modeled on Yang Xiong's "Justification Against Ridicule", Zhang was an early writer and proponent of the Chinese literary genre shelun, or hypothetical discourse. Authors of this genre created a written dialogue between themselves and an imaginary person (or a real person of their entourage or association); the latter poses questions to the author on how to lead a successful life. He also used it as a means to criticize himself for failing to obtain high office, but coming to the conclusion that the true gentleman displays virtue instead of greed for power. In this work, Dominik Declercq asserts that the person urging Zhang to advance his career in a time of government corruption most likely represented the eunuchs or Empress Liang's (116–150) powerful relatives in the Liang clan. Declercq states that these two groups would have been "anxious to know whether this famous scholar could be lured over to their side", but Zhang flatly rejected such an alignment by declaring in this politically charged piece of literature that his gentlemanly quest for virtue trumped any desire of his for power. Zhang wrote about the various love affairs of emperors dissatisfied with the imperial harem, going out into the city incognito to seek out prostitutes and sing-song girls. This was seen as a general criticism of the Eastern Han emperors and their imperial favorites, guised in the criticism of earlier Western Han emperors. Besides criticizing the Western Han emperors for lavish decadence, Zhang also pointed out that their behavior and ceremonies did not properly conform with the Chinese cyclical beliefs in yin and yang. In a poem criticizing the previous Western Han Dynasty, Zhang wrote: Achievements in science and technology Mathematics For centuries the Chinese approximated pi as 3; Liu Xin (d. AD 23) made the first known Chinese attempt at a more accurate calculation of 3.1457, but there is no record detailing the method he used to obtain this figure. In his work around 130, Zhang Heng compared the celestial circle to the diameter of the earth, proportioning the former as 736 and the latter as 232, thus calculating pi as 3.1724. In Zhang's day, the ratio 4:3 was given for the area of a square to the area of its inscribed circle and the volume of a cube and volume of the inscribed sphere should also be 42:32. In formula, with D as diameter and V as volume, D3:V