@MISC{_briefnotes, author = {}, title = {BRIEF NOTES}, year = {} }

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Abstract

by virtue of the celebrated "isoperimetric inequality " (which states that the area enclosed by a planar, simple, closed curve of fixed length, is a maximum when the perimeter is a circle). If z ' & 0, then the projected curve xi + yj, 0 < f < 2ir, is closed, but need not be simple, and its length is less than L. Consequently, the isoperimetric inequality is not directly applicable. Nonetheless, we can establish (14) in a manner similar to Hurwicz's proof of the isoperimetric inequality (cf. Courant and Hilbert (1953)). In view of equations (5) and (13), it follows that 0 l(.x')2+(y')2+(z')2-xy'+x'y]dt. (15) Under the conditions imposed upon p (cf., Section 2), we have the Fourier series representations