Along a characteristic u is constant. If it starts at (ξ,0), that constant is 1 + ξ² and its line is $y=(x-\xi)\sqrt{1+\xi^2}$. Passing through (0,1) requires $1=-\xi\sqrt{1+\xi^2}$ with ξ < 0. Squaring and setting a = ξ² gives a(1+a) = 1, so $a=(\sqrt5-1)/2$. Therefore $u(0,1)=1+a=(1+\sqrt5)/2=1.618034$, rounding to 1.618.
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