a Chinese puzzle consisting of a square cut into five triangles, a square, and a rhomboid, which can be combined so as to form a great variety of other figures.

1860–65; tang-, perhaps < Chinese Táng Tang, i.e., Chinese + -gram

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World English Dictionary
tangram (ˈtæŋɡræm)
a Chinese puzzle in which a square, cut into a parallelogram, a square, and five triangles, is formed into figures
[C19: perhaps from Chinese t'ang Chinese + -gram]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

"Chinese geometric puzzle," 1864, said to be an arbitrary formation based on anagram, etc. First element perhaps Chin. t'an "to extend," or t'ang, commonly used in Cantonese for "Chinese." Some suggest it is the name of the inventor, "but no such person is known to Chinese scholars" [OED]. Another theory
involves the Tanka people, who were involved in the opium trade, and Western sailors who discovered the puzzle from their Tanka girlfriends. Perhaps from an obscure sense of tram. The Chinese name is Ch'i ch'iao t'u "seven ingenious plan."
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Examines a lesson from a third-grade mathematics discussion of the geometric shapes of a tangram puzzle.
Students will recognize and create quadrilaterals using specified tangram pieces.
Identify each tangram piece by the name of its shape.
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