How Did Japan's First Encounter With China

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Influenced through encounters with China and the West, the Japanese explored mathematical topics that were relevant to their time, which led to Japan’s shift from wasan (和算, Japanese Mathematics) to yôsan (洋算, Western Mathematics) in the Meiji era, and ultimately various technological advancements.

As seen in Japan’s first encounters with the west, Sakoku (鎖国, the national seclusion policy) was the direct result of distrust of the Christian missionaries, which led to limited trade of ideas. In the Edo (江戸) era, Japan made its first encounters with the west, which led to the arrival of Christian missionaries to spread the religion. As the missionaries were so successful in spreading the religion, Ieyasu grew skeptical of their ‘political intentions’ (Deal, Early) Since Christianity was closely associated with the west,
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After the first import of mathematical ideas from the 6th century (Smith), there was no established notation for mathematics until Seki Takakazu (関 孝和) and his followers did so in the 17th century (Deal, Mathematics). As the Japanese language is written vertically from right to left, as opposed to horizontally from left to right, the resulting notation was very different to its western equivalents. The other prime example is enri. Similar to its western counterpart of calculus, this branch of mathematics was based on limits, except their derivations differed. While Isaac Newton was developing calculus to better explain physics in 16th to 17th century Europe, Japan was simultaneously and independently establishing enri to find areas of shapes (similar to integration) (Ogawa). Although calculus and enri had a similar foundation, their independent development of different applications led to Japan again creating an exclusive branch of mathematics.

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