universal data

Chapter 176 Thiessen Polygons

Hirano Fayu stood by Mr. Jiang's right hand, silent, but stared at Cheng Nuo with dark eyes.

4: 0!

Their island team, now, they have no way out.

In the last game, the island nation must win.

Otherwise, it will be completely abused by the Hua Guo team 5:0!

Once this happens, their island country will lose face.

As the captain of the island nation, Hoyu Hirano may be fine for the time being.But once I return to China, I will definitely be forced to film every day.

This is not the life Hoyu Hirano wants.He is tired of the life of filming, and he is obsessed with studying, unable to extricate himself!

"Mr. Hirano, come on! Defeat this great demon king of Hua Kingdom!" All the audience in the island country shouted wildly in their hearts.

Hirano Fayu is the strongest among the six players sent by the island country to participate in the battle.Therefore, the island audience also placed the greatest expectations on him.

They knew that Fayu Hirano was facing Cheng Nuo, the hexagonal warrior!
But still... They have great confidence in Hirano Fayu's strength.

"Let's take a look at the challenges of the two contestants."

Teacher Jiang motioned everyone to look at the big screen.

On the big screen, the screen flashed, and the five characters of "Tyson Polygon" slowly emerged from the big screen.

That's right, the name of the project that Cheng Nuo and Hirano Fayu challenged this time is called "Tyson Polygon"!
Thiessen polygon is a method proposed by climatologist A.H. Thiessen to calculate the average rainfall based on the rainfall of discretely distributed weather stations.

Its construction method cannot be said to be difficult.

To put it simply, first select a discrete point as the target point, and then connect this discrete point with the surrounding discrete points to form triangles one after another to form a triangular network.

Let the discrete point be o.Find a triangle with o as the vertex, set it as A; take another vertex of triangle A except o, set it as a, then the other vertex can also be found, which is f; then the next triangle must be of is the side, that is triangle F; the other vertex of triangle F is e, then the next triangle has oe as the side; and so on, until returning to the side oa.

Calculate the center of the circumcircle of each triangle with this discrete point as the fixed point, and connect them.

The triangle formed in this way is called... Thiessen polygon.Expressed by a formula, it is √∑ (Si-S)^2/n, (n=1, 2, 3,...)
Take a chestnut~~
The Water Cube in Kyoto is designed based on the principle of Thiessen polygons.

The challenge rules for the two contestants are as follows.

Two spheres, each with 5000 discrete points distributed on them.

Each sphere has 5000 discrete points, and each discrete point can form a Thiessen polygon, which is a total of 5000 Thiessen polygons.

Another sphere, also 5000 Thiessen polygons.

Out of this total of 10000 Thiessen polygons, there are exactly two Thiessen polygons, identical!

What the contestants need to do is to find these two identical Thiessen polygons in the shortest time and press the answering machine!

One point for a correct answer and one point for a wrong answer.

A total of three rounds are played, and the first to score two points wins.

This challenge project, at first glance, seems very simple, it is an upgraded version of the "find the difference" we usually play, find the same...

However, in fact, this challenge is the most difficult challenge among the five matches between Huaguo and Island nation today!
The overall strength of the players is a great consideration.

Calculation, memory, space, reasoning, creativity, observation, six abilities are indispensable.

The contestant does not know any position of two discrete points that can form the same Thiessen polygon.

That is, they need to be tried one by one.

From two spheres filled with discrete points, choose one at random.Observe 5000 discrete points on it.

Through observation, calculation and inference, the contestants can infer a Thiessen polygon corresponding to a discrete point.

The number of triangles formed by connecting each discrete point with surrounding discrete points is different.If it is simple, it may be three triangles. In this case, it is only necessary to connect the centers of the three circumscribed circles corresponding to the three triangles to form a Thiessen polygon.

Complex, there may be five or six triangles in the triangulation.When you can't use pen and paper and can only rely on your brain to calculate, it is easy to get confused when you calculate.

Most importantly, after you have got the shape of this Thiessen polygon, you need to remember it.Compare that with 5000 Thiessen polygons on another sphere.

In a simple calculation, if the two contestants want to find the answer, they need to judge 5000*50000, a total of 25000000 million times!
fear!Quite scary!
This problem requires a lot of calculations, and I am afraid that it will not be able to solve it in a short time with a computer.

…………

Rules, that's it.

The audience in the auditorium looked at me and I looked at you, all with dumbfounded faces.

Discrete points, TINs, circumscribed circles...

A series of mathematical terminology stunned the audience.

There is also the Thiessen polygon, just listening to the name, it is slowly getting better!

pity……

Although on the big screen, even the pictures and text explained for a long time, they still... didn't understand.

Well, the topic of the boss, we should not understand it.

Again, they have their own birth in mind, just to make up the numbers for humans.

On the stage, when everyone in the audience was still doubting their lives, Cheng Nuo and Heino Fayu were already sitting in their challenge chairs.

On the desktop in front of the two of them, there is a small screen.

On the left and right sides of the screen, there is a spherical surface with a diameter of about 3/4 of the screen height.

However, the two spherical surfaces at this time are gray and dark, and 10000 discrete points have not yet covered them.

"Next, please randomly generate 10000 discrete points in the background."

After Teacher Jiang's voice fell, among the audience, the two spheres on the screen in front of Cheng Nuo and He Ye Fayu began to twinkle with stars.Like stars in the dark.

At first, there were only one or two starbursts, but gradually, 10000 white light spots almost completely covered the two spheres.

Wow!
Dense, quite dense!
Originally, the area of ​​the sphere was not large. Once the 5000 discrete points are marked, in an instant, the spherical surface is almost completely covered by the discrete points when viewed from a distance.A large, densely packed area.

Everyone's scalp felt numb in an instant!
This is definitely the biggest torture for people with trypophobia.

"I declare, challenge, start!"

Teacher Jiang raised his volume, and after saying this, he immediately pressed the timer under his hand.

Timing begins!
Cheng Nuo and He Yefayu immediately looked at the screen.

In the last match between the Huaxia team and the Island nation team, who will finish the first question first, and the result will be announced soon...

(End of this chapter)