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Keywords:
Weierstrass’ elliptic functions; addition theorem
Weierstrass’ elliptic functions; addition theorem
Summary:
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.
References:
[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 0296.33003
[2] Matsuda A., Morita K.: Geometric Transformations between General Concurrent Charts and Tangential Contact Charts. Aplikace matematiky, 21 (1976), 237-240, 250. MR 0416078 | Zbl 0368.65065
[3] Epstein L. I.: Nomography. Interscience Publishers, Inc., New York, 1958, 118-129. MR 0107990 | Zbl 0084.11803
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