A Strange Map Projection (Euler Spiral) - Numberphile

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Numberphile : Poster and sticker based on this video: https://teespring.com/en-GB/euler-spiral-world-map

fishy paw : I love Hannah's presenting "style", relaxed but enthusiastic at the same time. I've always been a bit of nerd when it comes to peeling oranges. One of my favourites is to make a little lantern out of it. I also remember seeing (in my grandpa's magic book) a way of peeling an orange that allows you to remove the orange but the peel stays as a sphere that can expand to get the orange out but keeps the overall shape. I've forgotten how to do it though. I'll need to see if I can find out how to do it again. I doubt it would work as a map though, but it looks cool.

EmperorTigerstar : The Euler Spiral map both horrifies and intrigues me.

Hirudin : Oh no, wait until the flat orangers see this video...

auskott : This is all fake. CGI trickery. Oranges are flat.

jalabi99 : Hello, I am from the Flat Orange Society. Mind if we have a word?...

e4r : No oranges were hurt during the shooting of this video

c0ldc0ne : Introducing the Parker Map Projection.

Danny : I've learned about gaussian curvature when the Klein Bottle professor explained to me how to correctly hold a pizza slice!

TheCordlessOne : The sexual tension in the room is unbelievable.

Jay Benton : I thought it was pronounced "oiler"?

gussnarp : As a geographer, I really loved this video and learning about this new projection. This projection shares a feature with the Mercator projection. On the Mercator projection there is one place where there is zero distortion, which is the equator, where the cylinder would touch the sphere. The Euler spiral enables you to create a similar line of zero distortion that encompasses the whole globe. Of course, in both cases the true line of zero distortion is a one dimensional line, which is why you have to go to infinity in the spiral to get there, but I completely see the beauty in this. I love it.

J J : Euranges. Yummmmm.

Useless GTA V : *sexiest mathematician ever*

temujin9000 : "orange man bad!"

Combat folk : Hannah Fry should definitely do ASMR

Simon Moore : Imagine folding the Euler Spiral map in the car.

dingaia : love hannah <3 passion is infectious and such a wonderful personality, bet she's great fun to talk to!

Kentnstay : A Euler Spiral map would be a great piece of Numberphile merch.

lumer2b : I think it's important to say why/how Mercator is useful for navigation. A straight line in Mercator is not a straight line in real life, however, if you navigate with a compass, your compass will remain pointing to the same direction throughout your line.

Ultracer : When I see Hannah Fry, I click like ;)

Adam Charvát : New Hannah Fry video?!?!? It's like christmas to me

Samsul Hoque : Just wait until the Flat Orange Society finds out about this video.

Luis Mijangos : Hannah is amazingly intelligent and super lovable. Amazing math.

maigretus1 : As a retired US Navy officer, this is pretty interesting. It looks like this projection is what you would get by cutting along a rhumb line, which is the line you get by taking a constant compass course from one pole to the other. Or in other words, you cross every meridian at the same angle. The biggest virtue of the Mercator Projection, as Hannah noted is that every rhumb line on a Mercator Projection is a straight line. One of the faults of the Mercator Projection is that great circles (shortest distance between two points on the sphere) are not. I believe that, except for the meridians and the Equator, they are all sine waves on the Mercator projection. Would this projection also have great circles as straight lines, if chopped up straight lines?

Funsworth : Euler sounds like oil-er

geryon : Google maps doesn't use Mercator anymore. It's a globe now.

Sonny Mattsson : 5:34 Not anymore though...

Michael Wisslead : Lots of comments about Euler being mispronounced but what about Fresnel?

Dom : A Hannah video! Is it Christmas? Is it my birthday!?

Shruggz Da Str8-Faced Clown : Isn't Euler phonetically pronounced "Oiler", not "Yoo-ler"?

Dev Agarwal : This is spiralling out of control.

Mr Chains : but isn't e pronounced oiler and not yuler

Pierre Abbat : My upcoming math papers are about Euler spirals and transverse Mercator projections, so of course I clicked on this. Mercator is NOT projected from the center. That would magnify too much along the meridians. You project from the South Pole, then take the logarithm of the resulting y-coordinate.

Niclas Kristiansen : YES, one of my favorite people on this channel!

John Andrew Kypriotakis : Google maps changed to a spherical projection earlier this year :/

Tymski : My dad was peeling oranges into spirals

TheOfficialCzex : Very informative! I love map projection mathematics.

Batfan1939 : Does this mean a mathematically perfect Euler spiral is infinitely long, despite its finite area?

Asher Mooney : SEE ITS FLAT

Adriano Seresi : Who is this Youler...?

bob street : I've long harboured an urge to do exactly this. Hannah has saved me a lot of time and eventual disappointment with the outcome. I'm not sure if I feel relieved or cheated.

Nisarg Jain : The amount of rage people have here about youler and oiler makes me repel the mathematical community over youtube.

Seth Person : With an infinite number of cuts, doesn't the distortion if the first projection shown also tend to 0?

future62 : Would it be possible to approximate and align the infinite loops to be geometrically practical?

McLurr : This is a grapefruit!

Chongee : Even though I knew about these, I've still enjoyed the video ;)

HorzaPanda : Haha, I used to make a point of peeling my oranges like that, since it gives you a pretty result and feels like the most logical way to peel an orange all in one piece Who knew I was doing geometry and could have made maps with them? XD

Max Johnson : Orange man have glorious pubis. Very nice!

Tomasz Gałkowski : Google Maps no longer uses Mercator, they moved to showing 3D globe when you zoom out far enough.