Stereographic projection

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  • Опубликовано: 10 дек 2013
  • This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at shpws.me/q41V.

Комментарии • 580

  • @Tipen
    @Tipen 2 года назад +1806

    I’m really late, but this is just so simple but so elegant. Also it looks awesome, and I can actually see there being decent application for it

    • @natsudragneelthefiredragon
      @natsudragneelthefiredragon 2 года назад +7

      I got thos recommended to me as well, all of us within 1 day

    • @bradonhoover3002
      @bradonhoover3002 2 года назад +5

      Yooo you guys too?

    • @marclink0
      @marclink0 2 года назад +5

      Hey! Recommended gang rise up

    • @blueninja012
      @blueninja012 2 года назад +11

      I'm curious what application it could have

    • @lIlIIlIllIIIllIIllIlIllIllI
      @lIlIIlIllIIIllIIllIlIllIllI 2 года назад +27

      ​@@blueninja012 Maybe indicators for low height aircrafts like drones? If you could make a stereographic projection for a standardized navigation system and some solar powered LEDs, you could (non-destructively and with no modification to the building) make a pretty cool network of "landmarks" on rooftops for navigation. Swap them out with IR LEDs, and it's completely nonintrusive and doesn't create visible light pollution. :> (However, this *could* have an impact on insects with access to IR ranges of vision. It might not hurt to put them near gardens to attract pollinators.)
      It's more of a solution looking for an issue outside of the scope of art. The application, for right now, is looking cool... And that's totally fine.

  • @iamayin
    @iamayin 2 года назад +2488

    can't wait for this to get recommended to everybody

    • @rubyraptor
      @rubyraptor 2 года назад +29

      lol that do be how it works

    • @Walvortei
      @Walvortei 2 года назад +19

      It already did

    • @Leonardo-hr8qm
      @Leonardo-hr8qm 2 года назад +7

      How??????

    • @Nug_Lord
      @Nug_Lord 2 года назад +7

      It begins….

    • @cosmic2616
      @cosmic2616 2 года назад +9

      It did.
      Also ive never seen “2w ago” it’s always “14d ago”

  • @elmostos
    @elmostos 2 года назад +573

    This is cool, illustrates one reason why flat maps distort the globe; shapes that on the sculpture are obviously different sizes appear as equal squares when projected

    • @OmegaGenesisTrueEarth
      @OmegaGenesisTrueEarth 2 года назад +11

      It is the Global lie that distorts the maps... It's mostly flat and unmoving! Time to break the spell!

    • @itismethatguy
      @itismethatguy 2 года назад +4

      Yeah either the shape has to be changed or the land mass of countries towards either pole is increased (no country really close to the South Pole tho)

    • @kogasoldier9379
      @kogasoldier9379 2 года назад +19

      @@OmegaGenesisTrueEarth dammit I thought ferfers were laughed into irrelevance.

    • @AbandonedVoid
      @AbandonedVoid 2 года назад +19

      @@OmegaGenesisTrueEarth Yeah, those darn lizard people turning the frogs gay

    • @tomthepom98
      @tomthepom98 2 года назад +6

      @@OmegaGenesisTrueEarth I'm sorry, but the only thing you're breaking is my faith in humanity

  • @McArRuIzO
    @McArRuIzO 2 года назад +187

    Fun theory (not fact lol): Some scientists believe in physics similar to this that prove the entire universe itself is a sphere, like planets are. Most physicists consider the "fabric of space" to be a plane. But they feel its planar nature is a projection of sorts, one similar to this. It's far too complex to really explain in a comment, and I can't say I know all the theoretical physics behind it anyway.

    • @joshstamps6718
      @joshstamps6718 2 года назад +14

      I heard it was egg shaped, but not quite and egg, I mean, its all fluid and flowing right? The universe I mean, I want to believe it moves like water in zero g

    • @Mernom
      @Mernom 2 года назад +10

      Saying that it's shaped as a sphere is flat out wrong, since a sphere is a 3d object. The universe is a 4d space-time continuum.
      The theory is that the universe maps to a _hypersphede,_ not a regular plain 3d sphere. If it's true or not, depends on if spacetime has a positive curvature.
      This is the part I really don't get about this theory though, since so far all of their measurement methods I've heard about seem like they wouldn't work.

    • @rfacproductions6552
      @rfacproductions6552 2 года назад +1

      @@Mernom there is the n-sphere

    • @briancooley8777
      @briancooley8777 2 года назад +1

      The universe may be just an emergent property of some underlying process.

    • @pfzht
      @pfzht 2 года назад

      See also Eric Weinstein talking about E8.

  • @henryseg
    @henryseg  10 лет назад +130

    New thing: Stereographic projection. Using light rays to map from the sphere to the plane.

    • @PaulStickland
      @PaulStickland 10 лет назад +3

      Amazing Henry Segerman, some wonderful work in your posts.

    • @benschaeffer
      @benschaeffer 10 лет назад +4

      The math has more impact IMHO because it is happening in the real world. Diagrams or simulations have less of a magical quality. Great concept!

    • @MichaelKleber
      @MichaelKleber 10 лет назад +2

      Great work, Henry, excellent use of the medium.

    • @MarkDurbin
      @MarkDurbin 10 лет назад +1

      Brilliant, I love it!

    • @timcutho
      @timcutho 10 лет назад +7

      I was curious why it's "stereographic" (sounds like stereoscopy, but doesn't relate to binocular vision). Wiktionary (en.wiktionary.org/wiki/stereography) describes stereography as "Any technique for representing solid objects in two dimensions". So that's something I learned today :)

  • @diapermcgee8255
    @diapermcgee8255 7 лет назад +1169

    This is really cool! What software/instruments did you use to make the sculptures?

    • @henryseg
      @henryseg  7 лет назад +424

      I use the 3d CAD software Rhinoceros.

    • @official-obama
      @official-obama 2 года назад +218

      I’d use the drums and piano.

    • @mappycurry8107
      @mappycurry8107 2 года назад +93

      @@official-obama how about mayonnaise

    • @diagoleben
      @diagoleben 2 года назад +53

      No Patrick, mayonnaise is not an instrument!

    • @truthseeker7815
      @truthseeker7815 2 года назад +17

      @@diagoleben, it’s just the object you place on an escalator

  • @NickTheHunter
    @NickTheHunter 2 года назад +27

    Properly explaining something like this in 1 minute is a talent! Well done 👏

  • @johnslater8998
    @johnslater8998 2 года назад +61

    This could also be an excellent model to demonstrate Mercator projection in mapmaking. The two lines that are tangent to the plane would be analogous to the equator and prime meridian.

  • @Kram1032
    @Kram1032 8 лет назад +525

    neat! How about a version which actually has space for a single LED in the exact right position?

    • @henryseg
      @henryseg  8 лет назад +146

      +Kram1032 The problem is what the mount should look like - it would need a different design for every kind of LED.

    • @feedbackblues
      @feedbackblues 2 года назад +25

      @@henryseg you could make one with a hole at the dead centre that you could line up any old light to- phone flashlight, normal flashlight, etc

    • @VioletScarelli
      @VioletScarelli 2 года назад +26

      @@henryseg I could see something that has an LED inbuilt, along with a lil knob that moves the LED up and down to "focus" it

    • @satibel
      @satibel 2 года назад +5

      @@henryseg you could have a default mount and a plate that is swappable, but I think a hole for a standard 5mm led would be good enough. (I know this is 6 years old, but the object and customizable piece model is pretty useful to think about imo.)

    • @MrManningata
      @MrManningata 2 года назад

      Ikea sells a usb powered led lamp (halvklart) that has a magnet and a sticky back. It would be an ideal candidate for this

  • @xanderlewis
    @xanderlewis 4 месяца назад +1

    I love how I can open up my computer, type in 'stereographic projection', and immediately get back something like this that illustrates it beautifully (in two dimensions, anyway).

  • @stormysamreen7062
    @stormysamreen7062 5 лет назад +14

    This deserves s billion views.

  • @rqndxm
    @rqndxm 2 года назад +2

    Here before this blows up in everyone's recommended videos!

  • @serse8455
    @serse8455 2 года назад +4

    As a topology tutor, I want a 3d printer so bad.
    This would make for a cool demonstration

  • @AdamStallard
    @AdamStallard 10 лет назад +11

    Thank you. That helped me visualize SPs in my noggin much better.

  • @noslowerdna
    @noslowerdna 10 лет назад +12

    Beautiful, great work.

  • @darkrayc
    @darkrayc Год назад +1

    Hey Henry, loving your 3D prints and your designs... and this vid is 9 years old! How I wish I'd found your channel earlier 🥲

  • @Canale064
    @Canale064 2 года назад +3

    See you in 5 years when the algorithm recommends this to everyone

    • @nulle8935
      @nulle8935 2 года назад

      We're a bit early

  • @AkshayKumar-sd1mx
    @AkshayKumar-sd1mx 2 года назад

    That looks so beautiful

  • @LunaMapping_KR
    @LunaMapping_KR 2 года назад +7

    Simple yet elegant, very cool, to the point

  • @TheBuffaloPaladin
    @TheBuffaloPaladin 2 года назад

    This is something I didn’t know that I didn’t know and I enjoyed your quick, educational format. You’ve earned a like from me.

  • @ender8780
    @ender8780 2 года назад

    This has been recommended to me nonstop for at least a week

  • @CRlMZlN
    @CRlMZlN 2 года назад +2

    You've been blessed by the algorithm.

  • @muhammadkamranjamil8722
    @muhammadkamranjamil8722 4 года назад +1

    You made my students happy. Cheers

  • @boocchihitori4450
    @boocchihitori4450 2 года назад

    Such a cool demonstration

  • @zzzzs123
    @zzzzs123 Год назад +2

    these would be cool to use as lights in public places like car parks and stuff like that

  • @neelesh2003
    @neelesh2003 9 лет назад +7

    Finally this was what I was looking for

  • @channelname3385
    @channelname3385 2 года назад +1

    This is awesome! I'd love a lampshade like this

  • @natpbs
    @natpbs 10 лет назад +10

    Yay! You repeatedly fail to disappoint me.

    • @DanDart
      @DanDart 7 лет назад +3

      Can one fail something one never tries? :p

    • @emlmm88
      @emlmm88 6 лет назад

      Best compliment ever.

  • @SweetNipple
    @SweetNipple 2 года назад +3

    Very cool and interesting! Thanks for the video!

  • @AnkitKumar-si3zx
    @AnkitKumar-si3zx 5 лет назад +67

    Awesome! Straight and simple!

  • @OUTSKATE69
    @OUTSKATE69 2 года назад +1

    Excellent simple visual demonstration

  • @shonenbag6478
    @shonenbag6478 2 года назад +1

    I thought that was CG for a second! That's awesome!

  • @saskiagilmour5936
    @saskiagilmour5936 Год назад

    Nice, easy to understand definition that's well-illustrated. Thank you.

  • @shady6427
    @shady6427 2 года назад +2

    See yall in 3 weeks when this has 1.4 million views

  • @Alovatololo
    @Alovatololo 2 года назад +2

    Cool it's like the reverse of the cylindrical mirror pictures.

  • @RedPMD
    @RedPMD 2 года назад

    Incredibly satisfying

  • @Ghost145T
    @Ghost145T 2 года назад

    Reccomendations giving us hidden gems once again

  • @pantheon_1152
    @pantheon_1152 2 года назад

    This is so satisfying THANK YOU for sharing this ! I

  • @vuhnillagorilla
    @vuhnillagorilla 2 года назад

    thank you henry i very much enjoyed this

  • @mr_bones4875
    @mr_bones4875 2 года назад

    Huh new reprint of Commander’s Sphere lookin sick

  • @dudguys1194
    @dudguys1194 2 года назад +2

    I was here 8 years late, but man i cant imagine being that late!
    (This is towards all whom see this in their recommended years later)

  • @vampirebatjosieposie
    @vampirebatjosieposie 9 лет назад +7

    Cool, learned something new today :)

  • @EricCatlin425
    @EricCatlin425 2 года назад

    Concise demonstration. Good video

  • @ciarankelly3726
    @ciarankelly3726 2 года назад +3

    idk why this got recommended to me 8 years later but hey its pretty cool

  • @568dodo
    @568dodo 2 года назад +1

    THANK YOU for not making this 17 min video so you could say all that in the last 1:07 of the video!!

  • @blaketheawesome830
    @blaketheawesome830 2 года назад

    That was so nice to look at

  • @ServantProfessional
    @ServantProfessional 2 года назад

    This is amazing

  • @Sandtalon
    @Sandtalon 2 года назад

    This is incredible

  • @thestragequack3598
    @thestragequack3598 2 года назад

    2D Shadow of a 3D model. Wow!🔥

  • @undeadgaming1324
    @undeadgaming1324 2 года назад

    Uzui vs upper 6 looks really good.

  • @jorpese1
    @jorpese1 2 года назад

    Beautiful!

  • @CoolSs
    @CoolSs 2 года назад

    This could make an amazing base for cool coffee table. I actually want that.

  • @peco3474
    @peco3474 2 года назад

    This is about to blow up

  • @Bobalicious
    @Bobalicious 2 года назад

    That's really cool. Thanks.

  • @buffetgod1592
    @buffetgod1592 2 года назад

    Good job!!! I would love to have that pencil holder for my desktop 🥰

  • @MinecraftProLord
    @MinecraftProLord 2 года назад

    That's so cool.

  • @deleted_handle
    @deleted_handle 2 года назад

    This is so cool.

  • @zionsky3342
    @zionsky3342 2 года назад

    This is awesome

  • @cornishdinosaur
    @cornishdinosaur 2 года назад

    I don't quite know why this got into my recommended, but I'm very glad it did!

  • @patrickpeh2245
    @patrickpeh2245 2 года назад

    Cool idea and easy to make 👌🏻

  • @VladimirTolskiy
    @VladimirTolskiy 2 года назад +41

    Can this be used for indoor positioning systems, in combination with the Fresnel lens effect?

    • @satibel
      @satibel 2 года назад +4

      I don't know how you would distinguish between each square unless you count on counting ticks, where a distinction isn't necessary.
      Also I don't think the projection works if the balls don't touch the ground (which might be what you want to fix when you talk about fresnel, but if you're using a a fresnel lens, it would need to cover the whole area you need positioning on, also you need a direct top down line of sightq.)

  • @ColinRichardson
    @ColinRichardson 2 года назад

    I did something similar for an art project back when I was in school..
    I didn't take it to this level of trying to make perfect geometric shapes on the floor, but instead used layering to make unconnected parts look like solid shadow objects..
    I wish I had taken it to this level now..

  • @milkii_tea
    @milkii_tea 2 года назад +1

    this would make a really cool lampshade

  • @SocksWithSandals
    @SocksWithSandals 2 года назад

    Good simple explanation of stereographic projection.

  • @AveyHere
    @AveyHere 2 года назад

    Why does this suddenly recommended to me??
    Very cool :)

  • @nop3noperson
    @nop3noperson 2 года назад

    Holy shit im impressed. I never really thought about this.

  • @z0d0rZ
    @z0d0rZ 2 года назад +2

    This is pretty good for people who don't understand why maps are not 100% acurrate on scales

  • @xpndblhero5170
    @xpndblhero5170 2 года назад +1

    That's awesome..... I want a lamp shade like that now. 😁

  • @affablegiraffable
    @affablegiraffable 10 лет назад +1

    that is so cool!

  • @JoBot__
    @JoBot__ 2 года назад

    This is appearing in everyone's recommended after 8 years.

  • @t_o._.o_t
    @t_o._.o_t 2 года назад

    すっげぇ、、、

  • @ricbisa6092
    @ricbisa6092 3 года назад

    What a beautiful video

  • @KingPastapremiereDesignVIDEO
    @KingPastapremiereDesignVIDEO 2 года назад +1

    That's exactly why I love the witness

  • @jomon324
    @jomon324 2 года назад

    I was gonna subscribe, but I realize I'm already subscribed. Sweet!

  • @aerosma5021
    @aerosma5021 2 года назад

    Very cool!

  • @aesthetic5956
    @aesthetic5956 2 года назад

    this gon go viral

  • @Nooter_
    @Nooter_ 2 года назад

    thats so sick

  • @TazyBaby
    @TazyBaby 2 года назад

    That would make a really cool chandelier

  • @cons4943
    @cons4943 2 года назад

    this would be a brilliant candle holder!

  • @sakshamantil8314
    @sakshamantil8314 2 года назад

    Wow, this makes me understand how universe works.

  • @ur_pilot_4_2day82
    @ur_pilot_4_2day82 2 года назад

    accidentally watched this with my good headphones. man got the asmr mic

  • @GewelReal
    @GewelReal 2 года назад

    very nice ray tracing

  • @OmniCasper
    @OmniCasper Год назад

    What that's so cool I want a lamp like that now.. :D

  • @harshvardhanjha4611
    @harshvardhanjha4611 2 года назад +1

    very thought provoking

  • @carlosscesar448
    @carlosscesar448 3 года назад

    Great video! Thank you

  • @MitchPlease
    @MitchPlease 2 года назад +1

    The bg audio in this made me check to see if it was raining outside

  • @leonardodiddoro
    @leonardodiddoro 2 года назад

    There are certain voices that are just hypnotizing

  • @SyntheticCereal
    @SyntheticCereal 2 года назад

    thank you Mr Segerman!

  • @therhinosnake6938
    @therhinosnake6938 2 года назад

    Not to diminish how cool this is, but... that would make a really nice Candle Holder.

  • @orangeman5256
    @orangeman5256 2 года назад

    Glad this was recommended to me

  • @neeravchavda9921
    @neeravchavda9921 3 года назад

    This Video And some other Helps To More Understand The Shapes which are shown in Previous Videos

  • @GawainW
    @GawainW 2 года назад

    This would make for one awesome lamp

  • @sacrificialobama8786
    @sacrificialobama8786 2 года назад +39

    Cool! What applications is this used for in the real world?

    • @Koisheep
      @Koisheep 2 года назад +48

      Stereographic projection allows you to uniquely assign every point in the sphere a point on the plane (except for one of the poles, which is the light source). Think of it like sailors using maps to traverse the sea. In fact, this type of function is called "chart" because of that.
      Charts for the sphere are extremely useful in physics and mathematics, since they arise in many calculations.

    • @Koisheep
      @Koisheep 2 года назад +34

      A more direct application is that you can calculate the surface area of the sphere using charts. Alternatively, you can use something called the "divergence theorem".

    • @dIancaster
      @dIancaster 2 года назад +20

      Right, the other guy didn't actually answer your question for how you might use this in the real world: maps. Specifically, maps of continental size or greater, especially those of the whole Earth.

    • @arturmizuno
      @arturmizuno 2 года назад +6

      every flat map is a projection (you cant draw the information of a sphere precisely on a flat piece of paper, you need to distort form, or distort distance, or distort proportion), as an exaple search the wikipedia list of map projections, each projection is a way to represent the earth (roundish) to a paper/screen (flat on an euclidian plane)
      this is precisely (or precisely answering your question) a model for visualising the projection (representation) of one specific projection to an audience (like a group of students in a classroom or and educational youtube video)
      so its like using a string and a pencil to draw a circunference proving what a circunference is
      what i mean is that it is a tool for teaching

    • @juanitome1327
      @juanitome1327 2 года назад +4

      In my engineering class, we learned about stereographic projections to be able to represent layers of minerals and their intersections for later terrain movement (excavating, platform building, extraction of resources). It seemed the best way to do it because it allows you to represent lines with dots and planes with curved lines. It really simplifies everything and you can make yourself an idea of any (underground) terrain by just looking at its stereographic projection

  • @kristopherb8046
    @kristopherb8046 10 лет назад +1

    So cool.

  • @infadeldog13
    @infadeldog13 2 года назад

    Maths is beautiful!

  • @hiddenuchiha5959
    @hiddenuchiha5959 2 года назад +2

    Can this be used to demonstrate the continent deformation on a 2d map? In essence, instead of lines, can land masses be displayed?

  • @geekinmike5931
    @geekinmike5931 2 года назад

    Gonna have to leave my mark for when this gets recommended again to me

  • @tyomich1
    @tyomich1 2 года назад

    Finally! Grid projector

  • @Bulwark-
    @Bulwark- 2 года назад +1

    No one:
    RUclips 8 years later at 2 AM:

  • @dw-rh6fb
    @dw-rh6fb 3 года назад +26

    If you used that method to translate the globe map onto a flat surface, would that flat map be able to be used to accurately navigate without any further translation?

    • @HerrSurIix
      @HerrSurIix 2 года назад +5

      late answer, but that introduces the same problem of stretching the globe area as normal maps. In general it should be possible to use it as a map but as shown in the video the points near the northpole will be displayed with a huge distance in between, also if you want to cross the north pole, you'd leave the map at one side and enter at another. In principle it should be possible to navigate with that, but it seems highly unpractical

    • @dw-rh6fb
      @dw-rh6fb 2 года назад

      @@HerrSurIix lol. Have you even seen the Gleason map?

    • @HerrSurIix
      @HerrSurIix 2 года назад +3

      @@dw-rh6fb in fact i have not before, so thank you for showing me. I still stand by my opinion of this kind of map being impractical, as the outer rings seem way more apart than they are in reality. If you only need information about the northern hemisphere, then maybe it could be used

    • @dw-rh6fb
      @dw-rh6fb 2 года назад

      @@HerrSurIix your opinion doesn't matter now like it didnt matter before. Im just letting you know your idea of the flat map was hilarious.

    • @dav356
      @dav356 2 года назад +4

      @@dw-rh6fb You asked a question, got a good answer, asked a dumb question, got another good answer, and you're saying his opinion doesn't matter? The irony is hilarious. He also never presented any 'flat map', he just analyzed your idea, so there's minus a few points for reading comprehension as well.