Page 381 - Srednje skole - radovi

ELEMENTI SFERNE TRIGONOMETRIJE

Autor: EVGENIJA MIRĈESKI, II razred srednje škole,
Mentor: prof. VESNA RAJŠIĆ

REZIME

Korene trigonometrije srećemo još u starom veku, u Egiptu i Mesopotamiji. Stari Grci

zbog izuĉavanja astronomije razvijali su i sfernu trigonometriju (naroĉito Hiparh koji se naziva

’’ocem trigonometrije’’, kao i Menelaj iz Aleksandrije). Sferna trigonometrija nalazi primenu u
navigaciji, zemljomerstvu, mehanici. Ova oblast me je zainteresovala zbog svoje široke primene,

jer bez znanja osnova sferne trigonometrije nemoguće je rešiti mnoge zadatke iz oblasti sferne
astronomije, geodezije, kartografije, moreplovstva. U radu sam objasnila osnovne elemente

sferne trigonometrije, svojstva sfernih trouglova i teoreme koje su vaţne za razumevanje i
rešavanje zadataka iz ove oblasti.

Kljuĉne reĉi: trigonometrija, sfera, trougao, sferna trigonometrija, sferni trougao

SUMMARY

The earliest studies of trigonometry can be traced back to the ancient times, in Egypt and
Mesopotamia. The ancient Greeks (especially Hipparchus, who is now known as "the father of

trigonometry”, and Menelaus of Alexandria), developed spherical trigonometry because of

astronomical studies. Spherical trigonometry is of great importance for navigation, land survey,
and mechanical engineering calculations. This branch of mathematics aroused my interest

because it has numerous applications; without the basic knowledge of spherical trigonometry we

cannot solve many problems of spherical astronomy, geodesy, cartography and nautics. In this
paper, I have explained the basic elements of spherical trigonometry, properties of spherical

triangles and theorems which are important for understanding and solving problems in this area.

Key words: trigonometry, sphere, triangle, spherical trigonometry, spherical triangle