might have fallen flat...

Orange you happy with the result?

That orange pun was terrible! I bet helix windows.

gottem

I appreciate that pun

The Earth is a doughnut

the earth is hollow

The earth is a Potato

Earth is a planet

Only satanist christians think the world is round. Especially the capitalistic Christians from USA that love Trump the demon lord Nurgle. Ha ha I needed to write that sorry.

We need a history of the world day by day map on this projection.

That's the beauty of math

i am ONLY utterly horrified at the time waste, as it has 0 benefit how about that math -- cost, (trends to) infinite, and benefit, (trends to) 0.

HISTORY YEAR BY YEAR ON THIS MAP

Marcus Aurelius it has a certain amusement value and introduces the concept of the Euler spiral. An old saying about knowing the cost of everything but the value of nothing comes to mind.

Hey, a globe is the best kind of map we have! :)

@@GreeneyedApe Yup, hands down! Except when you want something you can fold up and put in a drawer or a glove box. Fred

@@ffggddss Inflatable globe! However, globes are rather impractical for typical driving directions.

A spiral would work, but I guess it was a more compact shape?

I wanna hear more about your grandpa's magic book

they use that map too

My reply would have been inappropriate!

😂😂

Lock the door

@@JLHunter61 can incels just get outta here?

@@americantoastman7296 lol dude the original comment was an obvious setup for lewd jokes. stop getting offended on behalf of other people, dickface.

Clive Stoll's video about it is great!

Cliff is very... enthusiastic :D

Yes! I was thinking of that video too.

*Klein bottle.

@@epajarjestys9981 thanks, edited ;)

Simon Moore No problem. You are not folding the spiral, you are folding a piece of paper with the flattened spiral on it. So it's like a nice long map that has one or two folds in the short direction and an easy harmonica in the other.

Nooooooooo...

@@johnfrancisdoe1563 yeah.. better than what I remember.

You could reel it up on two spindles.

@Multi Mason So basically like a new Torah?

You sound incredibly pompous

@@alandouglas2789 ?

It's just a little joke.

@@alandouglas2789 I will devour your mother.

Merry Christmas

To me to In Poland >30 years ago you would’ve seen oranges ONLY on Christmas

I was thinking the same thing!

Same here !!

Agreed :)

thanks, this helped me understand what they meant by "no distortion"!

gussnarp could you explain this further for me?

@@brendonholder2522 when you have a curved surface mapping it in 2d you get some distortion but when you make the strips since you can make them really tiny stripes while you still get distortion it will be smaller practically the centre line of each stripe will have no distortion which in practice means you will have more points of no distortion of your end map if you theoretical you can get stripes the size of line you will end with no distortion at all

ANIKHTOS that’s really interesting! I’m writing an paper (an Internal Assessment Math investigation for the IB Diploma Program) and I’m thinking of using an Euler spiral to make a map such that you can move in vectors on the map in a manner similar to that of a Mercator projected map. Any suggestions on how to go about investigating this?

@@brendonholder2522 well i have not seen any map but the most serious question is how the coordinate system would look like?? the longitude lines wil be inside the strip going up left to down right depending how you cut the spirals from the globe while the latitude will be almost vertical line at the strip i imagine the goals is the spiral will match the latitude lines to be one big line??? besides how weird it will look like since the map lets see reaches perfect of the globe that means you have 2d representation of a 3d surface so even if you make vectors in the map you need to have 3d geometry to calculate their values and that will be for the 2 circular parts what about the line that connects them?? some points (area of the globe ) will not be in either the 2 circular parts put in the line connecting them so you will have to split the formula for the circular part and the line part but we need a visual of this projection to see where everything has moved in is the spiral actually form a circular area or not?? or there is tiny gaps in between ?? or you will make a tine distortion there and make it a circular part? after all you will not be able to cut infinite stripes so you will introduce some distortion in the end

And neither would we really ever learn anything.

I came to the comments section for this. RU-vid: Numberphile in title My brain: HannahFryphile

I'm glad I'm not the only one with those embarrassing lapses in focus.

What? Sorry I wasn’t paying attention.

I'm so lazy, I probably still would.

We're using this to assemble big spherical concentrators in space to make really low mass solar power systems. So, we find it technically practical.

Shut your dirty mouth Hannah Fry is perfection

Gotta get the T Shirt!

@@williammook8041 That sounds very interesting. Who is the 'we' in that comment?

@@williammook8041 but still not geographically practical :(

The Earth is Flat. These are bunch of projections. This is not our real map. This is a small map of small part of Earth. Who knows what they're doing in Antarctica.

@@ancientindianguru1714 Hahahaha

@@ancientindianguru1714 if we end the federal government we can take back nasa and area 51 and we can find out whats really going on.

@@alfredodominguez2799 Yes, I heard they are developing some serious high tech pasta!!!

Thank your lucky stars you're not from the Flat Easy Peeler Society, I want to know why there's a conspiracy against my satsumas.

dingaia yes, “talk to”

Cutting earth spirally?

Yeah. Why not?

@Noel Coward "...get *completely around* the problem" ;)

Now you're playing with power!

Cristobal Jorje I prefer playing with surds to be honest.

Only if Hannah does the cutting.

yet.

I trust that by writing this comment I will be notified when this happens

I would like to be added to this list.

As would I

RemindMe! 2 days And yes this is the first entry in an impromptu petition to implement Reddit's RemindMe bot on RU-vid. Spread the word.

There couldn't have been! Don't be irrational.

That number does not belong to the set of countable numbers.

There wasn’t one. The queue for that title is infinite, so the person queuing for it, would have had nowhere to stand......

@@legislativequeery There is at least the 3,141,592nd subscriber (or 3,141,593rd if you round it up).

@@dwc1970 Yes, if π≠π such that π ∈ ℚ→ ∃ π*10⁵ ∈ ℕ But that would break math

It never used Mercator projection either. The projection that was used called Web Mercator.

Well, sorta…it still uses it for mobile :)

Interesting! You know, I don't think I've ever zoomed out enough to notice that

"Web Mercator" is just a shittier Mercator that's easier to compute.

@@AleksyGrabovski omegalul. "It's not English, It's British English!"

The video isn't specifically about the Mercator projection, dude

Would you happen to know if a reference that explains this in detail?

@@XenoghostTV Dr. Fry talks about Mercator and why it is used so commonly, especially in navigation. But a straight line (a geodesic) in the real world always corresponds to a curved line on a Mercator map. For example, the shortest path between Mumbai and New York passes through western Russia, Swender, Norway and Iceland. If you looked at the Mercator map you'd think it went through Arabia and North Africa, and those are quite far away. What lumer2b wrote is correct. Mercator is useful when navigating with a compass.

@@Banzybanz Okay but that's not the damn point of the video...

It’s called the rhumb line. It’s not far off the great circle route, with the advantage that you can steer a constant heading.

*Yooler*

Yes!

The trick is knowing when to stop... :-/

Cataphractos Contrafactum this may be a joke, but it will.

"Velcome to heeoodlraawlik plress channel...." Or "velcome to beyond depressed" (Beyond the Press, their second channel) "Vat de faak!?"

it will have tears and wrinkles because it has to go somewhere

That's because university is just a continuation of the public school indoctrination. Real scholars can do as well or better apart from the university...especially now that we have internet, and all the knowledge on earth is easily accessible to many millions.

@@rickbluecloud531 Stop bringing politics up where it doesn't belong. We get it, school bad because it teaches you about slavery. Shut up already

@@ChangedMyNameFinally69 there are political aspects to this issue that need to be considered if it's going to be correctly understood. And I'll continue sharing whatever I'm led to share by the Spirit. I have no regard for arrogant demands by rude people.

@@rickbluecloud531 What political aspects? Them teaching you that slavery happened? I'm genuinely curious. What Spirit?

@@ChangedMyNameFinally69 your comment is rather incoherent anyway. Maybe you should proofread and make corrections after you sober up.

You think you learned something, but it's just trivia. Popular science (or math) is not college science (or math).

@@Raison_d-etreof course one learns

[citation needed]

Eurth

Eurquator

Speurl

I'm using a Euler to measure this sentence

Acella, Multiverse Dweller Do you know how to pronounce Euler? But everything you’ve said makes no sense.

Dan Whiteman I prefer the Winkel-Tripel projection (or however you spell it); way less distortion than Mercator, but still familiar enough to be easily used.

Jam Kon much...

Naked Orange Peel man is same proportions as naked Orange Man according to Stormy...

maigretus1 Intuitively, I think any great circle would need to go through the long arm between the spirals, and so would not be a straight line.

You'd get a single line that is infinitely thin for an infinitely long line so it wouldn't preserve angles at all, so great circles couldn't be calculated very easily. The position of an object on the surface of the line (if it has a finite width, so not at the limit where it goes to infinity etc) would be a function of the width of the line and a periodic function. You could produce a version of this with different limits exactly how you describe, you're an engineer, you know this stuff, the limit being that your compass direction to produce an infinite line would be exactly east or west starting at exactly the north or south Pole. Given that this is a right angle, it would take some time to travel it.

That is because the earth is flat and they project it onto a 3d surface

which is then projected (with a different transform) onto a 2d surface

OSSSSHHHH The Earth is not flat.

OOh bro, it's off to the Gulags with you.

@@dixztube Like. I think IQ videos are supposed to animate us to life. Nobody should be thinking ASMR on a Geophysics video.

actually there is still distortion. The distortion is minimized and localized to the centroid of each facet in the icosahedron. It's flatter, but not on the same scale an this euler coil.

Jay Benton [🇺🇸-er]

It is.

It was his name, so it's pronounced the way he pronounced it, and it rhymes with "oiler".

Eh-yu-lehr

"oiler" is right.

You spelled mouth wrong :o

Pawel Kita looool

Absolutely right - what Hannah describes would give you the perspective cylindrical projection, not the Mercator.

The video brought to you by Anglo gang.

wheeler

1066 worst day of my life

freznel

@@chigginheadD mathS ;-)

10 minutes of inverse kinematics

Thomas Borgsmidt And Fresnel is pronounced “Freynel”, IIRC.

Thanks. I was pronouncing it as "Ew-ler" xD

Which proves that Australia does not exist. Or so I learned somewhere on the Internet..

Yeah, exactly what I was gonna say.

oiahlah

bob street well you could probably manage a much neater (flatter) one if you’re willing to devote the time to cutting the strips with infinitesimally narrow widths!