The paper presents the current and uniform approaches to sailing calculations highlighting recent developments. We published the first part of the paper in May 11. Here we present the concluding part.

Adam Weintrit Piotr Kopacz
The geometry of approximating structures implies the calculus essentially, in particular the mathematical formulae in the algorithms applied in the navigational electronic devices and systems. Thus, we place special emphasis on the geometrical base of the subject.

Zheng He’s Exploration of the Western Pacific Ocean and the Indian Ocean was an important event at the turning point of the world history. It was a golden opportunity for China to strengthen itself and make greater contributions to human beings. Unfortunately, to some extend, Zheng He’s magnificent feat in the history of navigation was later considered as a sheer waste of energy and money and a “failure policy”, and thus was put an end to. Zheng He’s trip, therefore, did not produce long-term effects. China still cut off itself from the out side world and stopped her exploration of ocean navigation, while Europeans, along the routes opened up by their expeditions, reached America, Africa and Asia and established colonies all over the world, which greatly promoted the capitalist development. In spite that the scale of Zheng He’s navigation far exceeded that of Columbus’s “Great Discovery” which followed some 80 years afterward, the former had much less effect on the progress of the world history.