The article deals with the issues of sociocultural interaction of Japan and Europe in scientific fields (in particular in mathematic), in the Edo Period (in the context of Sakoku Seisaku – the period of self-isolation of Japan). The article covers the history of the perception of European mathematical knowledge both through the Dutch learning scholars – Rangakusha, and through the mathematicians of Japanese mathematical school – Wasan. The author points two ways of sociocultural interaction. The first one was direct, meaning direct communication of Japanese with Europeans in a Dutch trading post on Dejima island, while the second one was indirect, reflecting the processes of indirect influence of Western science, for example, through the versions of European works translated on Chinese, transmitted into Japan and then available to a wider range of Japanese mathematicians, astronomers, geographers, bakufu officials, and translators. Therefore, besides finding such translations and investigating the history of their transmission, the author made an attempt to identify the scale of their influence on Japanese mathematical science and scientific community, both as a whole, and on the individual schools and trends. The article makes use of such examples of Chinese versions of Western mathematical books as Introduction to Astronomy (1629), Mei Wending’s work Complete Treatise on Calendar and Computation (1726), Compendium of Calendar Astronomy (1723), New Edition of the Compendium of Calendar Astronomy (1742), Basics of Analytical Geometry, Basics of Differential and Integral Calculus (1859), and others. The main attention is focused on identifying the earliest evidence of European mathematical knowledge transmission into Japan (particularly Trigonometry), as well as on the translation of terms and availability of dictionaries for Japanese mathematicians, like recently discovered work of Ichino Shigetaka in five volumes, containing more than a hundred mathematical terms, translated from Dutch into Japanese. The interaction of European and Japanese Science is considered in a historical context including such factors as the dominance of Zhu Xi’s philosophy, (namely, his Science Philosophy), as well as other sociocultural characteristics of the Edo Period, which interfered with the interaction, such as isolation of Japanese mathematical schools, the lack of access to other disciplines, and, furthermore, no connection of theoretical Mathematics with applied fields, like geography, topography, navigation, etc. It is suggested that borrowings from European science could bear just specific and local character.