BREAK A STICK INTO FOUR PIECES.
Can you always make a closed quadrilateral in the plane using the four pieces?
How many quadrilaterals can you make? How do you know?
Can you prove your answer?
Can you make any shape closed quadrilateral in the plane using
four sticks the sum of whose lengths is fixed?
Can you prove your answer?
What closed polygons with more than four sides can you make (and not make) if you break a stick into more than four pieces?