The master's thesis is based on a theoretical research approach. In this work, we
investigate different ways of calculating the volume of polytopes, mainly focusing on
the dimensions d = 2 and d = 3. Most often, we calculate the volume by definition,
that is, by evaluating the corresponding integral along the given polytope. Such
computation may be quite long and complicated. Therefore, in the master's thesis,
we focus on the calculation of the volume of polyhedra with the help of three important
theorems: Green's formula, Stokes' theorem and Gauss's divergence theorem.
A special method of calculating the volume of a polytope is the use of triangulation.
To use triangulation methods, we need a formula for the volume of a simplex. We
include the derivation of this formula and explain two methods of computing the
volume of polyhedra using triangulation. At the end of the thesis, we summarize
all the methods which were used. In the last chapter, we review how the volume
of polytopes is taught in the primary and secondary school education. We discuss
whether the methods of volume computation described in this thesis might be used
by teachers in the classroom.
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