Why do this problem?
involves the interpretation of a very simple
concrete structure, a linkage of 4 rods, and the angles that the
quadrilateral formed by the rods could make if the joints between
the rods at the vertices are totally flexible. Experimental
evidence will offer ideas which then need justification and proof
by forming convincing arguments.
The solution uses the cosine and sine rules. To find the
constraints on the angles in the general case requires an argument
You might allow time for learners to explore the quadrilateral
using strips of card or plastic and split pins, or a dynamic
geometry package. This will help them to identify what can be
varied and what not.
Discuss the freedoms and constraints within the problem, the impact
these might have and how they could influence the structure of any
investigation (what can be changed and what cannot).
Encourage groups to identify ideas that they would like to
investigate. Spend time planning what they might do and sharing
ideas before developing them.
Share findings and approaches.
- What are your variables?
- If you flex the quadrilateral can the angles be any size?
- Can you find a relation between the cosines of opposite
- What constraints would you like to impose? For example, that
the quadrilateral is cyclic.
Try the problem
Diagonals for Area,
also about bendy quads but only using the
area of a triangle.
Flexi Quad Tan