Paper size a number of different sizes were defined for large sheets of paper, and paper sizes were defined by the sheet name and the number of times it had been folded. Thus a full sheet of "royal" paper was 25 × 20 inches, and "royal octavo" was this size folded three times, so as to make eight sheets, and was thus 10 × inches. Imperial sizes were used in the United Kingdom and its territories. These sizes are no longer commonly used since the UK switched to ISO sizes. Many of these sizes were only used for making books (see bookbinding),
Vortex sheet consequence of Kelvin's circulation theorem, in the absence of external forces on the sheet, the circulation between any two material points in the sheet remains conserved, so formula_12. The equation of motion of the sheet can be rewritten in terms of formula_8 and formula_5 by a change of variable. The parameter formula_3 is replaced by formula_8. That is, formula_17 This nonlinear integro-differential equation is called the Birkoff-Rott equation. It describes the evolution of the vortex sheet given initial conditions. Greater details on vortex sheets can be found in the textbook by Saffman (1977). A flat vortex sheet with periodic boundaries