Chebyshev's interest in approximation theory

2.2 Chebyshev's interest in approximation theory

Chebyshev was since his childhood interested in mechanisms. The theory of mechanisms played in that time an important role, because of the industrialisation.
In 1852 , he went to Belgium, France, England and Germany to talk with mathematicians about different subjects, but most important for him was
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to talk about mechanisms. He also collected a lot of empirical data about mechanisms, to verify his own theoretical results later.
According to Chebyshev, the foundations of approximation theory were established by the French mathematician Jean-Victor Poncelet. Poncelet approximated roots of the form , and uniformly by linear expressions (see [1] for Poncelet's Approximation Formulae).
Another important name in approximation theory was the Scottish mechanical engineer James Watt. His planar joint mechanisms were the most important mechanisms to transform linear motion into circular motion. The