Exploring 3D space with a computer – Part 3: building models from plans
Adrian Oldknow
New Blank Pages
Also in Cabri 3D you can use the `Document' menu to add a blank page, to create new views and to write text. So for example the figure alongside shows an oblique view of the brick model.
Of course your box of bricks need not only contain cubes - you might have columns (cylinders) or wedges (prisms).
In a moment we will look at another link between 2D and 3D representations, called `nets'. But first a challenge.
If the edges of a cube are each 1 unit long, then the longest line segment we can fit inside a cube is one of its `long diagonals' of length 
3.
What is the biggest square we can fit inside a cube?
Clearly its four vertices must lie on the edges of the cube. It's also going to have to lie in a symmetric way in some sense - so it's probably going to have to contain the centre point O of the cube. There is a working model for you to download to experiment with: 
Square in cube testbed.cg3 [Download] .
A and B are draggable points on two adjacent edges of the cube. The plane defined by O, A and B cuts the corresponding edges of the cube in points C and D . The blue circle is in the plane of ABCD and has AC as diameter - so you can use it to check when your quadrilateral shape has equal diagonals (i.e. a rectangle). The red circle is in the same plane with A as centre and AB as radius - so you can use it check when your quadrilateral shape has equal sides (i.e. a rhombus). Used together these will tell you when you have a square. Perhaps you can estimate (or actually calculate) the positions of A and B which give the biggest square?
