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What is an ansatz?

What is an ansatz? Here are some definitions.

Noun
  1. (mathematics) A mathematical assumption used to describe a certain phenomenon, posited in order to help provisionally solve an equation or other problem. [from 20th c.]
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Examples
Using this approximation ansatz, several problems concerning planar rods reduce to elementary geometry, as seen from the following simple but illustrative examples.
In such cases, scientists often make an ansatz, an educated guess if you like, and then proceed to compute the consequences of the guess.

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