BRAHISTOHRONE

Pitanje po kom obliku putanje će čestica za najkraće vreme preći rastojanje između dve tačke u prostoru predstavlja problem brahistohrone (βραχίστος, grčki = najkraće; χρόνος, grčki = vreme).
Istorija problema brahistohrona

Johan Bernuli postavio je problem brahistohrona čitaocima Acta Eruditorum u junu 1697. Rešenje je objavio sledeće godine u maju u istom časopisu i naglasio da ovu nedoumicu rešava kriva koja je poznata kao Hajgensova tautohrona kriva. Ranije, 1638. Galileo je probao da reši sličan problem za putanju kojom se telo može najbrže spustiti između dve tačke na različitim visinama u svom delu Two New Sciences. Nacrtao je rešenje (Third Day, Theorem 22, Prop. 36) u kojem luk krive uvek predstavlja brži put, nego bilo koja tetiva krivih koja spaja dve tačke. (Galilej je tada rekao: „Ako neko smatra da je najkraće rastojanje izmeću početne i krajnje tačke prava linija, možda nije u pravu jer se ispostavlja da to i nije baš tako“). Aparaturu na slici napravio je Francesco Spighi i čuva se u Museo Galileo u Firenci.



BRACHISTOCHRONE

The question on which form of trajectory shall a particle cross the distance between two points in space in the shortest possible time represents the problem of the brachistochrone (βραχίστος, Greek = shortest; χρόνος, Greek = time).

The history of the brachistochrone

            Johann Bernoulli presented the problem of brachistochrone to the readers of Acta Eruditorum in June 1697. He published the solution to the problem in May next year in the same journal and he emphasized that this dilemma can be solved by means of a curve known as Huygens tautochrone curve. Earlier than that, in 1638, Galileo tried to solve a similar problem of the path on which the body can descend the fastest between two points at different heights in his book Two New Sciences. He drew the solution (Third Day, Theorem 22, Prop. 36) in which arc of the curve always presents a faster path than any of the curve chords that connect the two points. (At the time, Galileo said: “If someone believes that the shortest distance between the start and the end point is a straight line, they may be wrong because it turns out that it is not quite so”). The apparatus in the picture was made by Francesco Spighe and it is kept at the Museo Galileo in Florence.