Wersja z 2015-09-12

Część poprzednia Spis treści Część następna

Grzegorz Jagodziński

1 2 3 4 5 6

Tabela rozkładu ułamków na trzy składniki

ułamek warunek `a` różnica `a` warunek `b` różnica `b` rozkład  
`4/5` `1.25 < a < 3.75` `3` `4/5 - 1/3 = 7/15` `2.14 < b < 4.29`, `b > 3` `4` `7/15 - 1/4 = 13/60`  
`2` `4/5 - 1/2 = 3/10` `3.33 < b < 6.67` `6` `3/10 - 1/6 = 2/15`
`5` `3/10 - 1/5 = 1/10` `4/5 = 1/2 + 1/5 + 1/10`
`4` `3/10 - 1/4 = 1/20` `4/5 = 1/2 + 1/4 + 1/20`
 
`3/7` `2.33 < a < 7` `6` `3/7 - 1/6 = 11/42` `3.82 < b < 7.64`, `b > 6` `7` `11/42 - 1/7 = 5/42`  
`5` `3/7 - 1/5 = 8/35` `4.38 < b < 8.75`, `b > 5` `8` `8/35 - 1/8 = 29/280`
`7` `8/35 - 1/7 = 3/35`
`6` `8/35 - 1/6 = 13/210`
`4` `3/7 - 1/4 = 5/28` `5.6 < b < 11.2` `11` `5/28 - 1/11 = 27/308`
`10` `5/28 - 1/10 = 11/140`
`9` `5/28 - 1/9 = 17/252`
`8` `5/28 - 1/8 = 3/56`
`7` `5/28 - 1/7 = 1/28` `3/7 = 1/4 + 1/7 + 1/28`
`6` `5/28 - 1/6 = 1/84` `3/7 = 1/4 + 1/6 + 1/84`
`3` `3/7 - 1/3 = 2/21` `10.5 < b < 21` `20` `2/21 - 1/20 = 19/420`
`19` `2/21 - 1/19 = 17/399`
`18` `2/21 - 1/18 = 5/126`
`17` `2/21 - 1/17 = 13/357`
`16` `2/21 - 1/16 = 11/336`
`15` `2/21 - 1/15 = 1/35` `3/7 = 1/3 + 1/15 + 1/35`
`14` `2/21 - 1/14 = 1/42` `3/7 = 1/3 + 1/14 + 1/42`
`13` `2/21 - 1/13 = 5/273`
`12` `2/21 - 1/12 = 1/84` `3/7 = 1/3 + 1/12 + 1/84`
`11` `2/21 - 1/11 = 1/231` `3/7 = 1/3 + 1/11 + 1/231`
 
`5/7` `1.4 < a < 4.2` `4` `5/7 - 1/4 = 13/28` `2.15 < b < 4.31`, `b > 4`  
`3` `5/7 - 1/3 = 8/21` `2.63 < b < 5.25`, `b > 3` `5` `8/21 - 1/5 = 19/105`
`4` `8/21 - 1/4 = 11/84`
`2` `5/7 - 1/2 = 3/14` `4.67 < b < 9.33` `9` `3/14 - 1/9 = 13/126`
`8` `3/14 - 1/8 = 5/56`
`7` `3/14 - 1/7 = 1/14` `5/7 = 1/2 + 1/7 + 1/14`
`6` `3/14 - 1/6 = 1/21` `5/7 = 1/2 + 1/6 + 1/21`
`5` `3/14 - 1/5 = 1/70` `5/7 = 1/2 + 1/5 + 1/70`
 
`6/7` `1.17 < a < 3.5` `3` `6/7 - 1/3 = 11/21` `1.91 < b < 3.82`, `b > 3`  
`2` `6/7 - 1/2 = 5/14` `2.8 < b < 5.6` `5` `5/14 - 1/5 = 11/70`
`4` `5/14 - 1/4 = 3/28`
`3` `5/14 - 1/3 = 1/42` `6/7 = 1/2 + 1/3 + 1/42`
 
`7/8` `1.14< a < 3.43` `3` `7/8 - 1/3 = 13/24` `1.85 < b < 3.69`, `b > 3`  
`2` `7/8 - 1/2 = 3/8` `2.67 < b < 5.33` `5` `3/8 - 1/5 = 7/40`
`4` `3/8 - 1/4 = 1/8` `7/8 = 1/2 + 1/4 + 1/8`
`3` `3/8 - 1/3 = 1/24` `7/8 = 1/2 + 1/3 + 1/24`
 
`7/9` `1.29 < a < 3.86` `3` `7/9 - 1/3 = 4/9` `2.25 < b < 4.5`, `b > 3` `4` `4/9 - 1/4 = 7/36`  
`2` `7/9 - 1/2 = 5/18` `3.6 < b < 7.2` `7` `5/18 - 1/7 = 17/126`
`6` `5/18 - 1/6 = 1/9` `7/9 = 1/2 + 1/6 + 1/9`
`5` `5/18 - 1/5 = 7/90`
`4` `5/18 - 1/4 = 1/36` `7/9 = 1/2 + 1/4 + 1/36`
 
`8/9` `1.13 < a < 3.38` `3` `8/9 - 1/3 = 5/9` `1.8 < b < 3.6`, `b > 3`  
`2` `8/9 - 1/2 = 7/18` `2.57 < b < 5.14` `5` `7/18 - 1/5 = 17/90`
`4` `7/18 - 1/4 = 5/36`
`3` `7/18 - 1/3 = 1/18` `8/9 = 1/2 + 1/3 + 1/18`
 
`9/10` `1.11 < a < 3.33` `3` `9/10 - 1/3 = 17/30` `1.76 < b < 3.53`, `b > 3`  
`2` `9/10 - 1/2 = 2/5` `2.5 < b < 5` `4` `2/5 - 1/4 = 3/20`
`3` `2/5 - 1/3 = 1/15` `9/10 = 1/2 + 1/3 + 1/15`
 
`5/11` `2.2 < a < 6.6` `6` `5/11 - 1/6 = 19/66` `3.47 < b < 6.95`, `b > 6`  
`5` `5/11 - 1/5 = 14/55` `3.93 < b < 7.86`, `b > 5` `7` `14/55 - 1/7 = 43/385`
`6` `14/55 - 1/6 = 29/330`
`4` `5/11 - 1/4 = 9/44` `4.89 < b < 9.78` `9` `9/44 - 1/9 = 37/396`
`8` `9/44 - 1/8 = 7/88`
`7` `9/44 - 1/7 = 19/308`
`6` `9/44 - 1/6 = 5/132`
`5` `9/44 - 1/5 = 1/220` `5/11 = 1/4 + 1/5 + 1/220`
`3` `5/11 - 1/3 = 4/33` `8.25 < b < 16.5` `16` `4/33 - 1/16 = 31/528`
`15` `4/33 - 1/15 = 3/55`
`14` `4/33 - 1/14 = 23/462`
`13` `4/33 - 1/13 = 19/429`
`12` `4/33 - 1/12 = 5/132`
`11` `4/33 - 1/11 = 1/33` `5/11 = 1/3 + 1/11 + 1/33`
`10` `4/33 - 1/10 = 7/330`
`9` `4/33 - 1/9 = 1/99` `5/11 = 1/3 + 1/9 + 1/99`
 
`7/11` `1.57 < a < 4.71` `4` `7/11 - 1/4 = 17/44` `2.59 < b < 5.18`, `b > 4` `5` `17/44 - 1/5 = 41/220`  
`3` `7/11 - 1/3 = 10/33` `3.3 < b < 6.6` `6` `10/33 - 1/6 = 3/22`
`5` `10/33 - 1/5 = 17/165`
`4` `10/33 - 1/4 = 7/132`
`2` `7/11 - 1/2 = 3/22` `7.33 < b < 14.67` `14` `3/22 - 1/14 = 5/77`
`13` `3/22 - 1/13 = 7/286`
`12` `3/22 - 1/12 = 7/132`
`11` `3/22 - 1/11 = 1/22` `7/11 = 1/2 + 1/11 + 1/22`
`10` `3/22 - 1/10 = 2/55`
`9` `3/22 - 1/9 = 5/198`
`8` `3/22 - 1/8 = 1/88` `7/11 = 1/2 + 1/8 + 1/88`
 
`8/11` `1.38 < a < 4.13` `4` `8/11 - 1/4 = 21/44` `2.10 < b < 4.19`, `b > 4` *
`3` `8/11 - 1/3 = 13/33` `2.54 < b < 5.08`, `b > 3` `5` `13/33 - 1/5 = 32/165`
`4` `13/33 - 1/4 = 19/132`
`2` `8/11 - 1/2 = 5/22` `4.4 < b < 8.8` `8` `5/22 - 1/8 = 9/88`
`7` `5/22 - 1/7 = 13/154`
`6` `5/22 - 1/6 = 2/33`
`5` `5/22 - 1/5 = 3/110`
 
`9/11` `1.22 < a < 3.67` `3` `9/11 - 1/3 = 16/33` `2.06 < b < 4.13`, `b > 3` `4` `16/33 - 1/4 = 31/132` *
`2` `9/11 - 1/2 = 7/22` `3.14 < b < 6.29` `6` `7/22 - 1/6 = 5/33`
`5` `7/22 - 1/5 = 13/110`
`4` `7/22 - 1/4 = 3/44`
 
`10/11` `1.1 < a < 3.3` `3` `10/11 - 1/3 = 19/33` `1.74 < b < 3.47`, `b > 3` *
`2` `10/11 - 1/2 = 9/22` `2.44 < b < 4.89` `4` `9/22 - 1/4 = 7/44`
`3` `9/22 - 1/3 = 5/66`
 
`11/12` `1.09 < a < 3.27` `3` `11/12 - 1/3 = 7/12` `1.71 < b < 3.43`, `b > 3`  
`2` `11/12 - 1/2 = 5/12` `2.4 < b < 4.8` `4` `5/12 - 1/4 = 1/6` `11/12 = 1/2 + 1/4 + 1/6`
`3` `5/12 - 1/3 = 1/12` `11/12 = 1/2 + 1/3 + 1/12`

Gwiazdka w ostatniej kolumnie oznacza, że rozkład na trzy składniki nie istnieje i należy odszukać ułamek w następnej tabeli.

Część poprzednia Spis treści Część następna