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An algebraic addition-theorem for Weierstrass' elliptic function and nomograms
Applications of Mathematics, Tome 24 (1979) no. 5, pp. 372-381
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A dual transformation is discussed, by which a concurrent chart represented by one equation is transformed into an alignment chart or into a tangential contact chart. Using this transformation an alignment chart where three scales coincide and a tangential contact chart consisting of a family of circles, which represent the relation $u+v+w=0$, are constructed. In this case, a form of the addition-theorem for Weierstrass' function involving no derivative is used.
A dual transformation is discussed, by which a concurrent chart represented by one equation is transformed into an alignment chart or into a tangential contact chart. Using this transformation an alignment chart where three scales coincide and a tangential contact chart consisting of a family of circles, which represent the relation $u+v+w=0$, are constructed. In this case, a form of the addition-theorem for Weierstrass' function involving no derivative is used.
DOI : 10.21136/AM.1979.103817
Classification : 30D30, 33E05, 65D99
Keywords: Weierstrass’ elliptic functions; addition theorem 
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Matsuda, Akira. An algebraic addition-theorem for Weierstrass' elliptic function and nomograms. Applications of Mathematics, Tome 24 (1979) no. 5, pp. 372-381. doi: 10.21136/AM.1979.103817

[1] Tannery J., Molk J.: Éléments de la Théorie des Fonctions Elliptiques. Tome 3, (Paris 1893), Chelsea Publishing Company, New York, 1972, 96-98. | Zbl

[2] Matsuda A., Morita K.: Geometric Transformations between General Concurrent Charts and Tangential Contact Charts. Aplikace matematiky, 21 (1976), 237-240, 250. | MR | Zbl

[3] Epstein L. I.: Nomography. Interscience Publishers, Inc., New York, 1958, 118-129. | MR | Zbl

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