User talk:Brian

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<ref>Phoenix: The Peoples of the Hills: Ancient Ararat and Caucasus by Charles Burney , David Marshall Lang, Phoenix Press; New Ed edition (December 31, 2001)</ref>


Finally, [math]\{u_1, u_2, u_3\} = \{ 1, 2\sqrt{3}(t-1/2), 6\sqrt{5}(t^2-t+1/6) \}[/math].

(b) Let [math]B = \{u_1,u_2,u_3\}[/math] be the orthonormal basis found above. For any [math]f(t) = at^2+bt+c \in U[/math]
[math] f(t) = \sum_{i=1}^3 a_iu_i(t) = \left( \frac{a}{3}+\frac{b}{2}+c \right) + \left( \frac{\sqrt{3}}{3}(a+b) \right) 2\sqrt{3} \left( t-\frac{1}{2} \right) + \left( \frac{\sqrt{5}}{30}a \right) 6\sqrt{5} \left( t^2-t+\frac{1}{6} \right) [/math]
[math] = \frac{a}{3}+\frac{b}{2}+c - a - b + 2at + 2bt + at^2 - at + \frac{a}{6} [/math]
[math] = at^2 + t (a+2b) -\frac{1}{2}(a+b-2c) [/math]


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