There is a mathematical Pythagorean theorem problem It is known that there are two fishing boats in port B. ship a and ship b set out at the same time. If ship a goes along the direction of 60 degrees north by east at a speed of 8 nautical miles per hour, ship B sails along the direction of 30 degrees south by East with a speed of 9 nautical miles per hour. Two hours later, ship a arrives at Island m and ship B sails to island P. please estimate the distance between island m and island P

Root sign (square of 18 + square of 16)

A mathematical Pythagorean theorem If the lengths of three sides of a right triangle are a, B, C and C are oblique sides, if M = a + B-C, the ratio of the area to the perimeter of the triangle is expressed by the formula containing M

1. Area s = a * B / 2
2. Perimeter L = a + B + C
3. Pythagorean theorem has a ^ 2 + B ^ 2 = C ^ 2
That is (a + b) ^ 2-2ab = C ^ 2, substituting m + C = a + B, there is (M + C) ^ 2-C ^ 2 = (M + 2C) * m = 2Ab
S:L=ab:2(a+b+c)=(m+2c)*m:4(m+2c)=m/4

Pythagorean number in accordance with Pythagorean theorem Such as 3, 4, 5, etc

k(m^2-n^2)
2kmn
k(m^2+n^2)
Any positive integer k, m, n can be substituted

Pythagorean theorem is very important. Can you give me some sets of Pythagorean numbers?

3,4,5；
5,12,13

Mathematical Pythagorean theorem If we know that in △ ABC, ab = 1, BC = radical 2, AC = radical 3, then the length of the central line BD on the edge of AC is____

According to the inverse operation of Pythagorean theorem, it is calculated that:
Angle B = 90 degrees,
According to the theorem
The center line on the hypotenuse of a right triangle is half of the hypotenuse
So BD = 1 / 2Ac = 2 / 2 root sign 3

Pythagorean theorem mathematics In the RT triangle, we know

Let a = t b = 2T
a^2+b^2=c^2
5t^2=25 t^2=5 t=√5
a=√5

Ancient Chinese mathematician Zhao Shuang's "Pythagorean circle diagram" is a large square composed of four congruent right triangles and a small square in the middle (as shown in the figure). If the area of the big square is 13, the area of the small square is 2, and the two right sides of the right triangle are a and B, the value of (a + b) 2 is clear. The area of the small square is 2! Not 1!

∵ the area of the big square is 13, and the area of the small square is 1,
The sum of the areas of the four right triangles is 13-1 = 12, that is, 4 × 1 / 2 ab = 12,
That is, 2Ab = 12, A2 + B2 = 13,
∴（a+b）2=13+12=25．

The logo of the International Mathematics Conference held in Beijing in August 2002 was drawn from the "Pythagorean circle diagram" by ancient Chinese mathematician Zhao Shuang. It is a large square (as shown in the figure) composed of four congruent right triangles and a small square in the middle. If the area of the large square is 13, the area of the small square is 1, the shorter right angle side of the right triangle is a, and the longer right angle side is B, Then the value of (a + b) 2 is () A. 13 B. 19 C. 25 D. 169

(a + b) 2 = A2 + B2 + 2Ab = the area of a large square + the sum of the areas of four right triangles = 13 + (13-1) = 25
Therefore, C

As shown in the figure, in RT △ ABC, ∠ ACB = 90 °, CD ⊥ AB in D, AC = 3, ab = 5, then the length of ad is () A. 9 Five B. 5 C. 16 Five D. 5 Nine

In RT △ ABC, according to Pythagorean theorem, BC = 4
Then, according to the area formula of right triangle, we can get the following results:
CD=AC•BC
AB=12
5．
In RT △ ACD, according to Pythagorean theorem, we get ad=
32−(12
5)2=9
5．
Therefore, a

What is the earliest mathematical work in China?

Zhou Bi Suan Jing is one of the earliest mathematics classics in China. It was written between the Han Dynasty and the Han Dynasty. Some historians believe that it appeared earlier. It was conceived in Zhou Dynasty and was completed in the Western Han Dynasty. Some even say that it appeared 1000 years ago
Nine chapters on arithmetic was written around the time of A.D., which systematically summarized the mathematical achievements of China from the pre Qin period to the middle period of the Western Han Dynasty. The author of the book has no way to investigate it. He only knows that Zhang Cang and Geng shouchang, the famous mathematicians of the Western Han Dynasty, revised and supplemented it, Each category is a chapter
The southern and Northern Dynasties were the period of vigorous development of ancient Chinese mathematics
》Therefore, the mathematics education system at that time was of positive significance for inheriting ancient mathematics classics
In 600 A.D., Liu Zhuo of Sui Dynasty first put forward the quadratic interpolation formula of equal interval in the world when he formulated Huangji calendar; in Tang Dynasty, monk Yixing developed it into unequal interval quadratic interpolation formula in his Dayan calendar
Jia Xian put forward the "method of increasing, multiplying and opening" in the Yellow Emperor's nine chapters algorithm. The same method was not discovered by Horner of England until 1819. Jia Xian's binomial theorem coefficient table is similar to the "basga triangle" which appeared in Europe in the 17th century. Unfortunately, the manuscript of Jia Xian's nine chapters algorithm of Yellow Emperor has been lost
Qin Jiushao was an outstanding mathematician in the Southern Song Dynasty. In 1247, he extended the "multiplication and opening method" in "nine chapters of mathematical books", discussed the numerical solution of higher order equations, and cited more than 20 solutions of higher order equations (up to the 10th order equation) which were based on practice. In the 16th century, Italian Philo proposed the solution of cubic equation, Qin Jiushao also studied the theory of first degree congruence
In 1248, Li Ye published "surveying the ocean mirror". This book is the first book to systematically discuss "tianyuanshu" (one dimensional higher order equation), which is of milestone significance in the history of mathematics. What is particularly rare is that in the preface of this book, Li Ye openly criticizes and belittles scientific practice activities, and demotes mathematics as "cheap skill" and "plaything"
In 1261 A.D., Yang Hui of the Southern Song Dynasty (whose birth and death date is unknown) calculated the sum of several types of high-order isochromatic Series in the detailed explanation of the nine chapters algorithm. In 1274, he also described the "nine return method" and introduced various calculation methods for multiplication and division. In 1280 ad, when Wang Xun and Guo Shoujing of Yuan Dynasty formulated the "service time calendar", The interpolation formula of cubic difference is listed. Guo Shoujing also uses geometric method to find two formulas equivalent to the current spherical triangle
In 1303 A.D., Zhu Shijie of Yuan Dynasty (the date of birth and death is unknown) wrote Siyuan Yujian. He extended "tianyuanshu" to "quaternion" (four element high-order simultaneous equation) and proposed the solution of elimination. In Europe, it was not until 1775 that Bezout, a Frenchman, proposed the same solution. Zhu Shijie also studied the summation of finite series, On this basis, the interpolation formula of high order difference is obtained. It was not until 1670 that Gregory of England and Newton of 1676-1678 put forward the general formula of interpolation
After the establishment of Ming Dynasty in the middle and late Ming Dynasty in the 14th century, the rulers pursued the imperial examination system characterized by eight part essay, and greatly reduced the content of mathematics in the national imperial examination. Since then, ancient Chinese mathematics began to decline in an all-round way
Abacus began to be popularized in China in Ming Dynasty. Zhizhi suafa Tongzong, compiled by Cheng Dawei in 1592, is a great work of abacus theory. However, some people think that the popularization of abacus is one of the main reasons to restrain the further development of ancient Chinese mathematics based on calculation
Since the end of the 16th century, Western missionaries in China introduced some Western mathematical knowledge to China. Mathematician Xu Guangqi learned Western mathematical knowledge from Matteo Ricci, an Italian missionary. Moreover, they co translated the first six volumes of the original geometry (completed in 1607). Xu Guangqi demonstrated the Pythagorean astrometry in China with western logical reasoning, Therefore, he wrote two works, the similarities and differences of Surveying and gouguyi. The great survey (Volume 2), the eight line table of cut circle (Volume 6) and Luo Yagu's complete meaning of survey (Volume 10) compiled by Deng Yuhan are the works introducing western trigonometry