Liu Hui

Liu Hui was a brilliant mathematician from ancient China.

He lived during the Three Kingdoms period, which lasted from 220 to 280 CE. He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty. In 263 CE, he published a famous commentary on a book called *Jiu Zhang Suan Shu*, or *The Nine Chapters on the Mathematical Art*. His work was not just about solving problems. He wanted to explain the logic behind mathematical methods. He focused on why certain techniques worked and why others failed. This deep thinking helped advance the field of mathematics significantly.

One of Liu Hui's most famous achievements involved the number pi (π). At the time, many people simply assumed that pi equaled 3. Liu Hui used a more complex method to find a more accurate value. He used the method of inscribing a polygon inside a circle. By calculating the perimeter of these shapes, he could approximate the circle. First, he used a polygon with 192 sides. This gave him an approximation of 157/50. Later, he used a much larger polygon with 3072 sides. This resulted in an approximation of 3.14159. This was more accurate than the calculations made by Archimedes or Ptolemy.

Liu Hui also made massive contributions to the study of shapes and volumes. This field is known as solid geometry. He was an expert at breaking complex shapes into simpler ones. For instance, he found that a wedge with a rectangular base could be split into a pyramid and a tetrahedral wedge. He also studied wedges with trapezoid bases. He discovered they could be separated into two tetrahedral wedges and a pyramid. He computed volumes for many shapes, including cones, cylinders, prisms, and tetrahedrons. Interestingly, he could not find the volume of a sphere. He noted that he was leaving that specific problem for a future mathematician to solve.

In addition to geometry, Liu Hui worked with advanced algebraic concepts. He provided a proof for a theorem that is identical to the Pythagorean theorem. He described his method using a diagram that showed the relationship between the hypotenuse and the other two sides. This allowed a person to find an unknown value from known values. He also developed a systematic method for solving linear equations with several unknowns. This is similar to what modern mathematicians call Gaussian elimination. Some historians believe he may have been the first to discover and use negative numbers. This would have been long before the Indian mathematician Brahmagupta began using them.

Liu Hui used a specific way to express his mathematical results. He used decimal fractions based on metrological units. These were units of length based on the number 10. For example, 1 chǐ equaled 10 cùn, and 1 cùn equaled 10 fēn. If a diameter was 1.355 feet, he would write it as 1 chǐ, 3 cùn, 5 fēn, and 5 lí. It was not until much later that mathematicians like Han Yen and Yang Hui moved toward the modern decimal system we use today.

Beyond pure math, Liu Hui applied his skills to the real world through surveying.

He wrote a manual called *Haidao Suanjing*, or *The Sea Island Mathematical Manual*. This book contained practical problems for measuring the world. He taught how to use tall surveyor's poles and horizontal bars set at right angles. Using these tools, people could measure the height of a tree on a hill or a pagoda tower. They could also measure the width of a river or the depth of a ravine. This knowledge was vital for mapping and construction.

His work had a direct impact on large-scale engineering projects. Liu Hui provided commentary on problems involving the building of canals and river dykes. His math helped determine the total amount of materials required for these projects. It also helped calculate the amount of labor and the time needed for construction. His influence was so lasting that his work was studied by later cartographers. Even his mathematical commentaries were highly valued, though the Tang mathematician Li Chunfeng later corrected some small errors. In modern times, his work was translated into French by Professor Guo Shuchun, a task that took twenty years to complete.