A New Discovery about Dodecahedrons - Numberphile
video description
If someone had told me -Hey, it's impossible to draw a straight line on a tetrahedron, that ends up in the same corner without crossing another corner. Same with the cube. But we dont know about the dodecahedron. - It would have been a 15min. Task to prove that it _is_ possible, and maybe a day, to give an answer about the solutions that are possible. I mean, if you draw this in 2D, you can always leave out the pentagons that arnt used. If you even wrote a small code, you could have had the opportunity to nust perfectly visualize only those pentagons that are crossed, no matter where you pull your line.
I'm 21y old non-mathematician and I must say that this kind of feels like it's too obvious. If there was ever a person, let's say 100y ago, that said: -Hm, this thing made out of triangles can be unfolded and then you can connect corners, but oh, you always cross another corner if you want to connect one with itself. Let's look at the cube, and the hexagon structure- then why in gods name wouldnt he look at the dodecahedron, that obviously existed already that time? It is too easy to be found out now! Waaaay to easy! It's not even connected to the possibilities of this time, even the old Egyptians could have found out about that.
In my opinion it is impossible that noone ever thought about that before!
Date: 2022-04-09
Related videos
Comments and reviews: 9
JT
When I think about living upon a Dodecahedron, I think of the way in which gravity would pull my body to the center. When you step down onto the perceptually declining plane, you would get the feeling of going down hill for a moment and adjust your stance to compensate. As you leave the edge of the plane, approaching the middle of that plane you would feel as if you were walking on flat ground, even though you are on the same planar surface. Then as you proceed to the opposite edge of that plane you would feel as if you are walking up hill. Perhaps you might perceive the plane as parabolic rather than flat to match the input you are getting from the pull of gravity. Perhaps generations of organisms would evolve to perceive the normally flat plane as having an inward curve, to match their sense of balance. While standing upon the apex where multiple faces meet, you might see angles between faces of 116. 57 degrees, but it would feel much steeper.
reply
When I think about living upon a Dodecahedron, I think of the way in which gravity would pull my body to the center. When you step down onto the perceptually declining plane, you would get the feeling of going down hill for a moment and adjust your stance to compensate. As you leave the edge of the plane, approaching the middle of that plane you would feel as if you were walking on flat ground, even though you are on the same planar surface. Then as you proceed to the opposite edge of that plane you would feel as if you are walking up hill. Perhaps you might perceive the plane as parabolic rather than flat to match the input you are getting from the pull of gravity. Perhaps generations of organisms would evolve to perceive the normally flat plane as having an inward curve, to match their sense of balance. While standing upon the apex where multiple faces meet, you might see angles between faces of 116. 57 degrees, but it would feel much steeper.
reply
Paul
So does this lend itself to diagramming the flow of electrons around the different kinds of stable sub-atomic or atomic particles?
Is the number of these and those the same?
If so, I suggest it does.
Also, if the number of routes (yellow brick roads) equals the amounts of electrons (atomic numbers) in any set or subset of atoms or sub atomic particles.
Someone should find out, using these intervals to tune equivalent wavelengths to select tonal vibrations and test whether they can have an effect on the stability or instability of these -elemental particles-.
I'm not the guy.
Please investigate these and you'll not oy be the guy, but you'll probably be the guy that creates zero-point atomic energy.
Which could literally tame space.
As well as you'll likely rediscover optimal harnessing of free ambient electric energy.
Please copy & paste this if you know a guy.
reply
So does this lend itself to diagramming the flow of electrons around the different kinds of stable sub-atomic or atomic particles?
Is the number of these and those the same?
If so, I suggest it does.
Also, if the number of routes (yellow brick roads) equals the amounts of electrons (atomic numbers) in any set or subset of atoms or sub atomic particles.
Someone should find out, using these intervals to tune equivalent wavelengths to select tonal vibrations and test whether they can have an effect on the stability or instability of these -elemental particles-.
I'm not the guy.
Please investigate these and you'll not oy be the guy, but you'll probably be the guy that creates zero-point atomic energy.
Which could literally tame space.
As well as you'll likely rediscover optimal harnessing of free ambient electric energy.
Please copy & paste this if you know a guy.
reply
musikSkool
The few people in this world smart enough to solve any problem given them will never be given enough money, power, influence, or authority to solve the world's problems. The people that do have the power/money never have the intelligence or authority, and vice versa. Not only do we not know how to tell who can solve all the world's problems, we also don't know how to give them enough control of the world to do it. It is mathematically impossible to solve all the world's problems. If it wasn't already impossible, we don't even know how many people it would take and what to do if 2 people both decide that it only takes 1 person, and they believe that person is them. Another big war happens.
reply
The few people in this world smart enough to solve any problem given them will never be given enough money, power, influence, or authority to solve the world's problems. The people that do have the power/money never have the intelligence or authority, and vice versa. Not only do we not know how to tell who can solve all the world's problems, we also don't know how to give them enough control of the world to do it. It is mathematically impossible to solve all the world's problems. If it wasn't already impossible, we don't even know how many people it would take and what to do if 2 people both decide that it only takes 1 person, and they believe that person is them. Another big war happens.
reply
mikefromspace
Kepler was actually on to something however, as we now know every heavenly body with a molten core has the same ley line geometry which is the same used to pack power cables most efficiently! 16 around 10 on the surface with 5 centers above and below the equator, around 6 around 1. The 10 are seen easily as earth's 10 vile vortices. The 6 were seen as a hexagon at the pole in voyager's Saturn flyby. The 10 were also seen as average sunspot locations from 2007-2018 while we passed through the galaxy axis.
The dodecahedron solution seems it could also be a way to solve pi using differentials.
reply
Kepler was actually on to something however, as we now know every heavenly body with a molten core has the same ley line geometry which is the same used to pack power cables most efficiently! 16 around 10 on the surface with 5 centers above and below the equator, around 6 around 1. The 10 are seen easily as earth's 10 vile vortices. The 6 were seen as a hexagon at the pole in voyager's Saturn flyby. The 10 were also seen as average sunspot locations from 2007-2018 while we passed through the galaxy axis.
The dodecahedron solution seems it could also be a way to solve pi using differentials.
reply
Matthew
Triacontagon? These isometric shapes are kind of like prime numbers, you find them easily when you start out and they get more and more difficult to locate as the numbers get bigger. And what was the exact thickness of your line? I failed to see you mention that fact which is pretty critical to determining if the line crossed the point, convention dictates as you add more decimals and decrease the line width that there is less and less chance of it actually crossing the point which I assume is the minimum definable size possible? :-)
reply
Triacontagon? These isometric shapes are kind of like prime numbers, you find them easily when you start out and they get more and more difficult to locate as the numbers get bigger. And what was the exact thickness of your line? I failed to see you mention that fact which is pretty critical to determining if the line crossed the point, convention dictates as you add more decimals and decrease the line width that there is less and less chance of it actually crossing the point which I assume is the minimum definable size possible? :-)
reply
education
Why not just name the lines by the actual length of them? In order to determine the length of them, you'd have to define what length equals -1-, whether that's the length of one side of a pentagon, or some other imporant dimension. So, you might want to scale -1- by whatever length ends up creating the most novel or interesting lengths of paths around the dodecahedron, and then name the lines after those lengths.
reply
Why not just name the lines by the actual length of them? In order to determine the length of them, you'd have to define what length equals -1-, whether that's the length of one side of a pentagon, or some other imporant dimension. So, you might want to scale -1- by whatever length ends up creating the most novel or interesting lengths of paths around the dodecahedron, and then name the lines after those lengths.
reply
WhimpyPatrol
On a midterm I used a graphic argument to prove a combinatorics problem, but my Harvard PhD math professor rejected it only because it was graphic. My only restitution was several weeks later when he was 3 minutes into a lecture on a premise he pulled from Feller's vol 1 on probability to which I gave a one sentence verbal argument to disprove, and he thus had to terminate the class that day.
reply
On a midterm I used a graphic argument to prove a combinatorics problem, but my Harvard PhD math professor rejected it only because it was graphic. My only restitution was several weeks later when he was 3 minutes into a lecture on a premise he pulled from Feller's vol 1 on probability to which I gave a one sentence verbal argument to disprove, and he thus had to terminate the class that day.
reply
JT
It's interesting that the platonic solid consisting of a 3 sided shape has 5 shapes intersecting and the icosahedron made up of 5 sided shapes has intersections made up of 3 shapes. The same inverse relationship between shape sides and number of shapes involved in intersecting points is true of the cube and the Octahedron. I wish I knew enough to explain why in mathematical terms.
reply
It's interesting that the platonic solid consisting of a 3 sided shape has 5 shapes intersecting and the icosahedron made up of 5 sided shapes has intersections made up of 3 shapes. The same inverse relationship between shape sides and number of shapes involved in intersecting points is true of the cube and the Octahedron. I wish I knew enough to explain why in mathematical terms.
reply
r00t
Would be more interested to know how gravity would be affected on differing parts of the hypothetical dodecahedron planet. The vertices are further away from the center of the solid (which would make for a lower gravity experience, versus the center of each of the shape's faces (higher gravity area being those would be closer to the center of the mass.
reply
Would be more interested to know how gravity would be affected on differing parts of the hypothetical dodecahedron planet. The vertices are further away from the center of the solid (which would make for a lower gravity experience, versus the center of each of the shape's faces (higher gravity area being those would be closer to the center of the mass.
reply
Add a review, comment
Other channel videos
