Quadratic function y = (2 / 3) x ^ 2 image is above X axis, vertex coordinates (0,0) are origin A0, points A1, A2, A3 , A2008 on the positive half axis of y-axis, points B1, B Quadratic function y = (2 / 3) x ^ 2 image is above X axis, vertex coordinates (0,0) are origin A0, points A1, A2, A3 , A2008 on the positive half axis of y-axis, points B1, B2, B3 If the triangle a0b1a1, a1b2a2, a2b3a3 and a2007b2008a2008 are equilateral triangles, what is the side length of the triangle a2007b2008a2008?

Quadratic function y = (2 / 3) x ^ 2 image is above X axis, vertex coordinates (0,0) are origin A0, points A1, A2, A3 , A2008 on the positive half axis of y-axis, points B1, B Quadratic function y = (2 / 3) x ^ 2 image is above X axis, vertex coordinates (0,0) are origin A0, points A1, A2, A3 , A2008 on the positive half axis of y-axis, points B1, B2, B3 If the triangle a0b1a1, a1b2a2, a2b3a3 and a2007b2008a2008 are equilateral triangles, what is the side length of the triangle a2007b2008a2008?

Let B1a ⊥ Y axis be a, B2B ⊥ Y axis be B, B3c ⊥ Y axis be c. let Aa1 = a, Ba2 = B, Ca2 = C in equilateral △ a0b1a1, △ a1b2a2, △ a2b3a3. ① in equilateral ⊥ a0b1a1, a0a = a, so B1a = atan60 ° = root 3a, substitute it into the analytical formula to get 2 / 3 × (root 3a) 2 = a, and the solution to get a = 0 (rounding off) or a = 1 / 2