Records of ancient vertical and horizontal diagrams

At the end of the Eastern Han Dynasty in China, Zheng Xuan (129 ~ 200) annotated "Yi Gan Wei Chishui": "Taiyi takes the number to go to Jiugong, and the four positive and four dimensions are all in fifteen", and the number of Jiugong is obtained, that is, the third-order Rubik's Cube (left [third-order vertical and horizontal map]). In the Book of Rites of the Western Wei Dynasty, Northern Zhou Lu annotated "294, 7, 5, 3, 6, 1, 8", and later Zhou Zhen Luan annotated: "Those who live in Jiugong have two or four shoulders, six or eight feet, left three right seven, left nine right five. It also coincides with the tortoise theory. The ancients burned nests on tortoise shells or bones with fire, which was a sign of good luck. Sometimes this arrangement of nests and grooves has special significance and is amazing, so it has become a myth handed down from generation to generation. Nine palace map has a long history.

There are many kinds of vertical and horizontal diagrams in Wang Wensu's Arithmetic Collection (1524). In the seventeenth year of Cheng Dawei, the vertical and horizontal maps 14 species of the unified clan (1592) were calculated, and one of the fronts of Zhuduyan (166 1) in the Middle Qing Dynasty was attached with vertical and horizontal maps 14 species, which was similar to that written by Yang Hui.

Juck Zhang (1650 ~? There are several kinds of vertical and horizontal diagrams supplemented by "algorithm diagram supplement" under the volume of Xinzhai Za. After Mei Cheng's "General Collection of Addition and Subtraction Algorithms" (1760) excluded the contents related to Hutuluo and the vertical and horizontal graphs, the vertical and horizontal graphs existed for about one hundred years. In the early Qing Dynasty, missionaries introduced the third-class axonometric drawings, listed eight kinds of vertical and horizontal drawings from the third to the tenth order, and pointed out the drawing method. There is a fourth-order vertical and horizontal diagram (Figure 2[ fourth-order vertical and horizontal diagram]) in the compilation of Gezhi (1878) edited by Englishman John Flair, which is a 16-character square diagram carved by A Dulle in 15 14. The study of vertical and horizontal mapping in Europe began in14th century. Du Yaquan (1872 ~ 1933), a native of China, started from 1900, but mostly followed the western theory.