Yang Hui

Yang Hui lived in China long ago.

He loved to study numbers. He worked with shapes and patterns. He showed how to use a special number triangle.

He also studied magic squares and circles. These are patterns made with numbers. He wrote books about these ideas. He even worked with parts of numbers.

His math work was very important. People still study his ideas today.

Yang Hui was a math writer in China. He lived a long time ago.

He studied many kinds of numbers and shapes. He is famous for a special number triangle.

This is called Yang Hui's triangle. A man named Jia Xian found it first. Yang used it to find square roots. He also used it to find cubic roots.

Yang Hui wrote many books about math. He studied magic squares and magic circles. These are patterns where numbers fit in special ways.

He also worked with decimal fractions. These are numbers that use a dot to show parts. One book showed how to multiply these parts.

Yang wanted to know why math worked. He did not like people who just used rules. He wanted to know the reason behind the math. He also wrote about shapes. He proved things about shapes like rectangles. His work was very smart for his time.

Yang Hui was a famous mathematician from China. He lived during the Southern Song and Yuan dynasties. He was born in a place called Qiantang. Today, people know this place as Hangzhou.

Yang Hui loved to study numbers and shapes. He was very curious about how math works. He wanted to find the real reasons behind every rule. This helped him become a great writer of math books. He studied many hard problems with numbers and patterns.

One of his most famous ideas is a special number triangle.

This triangle helps people find square roots and cubic roots. A man named Jia Xian discovered this method first. Jia Xian lived about 500 years before a man named Pascal. Yang Hui showed this method in his book about math. He used the triangle to help solve tricky math puzzles. This triangle is a very helpful tool for counting and measuring.

Yang Hui also studied very interesting patterns. He worked with magic squares and magic circles.

These are shapes where numbers are placed in special ways. He wrote rules on how to build these patterns. He also studied how to use decimal fractions. These are numbers that use a dot to show parts. He even showed how to multiply these decimal numbers together. He used these numbers to measure the size of rectangular fields.

Yang Hui was a very bold thinker for his time. He often criticized other math writers from the past. He did not like it when people used rules without knowing why. He believed that mathematicians must understand the theoretical origin of their work.

He also wrote about the properties of shapes like rectangles. His ideas about shapes were very similar to the Greek mathematician Euclid. Euclid lived a long time before Yang Hui did. Yang's work shows he was a very deep thinker.

Many people still remember Yang Hui's great work today. There is even a special prize called the Yang-Hui Award. This award goes to scientists and mathematicians who do amazing things. It was given to people like Salvatore Capozziello and Mahouton Norbert Hounkonnou. In 2023, Delfim F. M. Torres won it for his math models.

His name stays important in the history of math. He helped the world understand numbers much better.

Yang Hui was a highly influential Chinese mathematician and writer. He lived during the Southern Song and Yuan dynasties. He was born around 1238 in Qiantang. This city is known today as Hangzhou in the Zhejiang province. Yang Hui focused his studies on complex mathematical structures. He explored magic squares, magic circles, and the binomial theorem. He is most famous for his work involving a specific number triangle.

This number triangle is a tool used to find square roots and cubic roots. While often called Pascal's triangle in the West, it was actually discovered earlier by Jia Xian. Jia Xian worked around 1100 AD, about 500 years before the French mathematician Blaise Pascal. Yang Hui used this triangle to explain mathematical methods in his writings. The system was also known as the tabulation system for unlocking binomial coefficients. This method appeared in the 1303 publication by Zhu Shijie.

Yang Hui produced several important mathematical books. His book titled Xiángjiě Jiǔzhāng Suànfǎ contained the earliest Chinese illustrations of this triangle. Fragments of this work were preserved in the Yongle Encyclopedia. Another book, titled Rújī Shìsuǒ, was known through his contemporary, Liu Ruxie. Around 1275 AD, Yang published two more books. These were the Xùgǔ Zhāijī Suànfǎ and the Suànfǎ Tōngbiàn Běnmò. The latter is often called the Yáng Huī Suànfǎ.

One major part of his work involved the study of patterns and arrangements. In his writings, he described how to arrange natural numbers in specific ways. He studied magic circles, which use concentric and non-concentric circles. He also worked with magic squares. These are vertical and horizontal diagrams of complex combinatorial arrangements.

Yang Hui provided the specific rules required to construct these mathematical patterns.

Yang Hui was known for his rigorous and modern approach to mathematical theory. He often criticized earlier mathematicians like Li Chunfeng and Liu Yi. He believed they used methods without understanding their theoretical origins. Yang argued that mathematicians should not just change names for different problems. He insisted on knowing the true basis of every mathematical principle. This focus on proof is similar to the work of the Greek mathematician Euclid. Yang provided proofs for geometric properties involving parallelograms and rectangles.

Beyond geometry and patterns, Yang Hui was skilled in decimal fractions. He demonstrated how to manipulate and multiply these numbers for practical use. For example, he could multiply dimensions of a rectangular field using decimal parts. He calculated a field with a breadth of 24.68 paces and a length of 36.56 paces. His calculation resulted in an area of 902.3008. His work also included quadratic equations with negative coefficients.

Today, Yang Hui's legacy is honored through the Yang-Hui Award. This international award recognizes mathematicians and scientists for exceptional career contributions. It has been awarded to researchers like Salvatore Capozziello for his work on Noether symmetries. It was also given to Mahouton Norbert Hounkonnou for his work in deformed quantum algebras. In 2023, Delfim F. M. Torres received the award for his mathematical modelling of COVID-19. This award was presented at a conference in Shanghai, China. His name remains a vital part of mathematical history.