I calculate the length of the stick in terms of a, b and q. From the figure I observe that the length of the stick could be seen as the sum of two hypotenuses of two right-angled triangles. Its length is:

l(q) = a sinq + b cosq .

Now, I have to calculate the minimum of this expression, in order to make the stick pass through the corner. For this, I calculate the derivative of l(q) and equate it to 0. I must say from the beginning that derivatives are not so familiar to me. For a minimum value of the length:

dl dq = -acosq sin2 q + bsin q cos2 q =0.

So for a minimum value acos³ q = bsin³ q and

tanq = æ ç è a b ö ÷ ø 1/3   .

Now, I have to calculate sinq and cosq as functions of tanq. I know that:

cosx = 1 Ö 1+tan2x  and sinx = tanx Ö 1+tan2x

In the case of the problem, I have:

1 cosq =   æ  ú Ö 1+( a b )2/3

and

1 sinq = ( b a )1/3   æ  ú Ö 1+( a b )2/3

So the minimum length is

a sinq + b cosq =(a2/3b1/3 + b)   æ  ú Ö a2/3+b2/3 b2/3   = (a2/3 + b2/3)3/2 .

The result issymmetric in a and b.

If a=65cm and b=75cm then 65^2/3+ 75^2/3=16.16623563 + 17.78446652=33.95070215 and 33.951^3/2=197.8213407 so an object of about 197 cm could be manoeuvred around the bend but it is not possible to manoeuvre a 200 cm object around this bend.