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**Authors: **Jacobi, Lee W.; Madden, Daniel J.

**Source:** American Mathematical Monthly, Volume 115, Number 3, March 2008, pp. 220-236(17)

**Publisher: **Mathematical Association of America

Euler's equation is specialized to a

While this construction can be used to find new Euler solutions, those it produces are very large. To find solutions of more moderate size, we add two additional variables. These allow us to construct an equation in 6 homogeneous variables that describes a higher dimensional surface covering the surface given by the specialized Euler equation. We give an explicit formula for transforming solutions to the new equation into solutions of Euler's equation. The new equation is such that any one solution easily leads to many others. The construction provides any number of ways of changing one solution into another. Thus it is possible to add more examples to previously known 88 solutions to Euler's equation. The paper ends with a list of new solutions to Euler's equation obtained this way.

**Document Type:** Research Article

Publication date: March 1, 2008

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**In this:**publication**By this:**publisher**In this Subject:**Mathematics and Statistics , Education**By this author:**Jacobi, Lee W. ; Madden, Daniel J.

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