Abstract:

Mathematics, being a subject that addresses a wide variety of topics, whose deep connections are not always accessible, is often perceived as an abstract science with very little evident connection to reality.
To appreciate the value of Mathematics as a whole and its importance in the description of physical phenomena should be one of the major goals of our teaching, but the attempt to study this subject in the school environment and in a “real life” context leads, in many cases, to create problems which are completely artificial and disconnected from any real application in everyday life, which adds to the disbelief in the usefulness of this science.
An analysis, though superficial, of a few episodes in the history of Mathematics, shows us how this science is actually fundamental to the progress of the various branches of knowledge. And if we go back to Antiquity, we find the brilliant deeds of Greek astronomers who, using elementary geometry, were able to determine the dimensions of the radii of the Earth, the Moon and the Sun.
The construction of a sundial, one of the first instruments to measure time, provides the visualization of various topics in mathematics, such as geometry in plane and in space, vector algebra, trigonometry and differential equations. Taking as a starting point the construction of these instruments, in this article we intend to show how it is possible, using a simple spreadsheet, to develop computational modules which facilitate the understanding of some fundamental mathematical concepts, as well as the simulation of the astronomical phenomena which substantiate their construction and influence the functioning of these instruments.

Keywords:

Gnomon, Ecliptic, Orbit, Analemma, Excel.