Alice's netball squad warms up by spacing themselves equally around a circle, facing inwards, and doing the following exercises.
In the first exercise, each girl passes the ball to the first player on her left, starting and ending with Alice. In the second exercise, they pass to the second girl to their left; in the third exercise to the third girl to their left , and so on.
Each exercise starts and ends with Alice. The angle of an exercise is the between the lines along which a player receives and passes on the ball.
Eg. With 8 players, throwing to the person on the left, the angle is 135 degrees.
With 8 players, throwing to the 2nd person on the left the angle is 90 degrees.
With 8 players, throwing to the 3rd person on the left the angle is 45 degrees.
With 8 players, throwing to the 4th person on the left the angle is 0 degrees. (The throw is just between two people.)
So, the path which the ball follows for exercise 5 is the same as the path for exercise 3, but with the direction of the ball movement reversed (first-left then right). The same applies to the paths for exercises 2 and 6 and for exercises 1 and 7.
Q: Find, with proof, the angle of the fourth exercise (throwing the ball to the fourth person on the left) with 9 players.
Q: At one training session the coach suggests an exercise with an angle of 17.5 degrees. Alice protests that too many players would be needed. What is the smallest number of players required, and which exercise uses an angle of 17.5 degrees?
I see this Q, as taking into account the formula (n-2)180 = sum of angles inside a regular polyhedra.
(n-2)180 degrees in the sum of the interior angles each angle is (n-2)180/n...
The angles formed by drawing all diagonals of the polygon to
one specific vertex (Alice). These angles are all equal because they are
all inscribed angles cutting equal arcs. n-2 such angles at each vertex.
The sum of these is the interior angle .... so
But my way could be completly wrong, any thoughts would be appreciated.