Reinforced rubber reinforcement structure are placed under angles larger than 54.7 angular degrees, the fibres want to relocate to their optimal path when pressurized. This means that the fibres will re-orient themselves until they have reached their force equilibrium. In this case this will lead to an increase in length and a decrease in diameter. With angles smaller than 54.7 degrees the opposite will occur. A product which makes use of this principle is a pneumatic muscle. For a cylinder with a constant diameter the reinforcement angle is constant as well and is 54.7º. This also known as the magic angle or
Degrees of freedom (statistics) the vectors of residuals are constrained to lie in a space of smaller dimension than the number of components in the vector. That smaller dimension is the number of degrees of freedom for error, also called residual degrees of freedom. Perhaps the simplest example is this. Suppose are random variables each with expected value μ, and let be the "sample mean." Then the quantities are residuals that may be considered estimates of the errors "X" − μ. The sum of the residuals (unlike the sum of the errors) is necessarily 0. If one knows the values of any "n" −