Editing Josip Plemelj (section)

==Earliest contributions==
Plemelj had shown his great gift for mathematics early in elementary school. He mastered the whole of the high school syllabus by the beginning of the fourth year and began to tutor students for their graduation examinations. At that time he discovered alone [[series (mathematics)|series]] for [[sine|sin]] ''x'' and [[cosine|cos]] ''x''. Actually he found a series for [[cyclometric function]] [[Trigonometric function#Inverse functions|arccos]] ''x'' and after that he just inverted this series and then guessed a principle for coefficients. Yet he did not have a proof for that.

Plemelj had great joy for a difficult constructional tasks from geometry. From his high school days originates an elementary problem &mdash;  his later construction of regular sevenfold polygon inscribed in a circle otherwise exactly and not approximately with simple solution as an [[angle trisection]] which was yet not known in those days and which necessarily leads to the old Indian or Babylonian approximate construction. He started to occupy himself with mathematics in fourth and fifth class of high school. Beside in mathematics he was interested also in natural science and especially astronomy. He studied celestial mechanics already at high school. He liked observing the [[star]]s. His eyesight was so sharp he could see the [[planet]] [[Venus]] even in the daytime.