Zeguxizhai suanxue

work by Li Shanlan

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July 16, 2026

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Zeguxizhai suanxue is a collection of mathematical treatises by Li Shanlan, published in 1867. It is characterized by its extensive use of infinite series expansions for trigonometric and logarithmic functions, which were introduced to China by Jesuit missionaries. Li Shanlan was a Chinese mathematician known for integrating Western mathematical and scientific knowledge with traditional Chinese methods.1

His work also includes a combinatoric formula known as the "Li Renshu identity," which he derived using only traditional Chinese mathematical techniques. Li Shanlan's contributions were significant in modernizing Chinese mathematics.1

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Li Shanlan
…were later collected into his Zeguxizhai suanxue (1867; “Mathematics from the Zeguxi Studio”). These treatises are characterized by extensive use of infinite series expansions for trigonometric and logarithmic functions (see the
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…were later collected into his Zeguxizhai suanxue (1867; “Mathematics from the Zeguxi Studio”). These treatises are characterized by extensive use of infinite series expansions for trigonometric and logarithmic functions (see the
Read More