Blue Star Sea Diamond

"Everyone has to consider this question, the question extended by this conjecture."

The teacher is Zu Wenyuan. While writing complex and quirky symbols in black and white, he is drawing various diagrams representing abstract ideas.At this time, he wanted to just throw the world's problems to his students.

Suddenly I saw a student answer: "What kind of simple geometry and construction method are used to make a specific sequence, and then construct the complex geometry we want? I don't think it is difficult!"

Zu Wenyuan looked at Xia Shangbu and wanted to laugh when he heard these words.Although he wanted to throw this kind of problem to the students to solve, Zu Wenyuan was still a little disgusted with such a careless answer.

"Don't be anxious to say that, you can tell me, is there any way?"

Xia Shangbu thought for a while and said: "A complex curved surface can be constructed from countless equilateral triangles."

Zu Wenyuan chuckled: "You just learned it, right? If you see a complicated surface, you can immediately know how to construct it with countless equilateral triangles? You are naive! First of all, these countless ones Are all equilateral triangles equal in size? If they are not equal, how should the size be chosen?"

"Cover with the largest one first, and see if the smallest place is covered with the largest one, and every gap is covered with the largest triangle possible, until the smallest one is covered." Xia Shangbu said. Words meant that they had to sacrifice their lives.

"Haha, what is the smallest cover? How small is it? Can it be within the error range and just leave it alone?" Zu Wenyuan followed Xia Shangbu's meaning and tried to derive, and was not eager to refute him. the opinion of.For Zu Wenyuan, solving problems is sometimes more worth cherishing than asking questions. The teacher's criticism should be level, instead of being an emotional big shot.

"I didn't do it. When doing a certain project, this kind of error is small and does not affect the project at all, and the way to make countless triangles like this is completely desirable." Xia Shangbu thought that he was perfect, as long as It is a problem that has been carefully considered, and there is no solution that cannot be solved.

"I found two problems. The first is to calculate the maximum shape of the covering triangle based on the shape. This cannot be calculated all at once. The second is that as the gap increases, the process of filling in the blanks with triangles will also change. It's extremely complicated and complicated." Zu Wenyuan wanted to test Xia Shangbu's ability in a rebuttal way. The most important thing is to test Xia Shangbu's endurance.

"If you can't give the shape quickly, use a random method to change the largest triangle, there is no need to traverse to compare which triangle area is the largest. For the process of filling in the blanks, you use software algorithms. Can you use distribution? The formula is solved to calculate.” Xia Shangbu thinks that this method is also advisable. It is not necessary to find the largest triangle. As long as it is large enough to be found randomly and quickly, the calculation process will speed up, and the following The calculation process will also be accelerated as a result.

Zu Wenyuan was thinking in his heart that the sequence of this structure is to first know the surface, then randomly draw triangles to fill it, and record the triangle information, and then record the information of a triangle without filling a triangle at random. The gap below is within the error range.

"Even if you use this method, the algorithm for finding the gap will still be very troublesome. Because you don't know if it's covered here or not." Zu Wenyuan was still confused.

"Then record each coverage, and then after encountering a gap, calculate the center coordinates of the gap. The center coordinates are outside the covered triangle. It is enough." Xia Shangbu continued, "You add directly to the sequence. Just follow this procedure."

"You said that you give the shape randomly, and determine that the gap is not covered by triangles, etc. This is the fuzzy problem in Hodge's conjecture. The gap is not covered by triangles, your algorithm may be wrong, in case there is a small gap , But the center of mass covers the concave structure at the center of the triangle. Even if you have other algorithms, it is still very complicated.” Zu Wenyuan used this method to tell everyone the difficulty of Hodge's conjecture.

Xia Shangbu became interested in an instant. He thought he should use basic geometry to collude with a complex three-dimensional shape.

In Xia Shangbu's mind, he started stacking objects of a shape with a regular tetrahedron structure, and tried to transform the object.