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Mathematics-Online problems:

# Solution to the problem of the (previous) week

Problem:

The logo
is produced by rolling a circle with radius 1 along the letter  M''. This process is illustrated in the following drawings for a slightly modified M'' with vertices and .

From the drawings to scale read the number of the revolutions the arrow accomplishes when the circle rotates once completely along the M''.
Determine the length the change of the rotation angle of the arrow between the positions and depending on length as well as the length itself.

 = = = = = = = =
(The results should be correct to three decimal places.)

Solution:

From the drawings we can see that

From the second drawing follows

Moreover, we obtain

The total angle is

and equating it with yields

[problem of the week]