Chinese astronomers observed the length of the solar shadow, knew of the winter solstice and the summer solstice and made a Chinese lunisolar calendar. They used a gnomon with a height of 8 Chi (about 240cm) because the length of the Sun’s shadow would be 6 Chi at the times of the vernal equinox and the autumnal equinox, that is to say, the ratio of the right-angle triangle would be 3:4:5 in the basin of the Huang He River.

Chinese astronomers founded the observation center where the length of the solar shadow was 1.6 Chi at the time of the summer solstice. Because the gnomon was 8 Chi height, the ratio was 5:1. This right-angle triangle can be constructed from another right-angle triangle which has sides with the ratio of 5:12:13.

On the other hand, one of the oldest books about the mathematical arts of the Shu was discovered in the 21st century in the Yuelu Academy at Hunan University in China. The book was presumably written during the years of the Qin Dynasty, B.C.E. 221－B.C.E. 206. In this book there was a right angle triangle with the ratio of 5:12:13. This indicates that ancient Chinese astronomers and mathematicians understood the nature of this triangle.

In the Eastern Han Dynasty, C.E. 25 - 220, Chinese astronomers moved to a new more southerly observation center because the length of the solar shadow on the day of the vernal equinox was computed to be 7.55 Chi, although the actual value proved to be 5.67 Chi. It was 6 Chi long on the day that was six days before the vernal equinox. The ratio of the right-angle triangle was 3:4:5.

Then the Zhoubi Suanjing was introduced to Japan at the 7th century, then Japanese mathematicians and astronomers studied it at the same condition of the Tang dynasty in China. In 731, however, Japanese emperor government made much of the Zhoubi Suanjing. If Japanese student would not pass the examination for the Zhoubi Suanjing, they would not graduate the national university. The authors thought that Japanese scalars did not make the Zhoubi Suanjing for astronomical arts, they considered this book to be a mathematics book.