From: George Tsetsenekos (tse0123(@)hotmail.com)
Date: Παρ 12 Σεπ 2003 - 15:59:45 EEST

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Oloi pisteuw na exete akousta ti xrisi analogia pou prwtos diatupwse o megas Puthagoras.
Mia mikri sinopsi ki apo emena, an exoume ena orthogwnio me pleures y kai x, ean isxuei: y/x=1,61..
tote: y/x=x/(y-x). An diladi "kovoume" ena tetragwno ti fora, me pleura ti mikroteri ek twn diastasewn tou orthogwniou tha prokupsei ws upoloipo ena orthogwnio me tin idia akrivws analogia. Auti i idiotita sunexizetai oses fores kai na epanalavoume ti diadikasia. Diavasa malista pws mporoume na kataskeuasoume ena tetoio orthogwnio me ton eksis aplo tropo:
Pairnoume ena tuxaio tetragwno kai to "kovoume sta duo" me mia eutheia pou pernaei apo ta mesa duo apenanti pleurwn tou kai fernoume ti diagwnio enos apo ta duo mikrotera orthogwnia. Sti sunexeia pairoume ena diaviti kai me kentro to meso tis mias pleuras (kai ena akro tou diagwniou) kai aktina ti diagwnio fernoume hmikiklio pros tin kateuthinsi tis idias pleuras. Ean twra proekteinoume tin pleura auti, kai sto simeio pou sunanta tin aktina xaraksoume ena orthogwnio (me mikri pleura tin pleura tou tetragwnou) auto tha exei tin xrisi analogia. Pragmati, meta apo ligous upologismous kataligei kaneis sto oti y/x=(sqrt(5)+1)/2, pou isoutai me to 1,61.. To erwtima mou einai an mporoume apo tin sxesi twn analogiwn [y/x=x/(y-x)=...] na kataliksoume sto noumero. Na episimanw pws DEN exw ti lisi, kathws apotelei vasika diki mou aporia.

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