@@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.
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
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.
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
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.
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 :)
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.
@@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.)
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).
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.)
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..
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.
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".
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.
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
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
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?
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 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 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.
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
I got thos recommended to me as well, all of us within 1 day
Yooo you guys too?
Hey! Recommended gang rise up
I'm curious what application it could have
@@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.
can't wait for this to get recommended to everybody
lol that do be how it works
It already did
How??????
It begins….
It did.
Also ive never seen “2w ago” it’s always “14d ago”
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
It is the Global lie that distorts the maps... It's mostly flat and unmoving! Time to break the spell!
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)
@@OmegaGenesisTrueEarth dammit I thought ferfers were laughed into irrelevance.
@@OmegaGenesisTrueEarth Yeah, those darn lizard people turning the frogs gay
@@OmegaGenesisTrueEarth I'm sorry, but the only thing you're breaking is my faith in humanity
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.
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
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.
@@Mernom there is the n-sphere
The universe may be just an emergent property of some underlying process.
See also Eric Weinstein talking about E8.
New thing: Stereographic projection. Using light rays to map from the sphere to the plane.
Amazing Henry Segerman, some wonderful work in your posts.
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!
Great work, Henry, excellent use of the medium.
Brilliant, I love it!
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 :)
This is really cool! What software/instruments did you use to make the sculptures?
I use the 3d CAD software Rhinoceros.
I’d use the drums and piano.
@@official-obama how about mayonnaise
No Patrick, mayonnaise is not an instrument!
@@diagoleben, it’s just the object you place on an escalator
Properly explaining something like this in 1 minute is a talent! Well done 👏
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.
neat! How about a version which actually has space for a single LED in the exact right position?
+Kram1032 The problem is what the mount should look like - it would need a different design for every kind of LED.
@@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
@@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
@@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.)
Ikea sells a usb powered led lamp (halvklart) that has a magnet and a sticky back. It would be an ideal candidate for this
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).
This deserves s billion views.
Here before this blows up in everyone's recommended videos!
As a topology tutor, I want a 3d printer so bad.
This would make for a cool demonstration
Thank you. That helped me visualize SPs in my noggin much better.
Beautiful, great work.
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 🥲
See you in 5 years when the algorithm recommends this to everyone
We're a bit early
That looks so beautiful
Simple yet elegant, very cool, to the point
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.
This has been recommended to me nonstop for at least a week
You've been blessed by the algorithm.
You made my students happy. Cheers
Such a cool demonstration
these would be cool to use as lights in public places like car parks and stuff like that
Finally this was what I was looking for
This is awesome! I'd love a lampshade like this
Yay! You repeatedly fail to disappoint me.
Can one fail something one never tries? :p
Best compliment ever.
Very cool and interesting! Thanks for the video!
Awesome! Straight and simple!
Excellent simple visual demonstration
I thought that was CG for a second! That's awesome!
Nice, easy to understand definition that's well-illustrated. Thank you.
See yall in 3 weeks when this has 1.4 million views
Cool it's like the reverse of the cylindrical mirror pictures.
Incredibly satisfying
Reccomendations giving us hidden gems once again
This is so satisfying THANK YOU for sharing this ! I
thank you henry i very much enjoyed this
Huh new reprint of Commander’s Sphere lookin sick
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)
Cool, learned something new today :)
Concise demonstration. Good video
idk why this got recommended to me 8 years later but hey its pretty cool
THANK YOU for not making this 17 min video so you could say all that in the last 1:07 of the video!!
That was so nice to look at
This is amazing
This is incredible
2D Shadow of a 3D model. Wow!🔥
Uzui vs upper 6 looks really good.
Beautiful!
This could make an amazing base for cool coffee table. I actually want that.
This is about to blow up
That's really cool. Thanks.
Good job!!! I would love to have that pencil holder for my desktop 🥰
That's so cool.
This is so cool.
This is awesome
I don't quite know why this got into my recommended, but I'm very glad it did!
Cool idea and easy to make 👌🏻
Can this be used for indoor positioning systems, in combination with the Fresnel lens effect?
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.)
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..
this would make a really cool lampshade
Good simple explanation of stereographic projection.
Why does this suddenly recommended to me??
Very cool :)
Holy shit im impressed. I never really thought about this.
This is pretty good for people who don't understand why maps are not 100% acurrate on scales
That's awesome..... I want a lamp shade like that now. 😁
that is so cool!
This is appearing in everyone's recommended after 8 years.
すっげぇ、、、
What a beautiful video
That's exactly why I love the witness
I was gonna subscribe, but I realize I'm already subscribed. Sweet!
Very cool!
this gon go viral
thats so sick
That would make a really cool chandelier
this would be a brilliant candle holder!
Wow, this makes me understand how universe works.
accidentally watched this with my good headphones. man got the asmr mic
very nice ray tracing
What that's so cool I want a lamp like that now.. :D
very thought provoking
Great video! Thank you
The bg audio in this made me check to see if it was raining outside
There are certain voices that are just hypnotizing
thank you Mr Segerman!
Not to diminish how cool this is, but... that would make a really nice Candle Holder.
Glad this was recommended to me
This Video And some other Helps To More Understand The Shapes which are shown in Previous Videos
This would make for one awesome lamp
Cool! What applications is this used for in the real world?
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.
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".
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.
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
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
So cool.
Maths is beautiful!
Can this be used to demonstrate the continent deformation on a 2d map? In essence, instead of lines, can land masses be displayed?
Gonna have to leave my mark for when this gets recommended again to me
Finally! Grid projector
No one:
RUclips 8 years later at 2 AM:
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?
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
@@HerrSurIix lol. Have you even seen the Gleason map?
@@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
@@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.
@@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.