Liu Hui’s Mathematical Works: A Journey of Translation into English

When were Liu Hui’s mathematical works first translated into English?

Liu Hui was a Chinese mathematician who lived in the 3rd century. He is best known for his work on geometry, particularly his commentary on the ancient Chinese mathematical text known as the “Nine Chapters on the Mathematical Art”.

The first translation of Liu Hui’s mathematical works into English occurred in the 19th century. In 1853, the Scottish Sinologist Alexander Wylie translated part of Liu Hui’s commentary on the “Nine Chapters on the Mathematical Art” in his book “Notes on Chinese Literature: With Introductory Remarks on the Progressive Advancement of the Art”.

Since then, various other translations and studies of Liu Hui’s mathematical works have been undertaken by scholars, making his contributions to mathematics more accessible to the English-speaking world.

Liu Hui’s Mathematical Discoveries: Unveiling Ancient Mathematical Brilliance

Liu Hui, an esteemed mathematician from ancient China, made remarkable contributions to the field of mathematics during the Eastern Han Dynasty (25-220 AD). His pioneering work in geometry, trigonometry, and numerical approximation has left an indelible mark on the history of mathematics. This article delves into the profound mathematical discoveries of Liu Hui, shedding light on his innovative ideas and their lasting significance.

The Genius of Liu Hui

Get an overview of Liu Hui’s background, his mathematical pursuits, and his reputation as a brilliant mathematician of his time.

Unraveling Ancient Geometry

Liu Hui’s geometric investigations

Explore Liu Hui’s advances in geometry, including his notable works on calculating the areas of polygons, investigating the properties of circles, and exploring the concept of pi.

The method of exhaustion

Discuss Liu Hui’s pioneering use of the method of exhaustion, a precursor to the integral calculus, and its application to solving geometric problems.

Trigonometry and its applications

Trigonometric tables

Examine Liu Hui’s efforts to construct accurate trigonometric tables, which played an important role in navigation, surveying, and architectural calculations during his time.

The Hinged Ladder Problem

Discuss Liu Hui’s solution to the hinged ladder problem, a classic trigonometric puzzle that demonstrated his mastery of trigonometry and analytical thinking.

Ingenious Numerical Approximations

Pi Approximation

Explore Liu Hui’s groundbreaking approximations for the value of pi, including his iterative algorithm that allowed for increasingly accurate estimates.

Square Root Approximations

Discuss Liu Hui’s methods for approximating square roots, demonstrating his innovative approach to numerical computation.

Legacy and Impact

Influence on Chinese Mathematics

Highlight how Liu Hui’s mathematical discoveries influenced subsequent developments in Chinese mathematics and served as a foundation for further advances.

Global Recognition

Examine the recognition and impact of Liu Hui’s mathematical contributions beyond China, highlighting his influence on the global mathematical community.

Contemporary Relevance

Modern applications

Discuss how Liu Hui’s mathematical discoveries continue to find applications in diverse fields such as engineering, computer science, and physics, highlighting their enduring relevance.
b. Inspirational Legacy: Emphasize Liu Hui’s lasting legacy as an inspiration to aspiring mathematicians, demonstrating the power of curiosity, ingenuity, and perseverance in pushing the frontiers of knowledge.


Liu Hui’s mathematical discoveries are a shining testament to his intellectual brilliance and innovative thinking. From his geometric investigations to his trigonometric advances and numerical approximations, Liu Hui’s contributions have left an indelible mark on the field of mathematics. By exploring his groundbreaking ideas, we gain a deeper appreciation for the genius of this ancient mathematician and the lasting relevance of his discoveries in shaping mathematical knowledge.


How did Liu Hui discover pi?

Quick method

Liu Hui discovered a shortcut by comparing the area differentials of polygons, and found that the proportion of the difference in area of successive order polygons was approximately 1/4.

What did Liu Hui discover?

Liu Hui also discovered that a wedge that has a trapezoid base and both sloping sides could be transformed into two tetrahedral wedges segregated by a pyramid.

What is Liu Hui known for?

Liu Hui was a Chinese mathematician who wrote a commentary of the Nine Chapters on the Mathematical Art.

When was Jiuzhang Suanshu written?

1st century ce

263) on Jiuzhang suanshu (Nine Chapters on the Mathematical Procedures), a Chinese classic probably compiled in the 1st century ce (see mathematics, East Asian: Mathematics in China).

In what year did the English start using the symbol for pi?

pi, in mathematics, the ratio of the circumference of a circle to its diameter. The symbol π was devised by British mathematician William Jones in 1706 to represent the ratio and was later popularized by Swiss mathematician Leonhard Euler.

Who was the first mathematician in the world?

Thales of Miletus

One of the earliest known mathematicians were Thales of Miletus (c. 624–c. 546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.

Who invented 0?


“Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628,” said Gobets. He developed a symbol for zero: a dot underneath numbers.

Who is the mother of math?

As one of the leading mathematicians of her time, she developed some theories of rings, fields, and algebras.

Emmy Noether
Awards Ackermann–Teubner Memorial Award (1932)
Scientific career
Fields Mathematics and physics
Institutions University of Göttingen Bryn Mawr College

Who is the smartest mathematician ever?

Born in Boston in 1898, William James Sidis made the headlines in the early 20th century as a child prodigy with an amazing intellect. His IQ was estimated to be 50 to 100 points higher than Albert Einstein’s. He could read the New York Times before he was 2.

Did the Chinese invent math?

Mathematics in China emerged independently by the 11th century BC. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (base 2 and base 10), algebra, geometry, number theory and trigonometry.

Who is a mathematician of the 3rd century who made a study of such equations?

Diophantus of Alexandria

The word Diophantine refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra.

Why is the book nine chapters on the mathematical art significant in the history of mathematics?

The influence of The Nine Chapters greatly assisted the development of ancient mathematics in the regions of Korea and Japan. Its influence on mathematical thought in China persisted until the Qing Dynasty era. Liu Hui wrote a very detailed commentary on this book in 263.

Who wrote nine chapters on the mathematical art?

The Nine Chapters on the Mathematical Art: Companion and Commentary: Shen Kangshen, Crossley, John N., Lun, Anthony W. -C.: 9780198539360: Books:

Who was Bhaskara II and why is he so important in mathematics history?

Bhāskara II, also called Bhāskarācārya or Bhaskara the Learned, (born 1114, Biddur, India—died c. 1185, probably Ujjain), the leading mathematician of the 12th century, who wrote the first work with full and systematic use of the decimal number system.

Who discovered the oldest document on mathematics?

The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC.

Who is the father of Indian mathematics?


Aryabhatta is the father of Indian mathematics. He was a great mathematician and astronomer of ancient India. His major work is known as Aryabhatiya.

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