/sci/ - Science & Math

It is obvious that if there is a point further from A than B, then it must be placed on the diagonal of the top face.

f is a function defining distance between A and S, point S is placed on the diagonal of the top face (pic rel)
f(x) = sqrt((3-x)^2+(1+x)^2) for 3/4≤x≤1
= sqrt(x^2+(2+x)^2) for 0≤x<3/4
Now we can determine through derivatives that function f is increasing on (0, 3/4) and decreasing on (3/4, 1), thus point Smax(3/4, 3/4) is the furthest point from A on the top face, moreover distance between points A and S (sqrt(65/8) is longer than distance between A and B (sqrt(8)). This anon >>10356765 was right.