A Strange Map Projection (Euler Spiral) - Numberphile
A Strange Map Projection Euler Spiral Numberphile

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Featuring Hannah Fry.... Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) Poster and sticker based on this video: https://teespring.com/en-GB/euler-spiral-world-map More links & stuff in full description below ↓↓↓ More Hannah on Numberphile: http://bit.ly/hannah_vids Hannah's Book (Hello World): https://amzn.to/2Ds1mQg Antipodal Points: https://youtu.be/G2Blr0LycOI The Euler Spiral paper Hannah mentions: https://arxiv.org/pdf/1202.3033.pdf Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Animation by Pete McPartlan Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Comments

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

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

Cataphractos Contrafactum : Send the orange man to the hydraulic press channel, and we'll see if he'll still have a positive gausian curve number

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

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

Gerardo Villarreal : Bradey: What is it doing that other maps aren't doing? Hannah: ... It's an Euler spiral Bradey, what more do you want? Exactly what I was thinking! haha

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.

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

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?

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

John Harley : Are you telling me there is no Euler Spiral map of the earth generated by computer with n=9999 anywhere on the internet?

Josh Griffiths : "I think we should prioritize mathematical beauty over geographical practicality." - Hannah Fry I can't tell you how much I love this statement.

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

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.

Straw Man : Tengen Toppa Gurren Lagann if u watch anime then you know what's up

Frank Meoño : I want a video about what the animator has to go through lol

Peter Shaw : "Mathematically beautiful, if Geographically impractical" 😂

Dev Agarwal : This is spiralling out of control.

Steve T : Great video, math rules! Just finished reading "Hello World" and completely enjoyed it. I'm sure the book will inspire some young people to study math and pursue math careers. Thank you.

Thomas Borgsmidt : Euler is pronounced: Oiler. Preferably with an Australian accent. Just for Your informationtion.

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

James Flames : What kind of a mathematician calls Euler "You-ler"?

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

radastir : Honor the noble sacrifice of the hero beach ball, martyr of science!

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

SteelSkin667 : Not great for navigation, but probably great for data storage.

Michael Anuzis : Math question: what's the probability the stem position at 1:10 is purely coincidence given its surface area relative to the orange? A) less than 0.01, B) 0.01 to 0.03 C) 0.03 to 0.05, or D) over 0.05

Cris Lr : Thank You! haha this one's great!

OceanBagel : There are two types of map projections: Winkle tripel and wrong.

TBrickman : Google Dymaxion projection

Dema Jaasa : "The Mathematical idea of pealing a 2D object into a sphere has stuck with me" why? I aspire to be like that

J J : Euranges. Yummmmm.

Wojciech Pitra-Ptaszek : Despite topic: Your freckles! OMG <3 gorgeous!

John Cartwright : What's the point of doing a film about the Euler projection if you're just going to ruin the whole thing by talking about "Juler"?

Brett Coryell : Map-matically beautiful projection. Love all the Hannah Fry vids. Keep 'em coming.

hamza olalekan : Well done. 1)U neglect the usage of such map which is essential 2) the longitudinal line is no longer straight

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.

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

Markus Aleksandr : To help us wrap our head AROUND today's video? Ha. Ha HA.

Gabriel Dos Santos : Or you could have the map drawn on a sphere

Charlie Metzler : Check out Buckminster Fuller's Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes.

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

Kenny Arias : 1:14 -I just realized that... -I KNOW EXACTLY

Lucas Kerper : Great video, thank you for sharing your idea with us. On a side note, I as well, always used to peel my grapefruits a in a spiral way!

James : Cheeky 1:09! The position of the stalk is just perfect 🍊 😂

Albert Batfinder : “We’ve only got this room booked for another hour.” Steady my trembling soul.

c0ldc0ne : Introducing the Parker Map Projection.

tabaks : The first one was carved to show his back. Btw, Hannah's personality impresses me solidly every time!