Finding messages in decimals
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A puzzle asked if there is message in the decimal expansion of $pi$, starting after the decimal point.
The answer, with $pi$= 3.1415, using A1-Z26 conversion, split 14|15 is no.
Trying this for $e$ we annoyingly get gah, which can be extended modulo 26 as bah, since:
2.7182818 → 7 | 1 | 8 | 28 | 1 | 8 → gahbah
For rational numbers I think we can decide:
$frac{1}{9}$ = 0.111... and as 111 mod 26 = 7, we may choose any length of 1's to pick a letter.
$frac{2}{9}$ = 0.222 ... and as an even number mod 26 is even we can't choose odd letters.
Are there general classes of real numbers, expressed as decimals, where if allowed to use any length of sequence modulo 26, a given message may be found, if it must start right after the decimal point?
modular-arithmetic recreational-mathematics real-numbers decimal-expansion
asked Dec 22 '18 at 9:41
TomTom
1166
$endgroup$
add a comment |
$begingroup$
A puzzle asked if there is message in the decimal expansion of $pi$, starting after the decimal point.
The answer, with $pi$= 3.1415, using A1-Z26 conversion, split 14|15 is no.
Trying this for $e$ we annoyingly get gah, which can be extended modulo 26 as bah, since:
2.7182818 → 7 | 1 | 8 | 28 | 1 | 8 → gahbah
For rational numbers I think we can decide:
$frac{1}{9}$ = 0.111... and as 111 mod 26 = 7, we may choose any length of 1's to pick a letter.
$frac{2}{9}$ = 0.222 ... and as an even number mod 26 is even we can't choose odd letters.
Are there general classes of real numbers, expressed as decimals, where if allowed to use any length of sequence modulo 26, a given message may be found, if it must start right after the decimal point?
modular-arithmetic recreational-mathematics real-numbers decimal-expansion
asked Dec 22 '18 at 9:41
TomTom
1166
$endgroup$
2
$begingroup$
I collected together a large number of Mathematics Stack Exchange questions related to this in my answer to Normal Numbers as members of a larger set?.
$endgroup$
– Dave L. Renfro
Dec 22 '18 at 18:23
add a comment |
$begingroup$
A puzzle asked if there is message in the decimal expansion of $pi$, starting after the decimal point.
The answer, with $pi$= 3.1415, using A1-Z26 conversion, split 14|15 is no.
Trying this for $e$ we annoyingly get gah, which can be extended modulo 26 as bah, since:
2.7182818 → 7 | 1 | 8 | 28 | 1 | 8 → gahbah
For rational numbers I think we can decide:
$frac{1}{9}$ = 0.111... and as 111 mod 26 = 7, we may choose any length of 1's to pick a letter.
$frac{2}{9}$ = 0.222 ... and as an even number mod 26 is even we can't choose odd letters.
Are there general classes of real numbers, expressed as decimals, where if allowed to use any length of sequence modulo 26, a given message may be found, if it must start right after the decimal point?
modular-arithmetic recreational-mathematics real-numbers decimal-expansion
asked Dec 22 '18 at 9:41
TomTom
1166
$endgroup$
A puzzle asked if there is message in the decimal expansion of $pi$, starting after the decimal point.
The answer, with $pi$= 3.1415, using A1-Z26 conversion, split 14|15 is no.
Trying this for $e$ we annoyingly get gah, which can be extended modulo 26 as bah, since:
2.7182818 → 7 | 1 | 8 | 28 | 1 | 8 → gahbah
For rational numbers I think we can decide:
$frac{1}{9}$ = 0.111... and as 111 mod 26 = 7, we may choose any length of 1's to pick a letter.
$frac{2}{9}$ = 0.222 ... and as an even number mod 26 is even we can't choose odd letters.
Are there general classes of real numbers, expressed as decimals, where if allowed to use any length of sequence modulo 26, a given message may be found, if it must start right after the decimal point?
modular-arithmetic recreational-mathematics real-numbers decimal-expansion
modular-arithmetic recreational-mathematics real-numbers decimal-expansion
asked Dec 22 '18 at 9:41
TomTom
1166
asked Dec 22 '18 at 9:41
TomTom
1166
edited Dec 22 '18 at 18:09
Tom
asked Dec 22 '18 at 9:41
TomTom
1166
asked Dec 22 '18 at 9:41
TomTom
1166
asked Dec 22 '18 at 9:41
TomTom
1166
1166
2
$begingroup$
I collected together a large number of Mathematics Stack Exchange questions related to this in my answer to Normal Numbers as members of a larger set?.
$endgroup$
– Dave L. Renfro
Dec 22 '18 at 18:23
add a comment |
2
$begingroup$
I collected together a large number of Mathematics Stack Exchange questions related to this in my answer to Normal Numbers as members of a larger set?.
$endgroup$
– Dave L. Renfro
Dec 22 '18 at 18:23
2
2
$begingroup$
I collected together a large number of Mathematics Stack Exchange questions related to this in my answer to Normal Numbers as members of a larger set?.
$endgroup$
– Dave L. Renfro
Dec 22 '18 at 18:23
$begingroup$
I collected together a large number of Mathematics Stack Exchange questions related to this in my answer to Normal Numbers as members of a larger set?.
$endgroup$
– Dave L. Renfro
Dec 22 '18 at 18:23
add a comment |
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I collected together a large number of Mathematics Stack Exchange questions related to this in my answer to Normal Numbers as members of a larger set?.
$endgroup$
– Dave L. Renfro
Dec 22 '18 at 18:23