DIGITALNA ARHIVA ŠUMARSKOG LISTA
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J. Zelić: RASTE LI DRVEĆE U ŠUMI PO PRAVILIMA ZLATNOG REZA I FIBONACCIJEVOG NIZA? Šumarski list br. 7–8, CXXX (2006), 331-343 LITERATURA – References Bezak, K. et all., 1989: Uputstva za izradu karte ekološko- gospodarskih tipova brdskog i planinskogpodručja (II9 SR Hrvatske, Institut za šumarskaistraživanja, Radovi broj 79, Jastrebarsko str. 1–119. Bezak, K., 2004: Kompleksne jednadžbe rasta i razvoja šuma, Hrvatske šume, d.o.o., interno. B en t l ey, P. J., 2004: Digitalna biologija, kako priroda preoblikuje našu tehnologiju, Izvori, Zagreb. D u b r a v a c, T., 2002: Zakonitosti razvoja strukturekrošanja hrasta lužnjaka i običnog graba ovisno o promjeru i dobi u zajednici “Carpino betuli- Quercetum roboris Anić et Rauš, 1969”, Disertacija, pp: 1–196, Zagreb. Levaković, A., 1938: Fiziološko-dinamički osnovifunkcija rastenja, Glasnik za šumske, pokuse, Šumarski fakultet Zagreb. Ko v a či ć , Đ., 1993: Zakon rasta i numeričko bonitiranje šume, Glasnik za šumske pokuse 29, Šumarski fakultet Zagreb. Pranjić, A., N. Lukić, 1997: Izmjera šuma, Sveučilište u Zagrebu, Šumarski fakultetet, Zagreb. Schwaller, R. A., de Lubitz, 2004: Hram u čovjeku, sveta arhitektura i savršeni čovjek, Teledisk, Zagreb. Špiranec, M., 1975: Prirasno prihodne tablice, Poslovno udruženje šumsko privrednih organizacija, Radovi br. 25, Zagreb, str. 1–109. Š p i r an ec , V., 2005: Sklad, Sveučilišna knjižnica Zagreb. Wells, D., 2005: Rječnik zanimljivih i neobičnih brojeva, Sveučilišna knjižara, Zagreb. Z e l i ć , J., 2000: Prilog raspravi o teoriji rast, prirasta i održivog razvoja, Šumarski list br. 9–10, str. 515 –531. Z e l i ć , J., 2005: Prilog modeliranju normaliteta regularnih srednjodobnih bukovih sastojina (EGT-IID- 10), Šumarski list, br. 1–2, str. 51–62. Zlatni rez, geometrija prirode ili prirodna geometrija, omjeri i razmjeri..., www.uazg.hr SUMMARY: The analysis of biometric parameters of growth (yield tables) of forest stands of beech EGT-II-D-11 (beech with sedge, Bezak et al, 1989) and pedunculate oak (Quercus robur L.), Bezak, 2004, provides a possible answer to the question: “Do trees in a forest grow by the rules of the Golden section and the Fibonacci series?” The Golden section or the Divine proportion was discovered in ancient cultures and civilizations. It has always been applied as the ideal proportion in art and construction. It is revealed in the live material world of natural patterns of plant and animal growth and development. Expressed with the number of the decade system, it is as follows: . = (. 5 +1) / 2 = 1,6180339 ... Closely related with the Golden section proportion is the Fibonacci series, a set of real numbers whose member in a series equals the sum of two previous ones, e.g. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 144, … It was found that growth of forest trees in diameter follows the rules of the Golden section and Fibonacci series; this relates to the growth of breast diameter, basal area, tree circumference and crown width as a linear dependent variable of breast diameter. The growth of a tree’s breast diameter can be expressed with a linear function of the following shape: d = a + b t, in which breast diameter is a dependent variable and tree age an independent one. Regression coefficient b shows the rate of tree growth or increment, which is different for particular tree species and environmental conditions in which a tree grows. It is expressed as a b-module, which together with the regression constant a represents geometric growth of an equilateral spiral within the so-called square whirl in relation to the golden section sides. During its life, a tree in a stand “tends” towards the average increment (growth speed) expressed with the value of the b-module. Speed of growth or diameter increment, represented y with a d mathematicall mathematicallmathematically wi f derivation of linear constant, provides the constant b a aas ss a aan nn expressio expressioexpression nn o oof har |