How to break into a math book

When Shen Siyi said this, everyone was stunned.

"Blindfolding? What do you mean?"

"Sun Wei's idea is not wrong. The level we are in is about trigonometric functions, so it must be related to trigonometric functions." Shen Siyi explained, "But if we only use the diameter of a circle, it is not enough to prove this level. and trigonometric functions."

He stood on the white stone platform at the center of the circle, looked around at the six points evenly distributed on the circumference, and then stretched his arms, pointing to the positions of the red stone platform and the yellow stone platform respectively, forming a 60-degree circle between the arms Angle: "In this 360-degree circle, the angle between the centers of every two points is 60 degrees. If we take the radius formed by the red stone platform and the white center as the starting point, the arc of the center angle of red, white and yellow It is 60 degrees, and the angle between red, white and blue is 120 degrees."

"This circle is like a color wheel, with the three primary colors of red, yellow, and blue, from which pink, light yellow, and light blue are derived. If you connect the three primary colors with trigonometric functions...the three most basic colors in the color spectrum It happens to correspond to the three most basic elementary functions in trigonometric functions, sine, cosine, and tangent."

Tang Bo is not interested in art, so he was at a loss when he heard about hue and color spectrum: "What is the corresponding relationship between color and trigonometric function?"

Shen Siyi smiled: "This is just one of the discoveries, let's take a look at the other discovery first."

"First take the three points that we know to be yellow, white, and light yellow on a straight line. The number represented by the yellow stone platform is 6, the white stone platform is equal to 3, and the light yellow stone platform is also 3. From the perspective of art, the color Generally speaking, if yellow is mixed with a little white, the color of yellow itself will become lighter, so light yellow can be obtained with yellow and white.”

Tang Bo wondered: "But the sum of the numbers of yellow and white is 63=9, and the number represented by the light yellow stone platform is 3, the two are not equal."

Shen Siyi smiled and said: "But haven't you discovered that the square of 3 is equal to 9, that is to say, the sum of the number on the yellow stone platform and the white number is exactly equal to the square of the number on the light yellow stone platform. After discovering this rule, In connection with the correspondence between the three primary colors and the three elementary trigonometric functions that I mentioned for the first time, you will quickly discover the laws."

The sine sin, cosine cos, and tangent tan correspond to the three primary colors of red, yellow, and blue respectively, and the results obtained can also be related to their corresponding light color systems...

Tu Hua frowned, his eyes wandered among the three red, yellow and blue stone platforms.Although he is poor in trigonometry, he still knows the most basic function values ​​and function transformations.Shen Siyi's words opened up a new way of thinking for him. Mathematics is not just about meaningless combination and transformation of numbers. It has a wide range of applications in terms of seemingly boring trigonometric functions.

In addition to the measurement of various dimensions in life, trigonometric functions are also related to art.The most basic hue circle in art painting is a circle. Starting from red, various colors are evenly distributed on the entire circle according to the temperature of the hue. Each color system has its specific arc range, which can be adjusted according to the size of the circle angle. Accurately identify complementary, contrasting, adjacent, and analogous colors.

Therefore, it is not unreasonable to set the three primary colors on the circumference of the circular string seven-star array. The system just wants to link colorful colors with trigonometric functions.

In this way, Tu Hua understood that all the conditions point to the same answer: "The number on the pink stone platform should be 2."

Shen Siyi looked at him approvingly.

Tang Bo, who was standing on the pink stone platform, didn't quite understand: "Why?"

Tu Hua and Shen Siyi looked at each other. This Shen Siyi was really unfathomable. In just a few minutes, he was able to connect so many information that others would hardly notice in such a way. His thinking Ability and logical ability are indeed hard to come by.

After his suggestion, Tu Hua figured out the reason: "The three primary colors of red, yellow, and blue are like the three elementary functions of sine, cosine, and tangent in the trigonometric functions. The most basic is the position of all hues. And the root of function transformation." Tu Hua pointed to the red stone platform under his feet, "So we can make an analogy, red represents the sine sin, yellow represents the cosine cos, and blue represents the tangent tan."

"Whether it is the order of our jumping grid or the order of the three primary colors, we all start from red, so in the angle of trigonometric functions, I should also start from the side of red." He gestured with his hand to the red stone platform The straight line connected with the white stone platform, "take the red and white line as the starting point, on the circumference, the angle of the point where the red stone platform is located is 0 degrees, and the angle of the point where the yellow stone platform is located is that of Shensi Yigang. The angle between red, white and yellow is 60 degrees; similarly, the angle of the blue point is 120 degrees."

"As I just said, the red, yellow, and blue points represent sine sin, cosine cos, and tangent tan respectively. We only need to assign their corresponding angles to trigonometric functions and we will find that sin0=0, cos60=1/2, tan120 = Negative square root 3." Tu Hua analyzed, "Comparing the assignments of these three trigonometric functions, we can find that tan120<sin0<cos60, sort them in this order and you will find that the blue tan120 is the smallest , ranked first, the red sin1 is the second, and the yellow cos0 is the largest and the third.”

Tu Hua pointed to the light yellow and light blue stone platforms that were on the same straight line as the yellow and blue, and said: "It just so happens that the stone platform on the light blue stone platform corresponding to the blue ranked first The number is exactly 1, and the number on the pale yellow stone platform corresponding to the third yellow stone platform is exactly 1."

"But the law you mentioned can only be regarded as the law of color and trigonometric functions at most, and has nothing to do with the numbers on the stone platform." Sun Wei was puzzled, "Is it too much to judge that the pink stone platform is equal to 2 based on this alone?" Hasty?"

沈思易接着涂化的分析道：“数字之间也是存在规律的，你记得我刚开始说的在同一直线上的黄色6白色3=淡黄3的2次方这件事情吗？淡蓝色石台上1就是1的1次方。”

"The three stone platforms of light blue, pink, and light yellow not only have a sequence relationship between the numbers they represent, but also have a sequence in the straight line calculation they are on." Shen Siyi said, "According to the order of the three primary colors of red, yellow and blue, red corresponds to The number on the pink stone platform represents the power of 3 when calculating, that is to say, the cube of the number 2 on the pink stone platform is equal to 8, the number on the red stone platform is 5, the white is 3, 53 is exactly equal to 8, and 53 is equal to 2 Similarly, the known yellow stone platform ranks second among the three primary colors, and the order of adding numbers on the straight line of yellow, white, and light yellow is exactly 63=9, which is 2 to the third power. "

"According to this order of reasoning, the addition of the unknown number on the blue stone platform to the 3 on the white stone platform should be exactly equal to the power of 1 on the light blue stone platform, which is 1."

Wang Boyu understood: "So the number on the blue stone platform is -2?"

沈思易道：“对。粉、淡黄、淡蓝这三个石台数字运算时次方的大小顺序，正好就是按照与之对应的红、黄、蓝三色顺序排序的。也就是说红色对应的是2的3次方，黄色对应3的2次方，蓝色对应1的1次方。”

This calculation method and rules are more difficult than they have encountered before. I don't know if it is because Shen Siyi, a high-level player, joined in, the system seems to increase the difficulty of the game for them.

这个复杂的填数规则其实主要包含三个要点：第一个，是每条直线上深色与白色相加可以得到与浅色相关的数字。红、白、粉这条直线上的数字就53=8；黄、白、淡黄就是63=9；蓝、白、淡蓝就是-23=1。

The second point is the ordering rule after the three primary colors correspond to the three elementary functions of trigonometric functions, and then are calculated according to the angle of the center of the circle.The three trigonometric functions sin0, cos60, and tan120 respectively represented by red, yellow, and blue are sorted after the calculated results, and the sorting order is exactly the numbers on the light-colored stone platforms corresponding to them.The first place is the tan120 blue stone platform with the smallest function value, and the number on the light blue stone platform corresponding to it is 1; the second place is the red stone platform of sin0, and the corresponding pink stone platform The number above is 2; the third place is the yellow stone platform of cos60, and the corresponding light yellow stone platform represents the number 3.

The third point is the most important numerical operation relationship.Sorting according to the order of the three primary colors of red, yellow, and blue, you can determine the power of their corresponding light-colored numbers in the calculation. According to the order, the power of the pink stone platform corresponding to red is 3, and the power of the light yellow stone platform corresponding to yellow is 2. The power of Taiwan is 1, and the power of light blue corresponding to blue is [-].

In this way, combined with the result of the addition of the three straight lines in the first point, the law contained in it can be clearly discovered.On the straight line of red, white, and pink, red plus white equals pink, that is, 53=8=2^3; on the straight line of yellow, white, and light yellow, yellow plus white equals light yellow, that is, 63=9=3^ 2; On the straight line of blue, white, and light blue, blue plus white equals light blue, which is exactly -23=1=1^1.

Therefore, according to this complex law, the numbers represented by the unknown pink stone platform and blue stone platform should be 2 and -2 respectively.

Wang Boyu was so dizzy that he knew the answer in a daze, but he was puzzled by the number in the answer: "-2, will there be a number -2? The numbers filled in this seven-star array should be all natural numbers? Besides, the ancient Are there negative numbers?"

"Of course there is." Tu Hua remembers this very clearly. The discovery of negative numbers is the most advanced achievement in the history of ancient Chinese mathematics. He was proud of it for a long time when he read it in a book. In the Western Han Dynasty, my country had already proposed the concept of negative numbers, and the "Nine Chapters of Arithmetic" also mentioned the exact algorithm of negative numbers, while foreign countries always believed that 1 means nothing at that time, and refused to admit the existence of negative numbers. Europeans It was only after the 0th century that we clearly realized the operation of negative numbers. Therefore, our country is very advanced in the understanding of negative numbers, and it is not impossible for the number -15 to appear here.”

Shen Siyi smiled and said: "This is what I think of as the 'blurring method'. This level has been misleading us, making us think that a straight line is the diameter of a circle, and using simple ancient math problems to make us think that the law of the seven-star array is not too difficult , and even has been misleading us with natural numbers, making us think that there can be no negative numbers here.”

"But the truth can only be produced after going through misunderstandings countless times." His eyes are full of wisdom, "It's like mathematics, both annoying and cute."