CONSTRAINED MODELS
In this task you are going to be asked to design and/or build some three dimensional
skeleton models given certain constraints. Whilst credit can be awarded for the actual
construction of the models, it needs to be pointed out that full credit can be obtained
without any such model actually being built, provided that the mathematical analysis
necessary for the construction of such a model is clearly given. In particular, the
quality of the model will not in general affect the grade.
The three models under consideration are
Model 1
A square based pyramid with the vertex directly above the
centre of the square base.
Model 2
A wedge. The horizontal base and vertical backplane of
the wedge are both rectangular. Angle ABC is ninety
degrees.
Model 3
A tetrahedron. The base ABC of the tetrahedron must be a
triangle right-angled at B. The vertex, V, must be
vertically above B.
Your task is to make, or imagine to make, at least one of the above models. You must
explain all of your working and record all of your results and calculations.
The constraints placed on you are that the model, or imagined model, MUST be made
out of material with a total length of exactly one metre. You may use wire, straws,
balsa wood or similar material that adds up to one metre, i.e. the sum of the edges of
the models is exactly one metre.