Zhao Shuang

Eastern Wu mathematician

open 33 entries with the same name

Collection

zero Useful+1

zero

Zhao Shuang, also known as Ying, was named Junqing. His life is unknown (about 182-250 years). Chinese mathematician. From the end of the Eastern Han Dynasty to the Three Kingdoms Period Wu kingdom People. He is a famous mathematician and astronomer in Chinese history.^{[1 ]}

Chinese name: Zhao Shuang
Alias: Zhao Ying
Nationality: China
Ethnic groups: Han nationality
date of birth: Ca. 182

Date of death: About 250 A.D
Occupation: mathematician, astronomer
Representative works: Notes to Pythagorean Round Square Diagram
word: Junqing
Times: Eastern Han Dynasty From the end to the Three Kingdoms Period

catalog

Profile

Announce

edit

Pythagorean circle square

Zhao Shuang (at the beginning of the 3rd century), a person from the end of the Eastern Han Dynasty to the Three Kingdoms Period, whose life is unknown, lived about the beginning of the 3rd century. With the word Junqing, Soochow People. It is reported that he has studied Zhang Heng His astronomy work Lingxian and Liu Hong "Arithmetic" is also mentioned in the "Ganxiang Calendar". His main contribution is that he studied deeply in about 222《 Zhou Bi Suanjing 》, wrote a foreword for it and made detailed notes.

Historical records

Announce

edit

Chordal graph

It is reported that he has studied Zhang Heng His astronomical works《 Lingxian 》And Liu Hong Of《 Hieroglyph calendar 》, also referred to "arithmetic". His main contribution was to make an in-depth study of Zhoubi, the oldest astronomical work in China, in about 222 years, which was renamed as《 Zhou Bi Suanjing 》The preface was written and detailed notes were made. This book concisely summarizes the profound principles of Pythagorean arithmetic in ancient China. One paragraph with more than 530 words“ Pythagorean circle square ”The note is History of mathematics The most valuable literature. He explained in detail《 Zhou Bi Suanjing 》Medium Pythagorean theorem The Pythagorean theorem is expressed as: "Pythagorean shares are multiplied and combined respectively, which is the chord real. The square root is divided, which is the chord." A new proof is also given: "According to Chordal graph ， also It can be multiplied by Pythagorean Zhu Shi 2、 Double is Zhu Shisi, and the difference between Pythagorean shares is the middle Yellow sthenia , plus difference, also The string is solid. " The words "you" and "you" indicate that Zhao Shuang believes that Pythagorean theorem can be proved in another way.

Personal research

Announce

edit

Principle of input and output phase compensation

That is, 2ab+(b-a) ²=c ², which can be simplified to a ²+b ²=c ². The basic idea is that the area of a figure will not change after it is cut and supplemented. Liu Hui In comments《 Chapter Nine Arithmetic 》More specifically Principle of input and output phase compensation This is the basis of later stage performance. Zhao Shuang proved that Pythagorean 24 propositions of trilateral and its relation of sum and difference. For example, √ (2 (c-a) (c-b))+(c-b)=a, √ (2 (c-a) (c-b))+(c-a)=b, √ (2 (c-a) (c-b))+(c-a)+(c-b)=c, etc. He also studied Quadratic equation Question, draw a conclusion with Veda's theorem Similar results, and get the second time Equation rooting One of the formulas. In addition, this method was used in multiplication and division by using "Homology", which was also given in "Old Altitude Graph Theory" Weightotherapy Proof of. Zhao Shuang's Mathematical thought And method pair Ancient Chinese Mathematics The formation and development of the system has a certain impact.

Zhao Shuang claimed to have paid less than half a day. He studied "Zhou Bi" and wrote a note on it. It can be seen that he is not divorced from physical labor Our astrologer. It is generally believed that《 Zhou Bi Suanjing 》 be published in book form Around 100 BC, it was a book that quoted fractional operations and Pythagorean theorem etc. Mathematical method elaborate Gaitian said His astronomical works. And about the same time《 Chapter Nine Arithmetic 》, the Pythagorean theorem and some solutions Pythagorean Question. Zhao Shuang's "Notes to Zhoubi Suanjing" explains the scriptures of Zhoubi paragraph by paragraph.

Pythagorean circle square

The most wonderful one is the Pythagorean circle square chart attached to the first chapter, which is just 500 words long and summarizes《 Zhou Bi Suanjing 》、《 Chapter Nine Arithmetic 》The achievements of the Chinese people on Pythagorean arithmetic since then include:

Pythagorean theorem (here, a, b and c represent right triangle The length of three sides of the hook, strand and chord) a ²+b ²=c ²

And its deformation b ²=c ² - a ²=(c-a) (c+a), a ²=c ² - b ²=(c-b) (c+b), c ²=2ab+(b-a) ²;

Yes Open band from square

A ^ 2+(b-a) a=1/2 [c ² - (b-a) ²] Check a

Square root A=[c ² - (c ² - a ²)] ^ 1/2 Check a

The method of calculating the chord difference c-a from square (c-a) ²+2a (c-a)=c ² - a ² for open band, and:

C=(c-a)+a, c+a=b ^ 2/(c-1), c-a=b ^ 2/(c+a), c=[(c=a) ^ 2+b ^ 2]/2 (c+a), a=[(c+a) ^ 2-b ^ 2]/2 (c+a) and other formulas are symmetric with the above formulas, and there are also formulas for finding b, c-b, c+b and c, b from c-b, c+b, and formulas for finding hook, strand and chord from hook chord difference and strand chord difference:

a=[2(c-a)(c-b)]^1/2 + (c-b), b=[2(c-a)(c-b)]^1/2 + (c-a),c=[2(c-a)(c-b)]^1/2 + (c-b) + (c-a)

And the relationship between Pythagorean difference b-a and Pythagorean union b+a

(a+b)^2=2c^2—(b-a)^2，a+b=[2c^2-(b-a)^2]^1/2, b-a=[2c^2-(b+a)^2]^1/2,

Furthermore, the formula b=1/2 [(a+b)+(b-a)], a=1/2 [(a+b) - (b-a)] for finding a and b is given. Finally, the difference between the chord union and the chord difference represented by chord and hook (or strand) is given:

(c+b)-(c-b)=[(2c)^2-4a^2]^1/2

(c+a)-(c-a)=[(2c)^2-4b^2]^1/2

Zhao Shuang proved the above formula by using the method of complementary in and out. These formulas are mostly related to《 Chapter Nine Arithmetic 》And Liu Hui The same is stated in the note, Method of proof Similarly, the last two formulas are not found in Liu Hui's notes, and the terms used are slightly different from Liu Hui's. It can be seen that these knowledge are Han and Wei Dynasties The consensus of mathematicians. 《 Biography 》It is said that the round square figure of Gougu is marked with "more than 500 words, and the number of the latter is more than 1000 words, all of which are profound and concise, and truly count the best".