As shown in the picture, it is a pattern of the emblem of the international mathematics education conference, which contains a lot of mathematics knowledge. In △AB 1 C, ∠C is a right angle, and AC=CB 1 = 1. ∫Rt△AB 1 C，AC=CB 1 = 1，

∴AB 1 = 1+ 1 = 2，

∴s△ab 1 c = 1 2× 1× 1 = 1 2；

∫Rt△AB 1 B2，B 1 B 2 = 1，AB 1 = 2+ 1 = 3，

∴ S △AB 1 B 2 = 2 2

…

∴ after the nth change, the right-angle side is always the same, and the length is1; The other right angle becomes n+ 1,

∴ The ratio of the area of the (n+ 1) th triangle to the area of the nth triangle is N2N+ 1.2, that is, N2N+ 1.

So the answer is: n n+ 1