Stránka se zabývá výzkumem struktur převrácených čísel a převrácených prvočísel, jako podklad a zdroj informací využívá výzkum ze stránky Číselné soustavy/Desítková soustava . Cílem je nalezení souvislostí, podobností ve struktuře převrácených čísel.
převrácená čísla
vzorec
číslo
rozklad
vzorec
proměnné
1/2
2: 0,500000000000... l.p. = 0+1pp
[
0
]
,
[
5
]
[
0
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[5][0][0]...[0]}
[
0
]
,
[
a
]
[
0
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[a][0][0]...[0]}
a=5
1/3
3: 0,333333333333... l.p. = 1
[
0
]
,
[
3
]
[
3
]
[
3
]
.
.
.
[
3
]
{\displaystyle [0],[3][3][3]...[3]}
[
0
]
,
[
a
]
[
a
]
[
a
]
.
.
.
[
a
]
{\displaystyle [0],[a][a][a]...[a]}
a=3
1/4
4: 0,250000000000... l.p. = 0+2pp
[
0
]
,
[
2
]
[
5
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[2][5][0]...[0]}
[
0
]
,
[
a
]
[
b
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[a][b][0]...[0]}
a=2; b=5
1/5
5: 0,200000000000... l.p. = 0+1pp
[
0
]
,
[
2
]
[
0
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[2][0][0]...[0]}
[
0
]
,
[
a
]
[
0
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[a][0][0]...[0]}
a=2
1/6
6: 0,166666666666... l.p. = 1+1pp
[
0
]
,
[
1
]
[
6
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[1][6][0]...[0]}
[
0
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,
[
a
]
[
b
]
[
b
]
.
.
.
[
b
]
{\displaystyle [0],[a][b][b]...[b]}
a=1; b=6
1/7
7: 0,142857142857... l.p. = 6
[
0
]
,
[
1
]
[
4
]
[
2
]
[
8
]
[
5
]
[
7
]
.
.
.
[
1
]
[
4
]
[
2
]
[
8
]
[
5
]
[
7
]
{\displaystyle [0],[1][4][2][8][5][7]...[1][4][2][8][5][7]}
[
0
]
,
[
a
]
[
b
]
[
c
]
[
d
]
[
e
]
[
f
]
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.
.
[
a
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[
b
]
[
c
]
[
d
]
[
e
]
[
f
]
{\displaystyle [0],[a][b][c][d][e][f]...[a][b][c][d][e][f]}
a=1;b=4;c=2;d=8,e=5;f=7
1/8
8: 0,125000000000... l.p. = 0+3pp
[
0
]
,
[
1
]
[
2
]
[
5
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[1][2][5][0]...[0]}
[
0
]
,
[
a
]
[
b
]
[
c
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[a][b][c][0]...[0]}
a=1; b=2; c=5
1/9
9: 0,111111111111... l.p. = 1
[
0
]
,
[
1
]
[
1
]
[
1
]
[
1
]
.
.
.
[
1
]
{\displaystyle [0],[1][1][1][1]...[1]}
[
0
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,
[
a
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[
a
]
[
a
]
[
a
]
.
.
.
[
a
]
{\displaystyle [0],[a][a][a][a]...[a]}
a=1
1/10
10: 0,100000000000... l.p. = 0+1pp
[
0
]
,
[
1
]
[
0
]
[
0
]
[
0
]
.
.
.
[
0
]
{\displaystyle [0],[1][0][0][0]...[0]}
[
0
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,
[
a
]
[
0
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[
0
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[
0
]
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.
[
0
]
{\displaystyle [0],[a][0][0][0]...[0]}
-
Dva výrazy 1/2=0,500... a 1/5=0,200... vykazují vlastnost zaměnitelnosti pro a=2 a b=5.
1
/
a
=
[
0
]
,
[
b
]
[
0
]
[
0
]
.
.
.
{\displaystyle 1/a=[0],[b][0][0]...}
1
/
b
=
[
0
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,
[
a
]
[
0
]
[
0
]
.
.
.
{\displaystyle 1/b=[0],[a][0][0]...}
Dva výrazy 1/4=0,2500...0 a 1/8=0,1250...0 vykazují vlastnost úměrnosti pro a=250 a b=125 kde b=a/2. a kde x=4 a y=8 kde x=y/2
1
/
x
=
[
0
]
,
[
a
]
[
0
]
[
0
]
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.
.
=
1
/
4
=
[
0
]
,
[
250
]
[
0
]
.
.
.
[
0
]
{\displaystyle 1/x=[0],[a][0][0]...=1/4=[0],[250][0]...[0]}
1
/
(
2
x
)
=
[
0
]
,
[
a
/
2
]
[
0
]
[
0
]
.
.
.
=
1
/
(
4
⋅
2
=
8
)
=
[
0
]
,
[
250
/
2
=
125
]
[
0
]
.
.
.
[
0
]
{\displaystyle 1/(2x)=[0],[a/2][0][0]...=1/(4\cdot 2=8)=[0],[250/2=125][0]...[0]}
Dva výrazy 1/3=0,3333...3 a 1/6=0,16666...6 vykazují vlastnost úměrnosti pro x=3 a a=0,3333...3 pro zjednodušení bylo použito ve výpočtu zaokrouhlení na a=0,334, proto i výsledek b=0,167 vyšel zaokrouhlenný přesnost výpočtu závisí na tom kolik proměnná a obsahuje platných cifer.
1
/
x
=
[
0
]
,
[
a
]
=
1
/
3
=
[
0
]
,
[
334
]
{\displaystyle 1/x=[0],[a]=1/3=[0],[334]}
1
/
(
2
x
)
=
[
0
]
,
[
a
/
2
]
.
.
.
=
1
/
(
2
⋅
3
=
6
)
=
[
0
]
,
[
334
/
2
=
167
]
{\displaystyle 1/(2x)=[0],[a/2]...=1/(2\cdot 3=6)=[0],[334/2=167]}
Dva výrazy 1/5=0,2000...0 a 1/10=0,1000...0 vykazují vlastnost úměrnosti pro x=5 a a=2.
1
/
x
=
[
0
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,
[
a
]
[
0
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[
0
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.
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[
0
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=
1
/
5
=
[
0
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[
2
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[
0
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[
0
]
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.
.
[
0
]
{\displaystyle 1/x=[0],[a][0][0]...[0]=1/5=[0],[2][0][0]...[0]}
1
/
(
2
x
)
=
[
0
]
,
[
a
/
2
]
[
0
]
[
0
]
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.
.
[
0
]
=
1
/
(
2
⋅
5
=
10
)
=
[
0
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,
[
2
/
2
=
1
]
[
0
]
[
0
]
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.
.
[
0
]
{\displaystyle 1/(2x)=[0],[a/2][0][0]...[0]=1/(2\cdot 5=10)=[0],[2/2=1][0][0]...[0]}
Tato stránka je součástí projektu:
![{\displaystyle [0],[5][0][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e1b0b4ffbeda8b00e98b3cb05c58e017b1b4ff0b)
![{\displaystyle [0],[a][0][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a53f4f546dd546443a5a820373d027610046198d)
![{\displaystyle [0],[3][3][3]...[3]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80942f06e59b7da7fbd766db456e3dab2db4a669)
![{\displaystyle [0],[a][a][a]...[a]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ef06f7f6cd9de2899a83d1d61ffc050e2fc3e32)
![{\displaystyle [0],[2][5][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/042bf50ebc5ee1a9e9a0f73d5752440f347b7cef)
![{\displaystyle [0],[a][b][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d14b2216e751e5b0b015d66f919510db1aa848f3)
![{\displaystyle [0],[2][0][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b62d6499fd62f10206c174bcd71a4f0ae5409c9)
![{\displaystyle [0],[1][6][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea9d896909b73132b762a2ca562821e8d3dfcc1d)
![{\displaystyle [0],[a][b][b]...[b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bc6ec4ff80d6c63ce7c64b0bcd6441b407629331)
![{\displaystyle [0],[1][4][2][8][5][7]...[1][4][2][8][5][7]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b1246c1b27d10ff27383f9fa197c258093512dc)
![{\displaystyle [0],[a][b][c][d][e][f]...[a][b][c][d][e][f]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/53e99afa7120428f2d3a57db94c7c21054b6c1e1)
![{\displaystyle [0],[1][2][5][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03f9baed1bd62a64ade06f27184194bc389f2339)
![{\displaystyle [0],[a][b][c][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/25d97a8f1d748a19fb6fbe1ce3dd23475374dd5d)
![{\displaystyle [0],[1][1][1][1]...[1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/deb839c48451bec2afbeae26c5ce03eabe7cf255)
![{\displaystyle [0],[a][a][a][a]...[a]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/346315fb5ff0747dffd274efc094d62b8416f162)
![{\displaystyle [0],[1][0][0][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/629b9be962dcf95d800d1f099d38beaa412f467b)
![{\displaystyle [0],[a][0][0][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41a1deca44f440163bbf54f42ce002abc46e1ada)
![{\displaystyle 1/a=[0],[b][0][0]...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf100582d5f44ecbc0ed84cdedaa6694fd913d98)
![{\displaystyle 1/b=[0],[a][0][0]...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0285c95c73c2c122e95ba7cb50c470cd7bd4e3af)
![{\displaystyle 1/x=[0],[a][0][0]...=1/4=[0],[250][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0da280215b587d7b027e963eb8c6daaed63047c)
![{\displaystyle 1/(2x)=[0],[a/2][0][0]...=1/(4\cdot 2=8)=[0],[250/2=125][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb6abf63bc835ea31756aee733b0a1ff9bb21cad)
![{\displaystyle 1/x=[0],[a]=1/3=[0],[334]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ef69898c465f4069da99fc4043dc749ba44b7a6)
![{\displaystyle 1/(2x)=[0],[a/2]...=1/(2\cdot 3=6)=[0],[334/2=167]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a84e433e8ab266823476f3aac453959298e3032)
![{\displaystyle 1/x=[0],[a][0][0]...[0]=1/5=[0],[2][0][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/937630278353be1be9585ccfe650f5f2eb4f1993)
![{\displaystyle 1/(2x)=[0],[a/2][0][0]...[0]=1/(2\cdot 5=10)=[0],[2/2=1][0][0]...[0]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8634dadc9ab317be37e1bdb1a7b7faf2bf651dda)