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Note on the Real Inflexions of Plane Curves

1902
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Transactions of the American Mathematical Society
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The determination of the possible situation of the real inflexions of a curve u = 0 is often practically very difficult. The work can sometimes be simplified by means of the fact that real inflexions lie only in the region for which m" u22 -u2X2 is zero or negative, where uxx, «22, uX2 are written for d2u/dx2, d2u/dy2, d2u/dxdy. This expression, G, depends on the relation of the curve u = 0 to the line z = Q ; a corresponding expression can of course be obtained with reference to any line, and

doi:10.2307/1986465
fatcat:hqdwljxsgvcd5kzy4e5hjpma74