Xinggang P丨text
According to the normal progress, the new episode in October 2023 is almost finished, I don't know which ones you have watched. Of course, what BB Ji wants to talk about today is not the plot of the drama.
Here's the thing, recently X (Twitter) had a Japanese math enthusiast find a blind spot in the "Buried Frilian" anime:
In the third episode, "Killing Magic", Faeron uses a spherical defensive magic barrier to resist the attacks of the demons.
However, this design is not reasonable, because according to Euler's theorem of polyhedra, it is impossible to form a sphere-shaped enchantment with only regular hexagons.
This topic immediately caused heated discussions on X, and many people didn't understand this, so they used the examples around them to verify it.
If you want to say that the most common ball with a hexagonism in life, it must be football...... We all know that the most classic black and white color style is a white hexagon + black pentagon.
And what if it's a little denser? What about golf balls, for example?
If you look closely, there are really some pentagons mixed in the hexagon, which makes things more interesting when you get serious.
If you take the game as an example, there is a hero called Void Mask in Dota 2, who is good at playing with time and space, and his ultimate is to control all the units in it with a spherical range.
There is an accessory (equivalent to a weapon skin) that transforms the original sphere into a polygonal sphere. If you look closely, you'll see that there are indeed inlaid pentagons inside.
Some netizens further explained:
Regular polyhedron should only have cubes, tetrahedrons, octahedrons, dodecahedrons, and icosahedrons, and if the "spherical" is not the above five, it is impossible to simply rely on a plane shape.
Friends who have recently played Baldur's Gate 3 or who usually have experience running a group should be familiar with it, after all, the dice are all in the shape of a regular polyhedron.
Of course, if you don't pursue a perfect "spherical shape", you can make it with a little bending. However, this spherical shape is more difficult to maintain at high latitudes, and will always be distorted and deformed, and it is impossible to maintain a perfect hexagon.
(Top or deformed)
(or no cap)
Designs like the Interstellar 2 Protoss also have a variety of hexagonal tessellations.
But if you look closely, it's either cylindrical, or the high-latitude part is cut off and turned into a ring like a tire, or a half-eggshell-like shape.
Going back to the original hexagon + pentagonal combo - we might interpret it as the enchantment has a cover door, and the strength is slightly lower than other units in some places, and enemy attacks are easier to penetrate.
If you don't want to kill your OCD, you can also split the polygon into small triangles, which will also increase the strength of the structure.
This method is called the "Buck Ball Construction" and is also known as the Fuller Ball, which originated from an architect named Buckminster Fuller.
The naming scheme is C2n (2n is the number of vertices), the pentagon is always no more than 12, and the hexagon is n-10.
(Iron Man)
(Disney theme parks' "Spaceship Earth")
For example, you should have learned in textbooks about an allotrope of carbon, carbon-60, also known as "football ene" and "fullerene", which is inspired by this.
The molecular structure is composed of 60 carbon atoms, with a total of 12 pentagons and 20 hexagons.
With the heated discussion on the Internet, the performance of enchantment skills in various animations and special effects works has also been excavated.
The teacher in charge of painting "Frilian the Buryed" also noticed the discussion among netizens and said that they had actually discussed this thing.
And explained: It is indeed impossible for a spherical barrier to be composed of only hexagons. They actually had a meeting to discuss the shape of the Rubik's Cube barrier, and they boldly didn't use the pentagon, considering that the number 6 was meaningful.
In the eighth episode, there are actually some shows of the magic enchantment, as for the specific relationship between the plot setting and the number 6, I have to sell it off, and I didn't reveal the follow-up.
I don't know if there's really a statement.
Some people may think that there is no need to look for reality in fictional stories, and the things of the wizarding world do not need to be so clear, but after reading the discussions of netizens, I still feel that mathematics is really amazing.
Of course, I'm not a professional math master, if there is a mistake, you can comment and leave a message to point it out.
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