Vol.2, No 1, 1999 pp. 1-5
UDC 514.752.4(045)

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THE 3RD DEGREE RECTILINEAR SURFACES
IN QUADRIC TUFTS
Miroslav Marković
Faculty of Civil Engineering, Beogradska 14, 18000 Niš, Yugoslavia

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Abstract. It is a known fact that the 2nd degree surfaces, regardless of their reality, induce the identical involutory series in the generatrices of a 3rd degree rectilinear surface whose 4th degree piercing curve of a 1st kind of the given surfaces are its double points. It is also known that two 2nd degree surfaces, regardless of their reality, determine a tuft of 2nd degree surface. The paper researches the 3rd degree rectilinear surfaces in the tufts of the quadrics, having in mind all the kinds of tufts, as well as the possibility of constructive determination of the generatrices of those surfaces. It is demonstrated that the number of those surfaces depends on the type of the tufts of the quadric as well as of the reality of the apexes and the faces of the common autopolar tetrahedron.
Key words: Rectilinear surface, the tufts of the quadrics, autopolar tetrahedron

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PRAVOIZVODNE POVRŠI 3. STEPENA
U PRAMENOVIMA KVADRIKA Poznato je da dve površi 2.stepena, bez obzira na svoj realitet, na izvodnicama jedne pravoizvodne površi 3.stepena induciraju identične involutorne nizove, čije su dvostruke tačke prodorna kriva 4.reda I.vrste datih površi. Isto tako je poznato da dve površi 2.stepena, bez obzira na svoj realitet, odreduju jedan pramen površi 2.stepena. U radu su izvršena istraživanja pravoizvodnih površi 3.stepena u pramenovima kvadrika, imajući u vidu sve vrste pramenova, kao i mogućnosti konstruktivnog odredjivanja izvodnica tih površi. Pokazano je da broj takvih površi zavisi od tipa pramenova kvadrika, kao i od realiteta temena i stranica zajedničkog autopolarnog tetraedra.