You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
A spider can reach a point on the floor of a cylindrical room, directly opposite from where it hangs on the ceiling, in two ways with equal distances:

1. It descends vertically and then continues along the diameter of the floor.
2. It travels along the curved surface of the cylinder. When the curved surface is unrolled flat, its path is a straight line.

Calculate the ratio of the height to the diameter of the cylinder.
user
\frac{m}{2r} = \frac{\pi^2 - 4}{8} \approx 0.7337
rule
A spider can reach a point on the floor of a cylindrical room, directly opposite from where it hangs on the ceiling, in two ways with equal distances:

1. It descends vertically and then continues along the diameter of the floor.
2. It travels along the curved surface of the cylinder. When the curved surface is unrolled flat, its path is a straight line.

Calculate the ratio of the height to the diameter of the cylinder.
train