# How to generate graphs random geometric shapes?

I would like to create practice problems, rather than reusing old exam questions, to help my students practice solving geometric problems. I would like to use sagetex to produce random variations similar the questions I have listed below. I would supply examples of the pictures, but I do not have enough points to post pictures.

I am wish to be able to make one worksheet where each time it is printed, the values would be randomly assigned and graph would be produced. I know how to assign a random integer value to a variable; however, how to produce the graphs I have no understanding of how to achieve that. Thus for each of the example problems how to make the graph and how to assign the random variability to that graph.

Example questions

The diagram below shows a child’s toy which is made up of a circular hoop, centre O, radius 7 cm. The hoop is suspended in a horizontal plane by three equal strings XA, XB, and XC. Each string is of length 25 cm. The points A, B and C are equally spaced round the circumference of the hoop and X is vertically above the point O.

• Calculate the length of XO.
• Find the angle, in degrees, between any string and the horizontal plane.
• Write down the size of angle AOB
• Calculate the length of AB.
• Find the angle between strings XA and XB.

ABCDV is a solid glass pyramid. The base of the pyramid is a square of side 3.2 cm. The vertical height is 2.8 cm. The vertex V is directly above the centre O of the base.

• Calculate the volume of the pyramid
• The glass weighs 9.3 grams per cm^3. Calculate the weight of the pyramid.
• Show that the length of the sloping edge VC of the pyramid is 3.6 cm
• Calculate the angle at the vertex, BVC
• Calculate the total surface are of the pyramid.
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Perhaps you can post pictures through imgbb, imgur, etc. and share the link?

In the question there appear two kinds of structures, graphs and planar or spatial figures. The examples are given for the geometric figures. What do have (general) graphs to deal with such figures? In the geometric figures, do you want to change only the float values? (Or also the figure...)

One can for instance produce a random graph by

sage: G = graphs.RandomBipartite( 3,3, 2/3 )
sage: G
Random bipartite graph of size 3+3 with edge probability 2/3: Graph on 6 vertices
sage: G.show()


but you certainly need some other kind of graph... There are special graphs also implemented, e.g. graphs.IcosahedralGraph? gives among others the "typo"...

EXAMPLES: Construct and show an Octahedral graph

sage: g = graphs.IcosahedralGraph()
sage: g.show()