Ulungelelwano Olumangalisayo Kwizityalo

NGABA ukhe waphawula ukuba izityalo ezininzi zikhula zilandela ulungelelwano oluthile? Ngokomzekelo, ipayina linamaxolo ali-8 ayila isangqa nama-5 okanye ali-13 akhula esiya kwelinye icala. (Bona umfanekiso 1.) Ukuba ujonge imbewu kajongilanga, usenokubona izangqa ezingama-55 nezingama-89 ezikhula phezu kwezinye mhlawumbi nezingaphezulu. Ezi zangqa usenokuzibona nakwikholiflawa. Xa ukwazi ukuphawula ezi zangqa, kusenokubangel’ umdla ukuya emarikeni. Kutheni izityalo zikhula ngale ndlela? Ngaba kukho into ebalulekileyo ngenani lezi zangqa?

Zikhula Njani Izityalo?

Inkoliso yezityalo ikhula amalungu amatsha, njengesiqu, amagqabi neentyatyambo, izinto ezivela kumbindi waso omncinane obizwa ngokuba yimeristem. Ilungu ngalinye elivelayo elibizwa ngokuba yiprimordium, likhula lisuka embindini liye kwelinye icala xa uthelekisa nelinye ilungu elitsha elikhulileyo. * (Bona umfanekiso 2.) Inkoliso yezityalo ivelisa ilungu elitsha elikwiengile eyila isangqa. Yiyiphi loo engile?

Khawucinge ngale ngxaki: Khawuzibone uzama ukuyila isityalo ukuze amalungu amatsha akhule ngolungelelwano kuze kungabikho sithuba. Masithi ukhetha ukuba ilungu elitsha likhule kwelinye icala lelinye ilungu elikhulayo. Ingxaki oya kujamelana nayo kukuba ilungu lesihlanu liya kukhula kwindawo efanayo yaye lijonge kwicala elifanayo. Loo malungu aya kwakha imiqolo enezithuba phakathi kweminye imiqolo. (Bona umfanekiso 3.) Inyaniso ikukuba, nawuphi na umqolo uya kuba nezithuba ezingavalekanga. Kuphela yinto ebizwa ngokuba yi-“golden angle” amaqoqo ali-137,5 avala sonke isithuba. (Bona umfanekiso 5.) Yintoni ebangela ukuba le engile ibe yekhethekileyo?

 Kaloku le engile ikhethekile kuba ayinakuchazwa njengenxalenye yomjikelo nje oqhelekileyo. Iceba elisisi-5/8 lisondele, kanti elisisi-8/13 lisondele ngakumbi, nelili-13/21 lisondele ngakumbi, kodwa alikho iceba elingena gingci. Ngoko ke, xa kukhula ilungu elitsha kwiengile ethile, alikho ilungu eliya kuze likhule lijonge kwicala elifanayo. (Bona umfanekiso 4.) Oku kuphumela ekubeni kungaze kubekho amalungu akhula ejongene ngokuthe ngqo, kodwa abumba isangqa.

Okumangalisayo kukuba, xa ezi engile zenziwe ngekhompyutha, zibumba isangqa esibonakalayo xa kuphela zenziwe kanye ngokuchanileyo. Ukuba kwenzeka impazamo enoba incinane kangakanani na, konke konakele.—Bona umfanekiso 5.

Mangaphi Amagqabi Entyatyambo?

Okubangel’ umdla kukuba inani lezangqa ezibangelwa ngamalungu amatsha akhulayo lisekelwe kweyona engile ichanileyo ngokuqhelekileyo eba linani ekuthiwa lelikaFibonacci. Eli nani lafunyanwa ngenkulungwane ye-13 sisazi semathematika saseItali uLeonardo Fibonacci. Eli nani lifumaneka ngale ndlela, inani ngalinye emva kwesinye lilingana nenani lokuqala nelesibini xa edityanisiwe, okuthetha ukuthi—1, 1, 2, 3, 5, 8, 13, 21, 34, 55, njalo njalo.

Inani leentyatyambo kwizityalo ezininzi lidla ngokulingana nenani likaFibonacci. Kuyamangalisa ukufumanisa ukuba ngokuqhelekileyo irozi yasendle neebuttercup ziba inamagqabi ezi-5, iidelphinium ezisi-8, iimarigold ezili-13, iiaster ezingama-21, iidaisy eziqhelekileyo ezingama-34, kanti zona iiMichaelmas daisy ezingama-55 okanye ezingama-89. (Bona umfanekiso 6.) Iziqhamo nemifuno nayo idla ngokuba nento ethile evumelana neli nani likaFibonacci. Ngokomzekelo, xa umthi webhanana uhlahlelwa uba namacandelo amahlanu.

“Yonk’ Into Uyenze Yantle”

Abazobi kudala baphawula ukuba ukudweliswa kwezinto nge-engile echanileyo kuyabukeka emehlweni. Yintoni ebangela ukuba izityalo zivelise amasebe kanye ngale engile? Abantu abaninzi bagqiba ngelithi lo ngomnye wemizekelo obonisa ubukrelekrele bokudalwa kwezinto eziphilayo.

Xa beqwalasela indlela eziyilwe ngayo izinto eziphilayo noyolo esilufumanayo kuzo, abaninzi bamothulel’ umnqwazi uMdali wazo ofuna ukuba sonwabe. Ithetha ngoMdali wethu iBhayibhile ithi: “Yonk’ into uyenze yantle ngexesha layo.”—INtshumayeli 3:11.

[Umbhalo osemazantsi]

[Imizobo ekwiphepha 24, 25]

Umfanekiso 1

(Yiya kwimpapasho)

Umfanekiso 2

(Yiya kwimpapasho)

Umfanekiso 3

(Yiya kwimpapasho)

Umfanekiso 4

(Yiya kwimpapasho)

Umfanekiso 5

(Yiya kwimpapasho)

Umfanekiso 6

(Yiya kwimpapasho)

[Umfanekiso okwiphepha 24]

Umfanekiso omkhulu wemeristem

[Inkcazelo]

R. Rutishauser, University of Zurich, Switzerland

[Inkcazelo Ngomfanekiso okwiphepha 25]

Iintyatyambo ezimhlophe: Thomas G. Barnes @ USDA-NRCS PLANTS Database