Z vedeck\u00fdch \u010d\u00edsel Pytagoras tvrdil dva r\u00e1dy: jeden ohrani\u010den\u00fd, nep\u00e1rny; druh\u00e9 nekone\u010dn\u00e9, p\u00e1rne \u010d\u00edslo (pod\u013ea pytagorejskej defin\u00edcie) je tak\u00e9, ktor\u00e9 prip\u00fa\u0161\u0165a rozdelenie na najv\u00e4\u010d\u0161ie a najmen\u0161ie; do najv\u00e4\u010d\u0161\u00edch ve\u013ekost\u00ed (pre polovice s\u00fa najv\u00e4\u010d\u0161ie \u010dasti); najmenej v mno\u017estve (preto\u017ee dva je najmen\u0161\u00ed po\u010det) pod\u013ea prirodzen\u00e9ho protikladu t\u00fdchto dvoch druhov. Zvl\u00e1\u0161tne je to, \u010do to nem\u00f4\u017ee trpie\u0165, ale je rozdelen\u00e9 na dve nerovn\u00e9.<\/p>\n
Pytagorejci pova\u017eovali \u010d\u00edsla za z\u00e1klad v\u0161etk\u00e9ho bytia a verili, \u017ee v\u0161etky javy vo vesm\u00edre sa daj\u00fa vysvetli\u0165 pomocou \u010d\u00edseln\u00fdch princ\u00edpov. P\u00e1rne a nep\u00e1rne \u010d\u00edsla vn\u00edmali nielen ako matematick\u00e9 kateg\u00f3rie, ale aj ako filozofick\u00e9 a mystick\u00e9 princ\u00edpy, ktor\u00e9 odr\u00e1\u017eaj\u00fa z\u00e1kladn\u00fa dualitu sveta.<\/p>\n
1. Z\u00e1kladn\u00e1 defin\u00edcia p\u00e1rnych a nep\u00e1rnych \u010d\u00edsel
\nP\u00e1rne \u010d\u00edsla s\u00fa tie, ktor\u00e9 sa daj\u00fa rozdeli\u0165 na dve rovnak\u00e9 \u010dasti (s\u00fa delite\u013en\u00e9 dvomi bez zvy\u0161ku).
\nPr\u00edklady: 2, 4, 6, 8, 10\u2026<\/p>\n
Nep\u00e1rne \u010d\u00edsla s\u00fa tie, ktor\u00e9 po rozdelen\u00ed zostan\u00fa nedelite\u013en\u00e9, v\u017edy z nich zostane jeden prvok navy\u0161e.
\nPr\u00edklady: 1, 3, 5, 7, 9\u2026<\/p>\n
Pytagorejci videli v \u010d\u00edslach symboliku protikladov, ktor\u00e9 tvoria z\u00e1klad cel\u00e9ho sveta. Tento syst\u00e9m bol z\u00e1kladom ich dvojic protikladov:
\nMu\u017e, \u017eena, dobro, zlo….<\/p>\n
Nep\u00e1rne \u010d\u00edsla boli pova\u017eovan\u00e9 za dokonal\u00e9 a harmonick\u00e9, preto\u017ee pri ich delen\u00ed v\u017edy zost\u00e1va \u201ejednotka\u201c, ktor\u00e1 symbolizovala duchovn\u00fa celistvos\u0165.<\/p>\n
P\u00e1rne \u010d\u00edsla boli sp\u00e1jan\u00e9 s nestabilitou a nekone\u010dnos\u0165ou, preto\u017ee sa daj\u00fa donekone\u010dna rozde\u013eova\u0165 na rovnak\u00e9 \u010dasti.<\/p>\n
\u010c\u00edslo 3 (nep\u00e1rne) \u2013 symbolizovalo harm\u00f3niu a dokonalos\u0165, preto\u017ee m\u00e1 za\u010diatok, stred a koniec.
\n\u010c\u00edslo 4 (p\u00e1rne) \u2013 bolo s\u00edce stabiln\u00e9, ale bolo vn\u00edman\u00e9 ako statick\u00e9 a pas\u00edvne.<\/p>\n
Pytagorejci pripisovali ka\u017ed\u00e9mu \u010d\u00edslu \u0161peci\u00e1lny v\u00fdznam:<\/p>\n
1 (Mon\u00e1da) \u2013 Princ\u00edp jednoty, bo\u017eskej podstaty, z\u00e1klad v\u0161etk\u00e9ho.
\n2 (Dy\u00e1da) \u2013 Princ\u00edp duality, rozdelenia, chaosu a neobmedzenosti.
\n3 (Tri\u00e1da) \u2013 Dokonalos\u0165, harm\u00f3nia (napr. trojuholn\u00edk je prv\u00fd stabiln\u00fd geometrick\u00fd \u00fatvar).
\n4 (Tetr\u00e1da) \u2013 Stabilita a z\u00e1klad \u0161trukt\u00fary (\u0161tvoruholn\u00edk).
\n5 (Pent\u00e1da) \u2013 Rovnov\u00e1ha medzi p\u00e1rnym a nep\u00e1rnym, symbolizovalo \u017eivot a man\u017eelstvo (2 + 3).
\n6 (Hex\u00e1da) \u2013 Harm\u00f3nia, preto\u017ee je s\u00fa\u010din prv\u00e9ho p\u00e1rneho a nep\u00e1rneho \u010d\u00edsla (2 \u00d7 3).
\n7 (Hept\u00e1da) \u2013 Posv\u00e4tn\u00e9 \u010d\u00edslo, spojen\u00e9 s duchovnom (napr. 7 planet\u00e1rnych sf\u00e9r).
\n10 (Dek\u00e1da) \u2013 Najposv\u00e4tnej\u0161ie \u010d\u00edslo, preto\u017ee je s\u00fa\u010dtom prv\u00fdch \u0161tyroch \u010d\u00edsel (1+2+3+4 = 10), \u010do tvor\u00ed tzv. Tetraktys.<\/p>\n
Geometrick\u00e9 ch\u00e1panie \u010d\u00edsel
\nPytagorejci nielen\u017ee pracovali s \u010d\u00edslami aritmeticky, ale ich aj vizualizovali geometricky. Nep\u00e1rne \u010d\u00edsla sa dali usporiada\u0165 do trojuholn\u00edkov\u00fdch \u00fatvarov (3, 5, 7).
\nP\u00e1rne \u010d\u00edsla sa usporad\u00favali do obd\u013a\u017enikov\u00fdch \u00fatvarov, \u010do vn\u00edmali ako nestabilnej\u0161ie.<\/p>\n
Napr\u00edklad:<\/p>\n
\u010c\u00edslo 3 sa d\u00e1 vizu\u00e1lne usporiada\u0165 ako trojuholn\u00edk, \u010do mu d\u00e1valo mystick\u00fd v\u00fdznam.
\n \u010c\u00edslo 4 sa dalo usporiada\u0165 do \u0161tvorca, \u010do ho robilo symbolom stability.<\/p>\n
Pytagorejci nevn\u00edmali \u010d\u00edsla iba ako abstraktn\u00e9 matematick\u00e9 entity, ale ako \u017eiv\u00e9 princ\u00edpy, ktor\u00e9 riadia svet. Nep\u00e1rne \u010d\u00edsla boli pova\u017eovan\u00e9 za akt\u00edvne, dokonal\u00e9 a harmonick\u00e9, zatia\u013e \u010do p\u00e1rne \u010d\u00edsla za pas\u00edvne, neobmedzen\u00e9 a menej stabiln\u00e9. Tento mystick\u00fd pr\u00edstup k \u010d\u00edslam ovplyvnil neskor\u0161iu numerol\u00f3giu, filozofiu Plat\u00f3na a v\u00fdvoj matematiky ako celku.<\/p>\n
Pytagoras, ako hovor\u00ed Timaeus, objavil k\u00e1non jedn\u00e9ho akordu \u2013 to je pravidlo Monochordu. Aristides rozpr\u00e1va, \u017ee kr\u00e1tko predt\u00fdm, ako zomrel, nab\u00e1dal svojich priate\u013eov, aby hrali na Monochorde; \u010d\u00edm sa nazna\u010duje, \u017ee v\u00fd\u0161ku, ktor\u00e1 je v hudbe, m\u00e1 prij\u00edma\u0165 sk\u00f4r rozum cez \u010d\u00edsla, ne\u017e zmysel cez u\u0161i.<\/p>\n
Mali by sme bu\u010f ml\u010da\u0165, alebo hovori\u0165 veci, ktor\u00e9 s\u00fa lep\u0161ie ako ticho. <\/p>\n
Je lep\u0161ie n\u00e1hodne hodi\u0165 kame\u0148om ako ne\u010dinn\u00e9 slovo. <\/p>\n
Pochopi\u0165 nie m\u00e1lo vec\u00ed mnoh\u00fdmi slovami, ale ve\u013ea vec\u00ed m\u00e1lo slovami. <\/p>\n","protected":false},"excerpt":{"rendered":"
Z vedeck\u00fdch \u010d\u00edsel Pytagoras tvrdil dva r\u00e1dy: jeden ohrani\u010den\u00fd, nep\u00e1rny; druh\u00e9 nekone\u010dn\u00e9, p\u00e1rne \u010d\u00edslo (pod\u013ea pytagorejskej defin\u00edcie) je tak\u00e9, ktor\u00e9 prip\u00fa\u0161\u0165a rozdelenie na najv\u00e4\u010d\u0161ie a najmen\u0161ie; do najv\u00e4\u010d\u0161\u00edch ve\u013ekost\u00ed (pre polovice s\u00fa najv\u00e4\u010d\u0161ie \u010dasti); najmenej v mno\u017estve (preto\u017ee dva je najmen\u0161\u00ed po\u010det) pod\u013ea prirodzen\u00e9ho protikladu t\u00fdchto dvoch druhov. Zvl\u00e1\u0161tne je to, \u010do to nem\u00f4\u017ee trpie\u0165, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-30506","post","type-post","status-publish","format-standard","hentry","category-knihy"],"_links":{"self":[{"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/posts\/30506","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/comments?post=30506"}],"version-history":[{"count":7,"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/posts\/30506\/revisions"}],"predecessor-version":[{"id":30513,"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/posts\/30506\/revisions\/30513"}],"wp:attachment":[{"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/media?parent=30506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/categories?post=30506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/extraslovensko.sk\/spravy\/wp-json\/wp\/v2\/tags?post=30506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}