Chapter 178: Tyson Polygon

Hirano Toru was standing on Teacher Jiang's right hand, silent, but the gloomy eyes kept staring at Cheng Nuo.
4:0!
Their island team, now, they have no way out.
The island team must win the last game.
Otherwise, they will be abused by the Hua Guo team 5:0!
Once this happens, their island country will lose face.
As the captain of the island national team, Hirano may be fine for the time being. But once I return to my country, I will definitely be forced to film every day.
This is not the life Hirano Tosuke wants. He is tired of the life of filming, and he is obsessed with studying, unable to extricate himself!
"Kun Hirano, come on! Defeat the great devil of China!" All the audience in the island country shouted in their hearts.
Hirano Noriu was the strongest among the six players sent by the island nation. Therefore, the island audience also placed the greatest hopes on him.
They knew that the opponent Hirano Fayu faced was Cheng Nuo, the hexagonal warrior!
But still... they have great confidence in the strength of Hirano Law Education.
"Let's take a look at the challenges of the two players."
Teacher Jiang motioned everyone to look at the big screen.
On the big screen, the picture flashed, and the five characters "Tyson Polygon" slowly emerged from the big screen.
That's right, the name of the project challenged by Cheng Nuo in this peaceful field training is called "Tyson Polygon"!
The Tyson polygon is a method proposed by the climatologist a·h·thiessen to calculate the average rainfall based on the rainfall of discretely distributed weather stations.
The method of construction is hard to say.
Simply put, first select a discrete point as the target point, and then connect this discrete point with the surrounding discrete points to form one triangle after another to form a triangulation network.
Let the discrete point be o. Find a triangle with o as the vertex and set it as a; take the other vertex of triangle a except o and set it as a, then the other vertex can also be found, which is f; then the next triangle must be of If it is a side, it is triangle f; if the other vertex of triangle f is e, then the next triangle has oe as the side; repeat this process until back to the oa side.
Calculate the center of the circumcircle of each triangle with this discrete point as the fixed point, and connect them.
In this way, the formed triangle is called...Tyson polygon. If expressed by the formula, it is √∑(si-s)^2/n, (n=1, 2, 3,...)
Give a chestnut~~
The Water Cube in Kyoto was designed based on the principle of Tyson's polygon.
The challenge rules for the two players are as follows.
Two spheres, each with 5000 discrete points distributed on each sphere.
Each sphere has 5000 discrete points, and each discrete point can form a Thiessen polygon, which is 5000 Thiessen polygons in total.
The other sphere is also 5000 Tyson polygons.
Among the total of 10,000 Tyson polygons, there are only two Tyson polygons, which are exactly the same!
What the player needs to do is to find these two identical Tyson polygons in the shortest time and press the answerer!
One point for correct answers, one point for wrong answers.
A total of three rounds are played, and the first two points wins.
This challenge project, at first glance, seems to be very simple. It is an upgraded version of the "find the difference" we usually play. Look for the same...
However, in fact, this challenge is the most difficult challenge among the five matches between China and the island nation today!
The overall strength of the players is a great consideration.
Computation, memory, space, reasoning, creativity, observation, six abilities are indispensable.
The contestant does not know that any position of two discrete points that can form the same Tyson polygon.
In other words, they need to try one by one.
Among the two spheres full of discrete points, one sphere is randomly selected. Observe 5000 discrete points on it.
Through observation, calculation, and inference, the player can figure out the Tyson polygon corresponding to a discrete point.
The number of triangles formed by each discrete point and the surrounding discrete points is different. In simple terms, there may be three triangles. In this case, you only need to connect the centers of the three circumcircles corresponding to the three triangles to form a Thiessen polygon.
Complicated, there may be five or six triangles in the triangulation network. When you can't use pen and paper, but rely on your brain to calculate, it's easy to get confused.
Most importantly, after you have gotten the shape of this Tyson polygon, you need to remember it. Compare with 5000 Tyson polygons on another sphere.
If you do a simple calculation, if two players want to find the answer, they need to judge 500050000, a total of 25 million times!
terror! Quite scary!
The computational complexity of this problem is so great that I am afraid that it will not be possible to do it in a short period of time with a computer.
…………
The rules are over.
The audience in the audience look at me and I look at you, all with a dumbfounded look.
Discrete point, triangle net, circumscribed circle...
A series of mathematical terms stunned the audience.
There is also the Tyson polygon, just listen to the name, it is slowly forced!
unfortunately……
Although on the big screen, even the image and the text were explained for a long time, they still... did not understand.
Well, we don't understand the problem of the big brother.
Once again, their own birth was raised in their hearts, just to give humanity the feeling of making up numbers.
On the stage, while everyone in the audience was still doubting their lives, Cheng Nuo and Pingye Fayu were already sitting in their challenge chairs.
On the desktop in front of them, there is a small screen.
The left and right sides of the screen each have a spherical surface with a diameter of about 3/4 of the screen height.
It's just that the two spheres at this time are gray and dark, with 10,000 discrete points, which have not yet been covered.
"Next, please randomly generate 10,000 discrete points in the background."
After Teacher Jiang's voice fell, the two spheres on the screen in front of Cheng Nuo and Heping Ye Fayu among the audience began to flicker with stars. Just like stars in the dark.
The starburst was just one or two points at first, but gradually, 10,000 white light points covered the two spheres almost completely.
Wow!
Dense ~EbookFREE.me~ quite dense!
Originally, the area of ​​the sphere is not large. 5000 discrete points are marked once, and instantly, when viewed from a distance, the sphere is almost completely covered by the discrete points. A large swath of densely packed.
Everyone instantly numbs their scalp!
This is definitely the biggest torment for people with intensive phobia.
"I declare, challenge, start!"
Teacher Jiang raised the volume, and after saying this, he immediately pressed the timer.
Timing begins!
Cheng Nuo and Heping Ye Fayu immediately looked at the screen.
In the last match between the Huaxia Team and the Island Nations, the first question is, who will be the first to complete it, and the result will be announced immediately...
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