page_title: Pascal's Triangle
hierarchical_section_title: Pascal's Triangle
caption_attribution_description: Drawing of en:Pascal's Triangle published in 1303 by en:Zhu Shijie (1260-1320), in his Si Yuan Yu Jian. It was called Jia Xian triangle or Yanghui Triangle by the Chinese, after the mathematician en:Jia Xian and en:Yang Hui. The fourth entry from the left in the second row from the bottom appears to be a typo (34 instead of 35, correctly given in the fifth entry in the same row).
context_page_description: Pascal's Triangle is a mathematical triangular array. It is named after French mathematician Blaise Pascal, but it was used in China 3 centuries before his time.
  Pascal's triangle can be made as follows. On the first row, write only the number 1. Then, to get the numbers of following rows, add the number that can be seen above and to the left and the number above and to the right to find the new value. For example, the numbers 1 and 3 in the fourth row are added to make 4 in the fifth row.
context_section_description: Pascal's Triangle is a mathematical triangular array. It is named after French mathematician Blaise Pascal, but it was used in China 3 centuries before his time.
  Pascal's triangle can be made as follows. On the first row, write only the number 1. Then, to get the numbers of following rows, add the number that can be seen above and to the left (if any) and the number above and to the right (if any) to find the new value. For example, the numbers 1 and 3 in the fourth row are added to make 4 in the fifth row.
caption: Yang Hui (Pascal's) triangle, as depicted by the Chinese using rod numerals.