Ještě k číslu â2: Babylon a řetězové zlomky - Dlab, Vlastimil; Bečvář, Jindřich (Učitel matematiky, 2017)
<span data-sheets-value="{"1":2,"2":"V \u010dl\u00e1nku jsou uvedeny 2 posloupnosti, kter\u00e9 konverguj\u00ed k \u010d\u00edslu \u221a2. Jsou to Babylonsk\u00e1 posloupnost a nekone\u010dn\u00fd \u0159et\u011bzov\u00fd zlomek. Na z\u00e1v\u011br je uvedena zaj\u00edmav\u00e1 v\u011bta, kter\u00e1 jednozna\u010dn\u011b vypl\u00fdv\u00e1 z p\u0159edchoz\u00edho textu a to: \ud835\udc35\ud835\udc4e\ud835\udc4f\ud835\udc66\ud835\udc59\ud835\udc5c\ud835\udc5b\ud835\udc60\ud835\udc58\u00e1 \ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc59\ud835\udc5c\ud835\udc62\ud835\udc5d\ud835\udc5b\ud835\udc5c\ud835\udc60\ud835\udc61 {\ud835\udc4e\ud835\udc61|0\u2264\ud835\udc61} \ud835\udc51\ud835\udc52\ud835\udc53\ud835\udc56\ud835\udc5b\ud835\udc5c\ud835\udc63\u00e1\ud835\udc5b\ud835\udc4e \ud835\udc5f\ud835\udc52\ud835\udc58\ud835\udc62\ud835\udc5f\ud835\udc67\ud835\udc56\ud835\udc63\ud835\udc5b\u011b \ud835\udc63\ud835\udc5c\ud835\udc59\ud835\udc4f\ud835\udc5c\ud835\udc62 \ud835\udc4e0=1 \ud835\udc4e \ud835\udc63\ud835\udc67\ud835\udc61\ud835\udc4e\u210e\ud835\udc52\ud835\udc5a (1)\ud835\udc57\ud835\udc52 \ud835\udc5d\ud835\udc5c\ud835\udc51\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc59\ud835\udc5c\ud835\udc62\ud835\udc5d\ud835\udc5b\ud835\udc5c\ud835\udc60\ud835\udc61\u00ed \ud835\udc58\ud835\udc5c\ud835\udc5b\ud835\udc63\ud835\udc52\ud835\udc5f\ud835\udc54\ud835\udc52\ud835\udc5b\ud835\udc61\u016f {\ud835\udc50\ud835\udc58|0\u2264\ud835\udc58} \u010d\u00ed\ud835\udc60\ud835\udc59\ud835\udc4e\u221a2. \ud835\udc4e\ud835\udc61=\ud835\udc50\u22121+2\ud835\udc59=\u221a2.(1+\u221a2)2\ud835\udc59+(1\u2212\u221a2)2\ud835\udc59(1+\u221a2)2\ud835\udc59\u2212(1\u2212\u221a2)2\ud835\udc59 , t\u22650."}" data-sheets-userformat="{"2":4480,"10":2,"11":3,"15":"Arial"}">V článku jsou uvedeny 2 posloupnosti, které konvergují k číslu â2. Jsou to Babylonská posloupnost a nekonečný řetězový zlomek. Na závěr je uvedena zajímavá věta, která jednoznačně vyplývá z předchozího textu a to: