In the broad field of mathematics, Shen Kuo mastered many practical mathematical problems, including many complex formulas for geometry, circle packing, and chords and arcs problems employing trigonometry. Shen addressed problems of writing out very large numbers, as large as (104)43. Shen's "technique of small increments" laid the foundation in Chinese mathematics for packing problems involving equal difference series. Sal Restivo writes that Shen used summation of higher series to ascertain the number of kegs which could be piled in layers in a space shaped like the frustum of a rectangular pyramid. In his formula "technique of intersecting circles", he created an approximation of the arc of a circle "s" given the diameter "d", sagitta "v", and length of the chord "c" subtending the arc, the length of which he approximated as "s" = "c" + 2v2/d. Restivo writes that Shen's work in the lengths of arcs of circles provided the basis for spherical trigonometry developed in the 13th century by Guo Shoujing (1231–1316). He also simplified the counting rods technique by outlining short cuts in algorithm procedures used on the counting board, an idea expanded on by the mathematician Yang Hui (1238–1298). Victor J. Katz asserts that Shen's method of "dividing by 9, increase by 1; dividing by 8, increase by 2," was a direct forerunner to the rhyme scheme method of repeated addition "9, 1, bottom add 1; 9, 2, bottom add 2".