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Mathematics-Online problems:

Interactive Problem 82: The Mathematics-Online Logo

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The logo
\includegraphics[width=0.8\linewidth]{moLogo_en.eps}
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 $ (\pm a, \pm a)$ and $ (0,0)$.
\includegraphics[width=0.6\linewidth]{moLogo1.eps}                  \includegraphics[width=0.6\linewidth]{moLogo2.eps}

From the drawings to scale read the number $ n$ of the revolutions the arrow accomplishes when the circle rotates once completely along the ``M''.
Determine the length $ x,$ the change of the rotation angle $ \alpha_k$ of the arrow between the positions $ k$ and $ k+1$ depending on length $ a,$ as well as the length $ a$ itself.


Answer:

$ n$ =
$ x $ =
$ \alpha_1 $ = $ a$ $ +$
$ \alpha_4 $ = $ a$ $ +$
$ \alpha_5 $ = $ a$ $ +$
$ \alpha_6 $ = $ a$ $ +$
$ \alpha_7 $ = $ a$ $ +$
$ a$ =
   
(The results should be correct to three decimal places.)


   

(From: Day of Mathematics 2002)
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  automatically generated: 8/11/2017