The book "Shu" is one of the books of Qin bamboo slips purchased by the Yuelu Academy in December 2007, and the Academy published the report on the "Shu" in 2011 with photographs of slips. We are investigating the "Shu" based on its photographs in the same manner as our previous work on the "Suanshu-shu." In this present paper, we discuss two mathematical problems and one cultural issue of the "Shu" compared with the "Suanshu-shu" and the other book of the Qin dynasty. This paper is based upon our works in "The research group of ancient Chinese mathematics" in Japan.
1. "Quxicheng" (slips no. 32 to 34)
In this problem, hemp taxes are calculated, but the phrase "3 bu 28 cun" was not comprehensible. We compared this problem with the "Quxicheng" in the "Suanshu-shu" and obtained a complete interpretation. The phrase means that a bundle of hemp 30 cun in circumference shrinks to 28 cun when it is dried, and the purpose of this problem is to calculate the area of a field that will yield a bundle of dried hemp 30 cun in circumference.
2. "Yufang" (slips no. 67 and 68)
In this problem, a square parcel of land is divided equally between three persons, with the exclusion of a small path that crosses the land. The Yuelu Academy explains that the path is on the edge of the land and that three portions are making a line beside the path. We propose an alternative possibility as in the following: Though the area of three portions are the same, their shapes are not the same. The path pierces through the land, and after excluding the path, one of the resulting portions is assigned to one person, and the other portion, whose area is double as large as the former's, is divided to two equal portions so that each one faces on the path.
3. Description regarding notches (slip no. 118)
On slip no. 118, there is a description "to notch ten million, thousand inside hundred; to notch hundred million, hundred on hundred." Dr. Ohkawa of our group, investigated the "Liye Qinjian" with Dr. Momiyama, Dr. Zhang Chunlong, and Dr. Hu Pingsheng, and they interpreted the meanings of "thousand inside hundred" and "hundred on hundred." There are notches on the side of many Qin slips, and the phrase explains the correspondence of shapes to values.