Question:
Given certain points on a square(including its sides),let these points and the verteces of the squares be the verteces of a certain number of smaller triangles, no vertices of a smaller triangle are on the sides of other smaller triangles. what is the minimum value of the biggest angle
?
I think this is interesting problem,and I think is nice. I guess this answer is $90^{0}$,But I can't prove it.and maybe this is old problem (maybe is Very famous problem)
Thank you
Best Answer
To make explicit Peter Taylor's lower bound: the corners of the square are $90^\circ$. If you don't split one of them, you have a $90^\circ$ angle. If you do, the largest small angle you can get is $45^\circ$. Then if the other two angles of that triangle are equal, they are $67.5^\circ$ This does not show that there is such a construction. I have found several constructions that result in a smaller square.