[math-fun] "OneSixOne" palindrome approx to phi
But why stop with 161; cf(phi) is also a palindrome. Harmony and balance will cost you 2400 euros. Smaller amounts of harmony and balance are denoted by "Tau" and cost you only 900 euros. So, for which bases is phi a palindrome for the first 3 digits? "ONESIXONE are the three first figures of the number that governs beauty, the golden ratio. The golden ratio attributes an aesthetic character to objects. Some even believe it has a mystical importance. Along the history it has been included in the design of various works of architecture and art. The golden ratio is synonym with balance, harmony and beauty because of its sound, its emotional charge, its visual and graphic balance. The sense of harmony that transmits being a palindrome number and representativeness of this number in the philosophy of the brand, as well as its their relationship with nature and architecture." http://onesixone.es/the-brand/
In the decimal approximation case, you get a palindrome if you truncate after three terms. In the cf you get one if you truncate after *any number* of terms! --Michael On Nov 23, 2015 5:06 PM, "Dan Asimov" <dasimov@earthlink.net> wrote:
In what sense? There is no orientation-reversing map of the sequence of C.F. integers to itself that maps each integer to itself.
—Dan
On Nov 23, 2015, at 1:38 PM, Henry Baker <hbaker1@pipeline.com> wrote:
But why stop with 161; cf(phi) is also a palindrome.
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Clearly. —Dan
On Nov 23, 2015, at 4:05 PM, Michael Kleber <michael.kleber@gmail.com> wrote:
In the decimal approximation case, you get a palindrome if you truncate after three terms. In the cf you get one if you truncate after *any number* of terms!
--Michael On Nov 23, 2015 5:06 PM, "Dan Asimov" <dasimov@earthlink.net> wrote:
In what sense? There is no orientation-reversing map of the sequence of C.F. integers to itself that maps each integer to itself.
—Dan
On Nov 23, 2015, at 1:38 PM, Henry Baker <hbaker1@pipeline.com> wrote:
But why stop with 161; cf(phi) is also a palindrome.
Rational numbers with palindromic repeat periods of length n are palindromic every n digits; The Thue-Morse constant (in binary) is palindromic at powers of 4 digits. What other sequences of palindromic truncation lengths are possible? On Mon, Nov 23, 2015 at 7:13 PM, Dan Asimov <asimov@msri.org> wrote:
Clearly.
—Dan
On Nov 23, 2015, at 4:05 PM, Michael Kleber <michael.kleber@gmail.com> wrote:
In the decimal approximation case, you get a palindrome if you truncate after three terms. In the cf you get one if you truncate after *any number* of terms!
--Michael On Nov 23, 2015 5:06 PM, "Dan Asimov" <dasimov@earthlink.net> wrote:
In what sense? There is no orientation-reversing map of the sequence of C.F. integers to itself that maps each integer to itself.
—Dan
On Nov 23, 2015, at 1:38 PM, Henry Baker <hbaker1@pipeline.com> wrote:
But why stop with 161; cf(phi) is also a palindrome.
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At 01:38 PM 11/23/2015, Henry Baker wrote:
But why stop with 161; cf(phi) is also a palindrome.
Harmony and balance will cost you 2400 euros.
Smaller amounts of harmony and balance are denoted by "Tau" and cost you only 900 euros.
So, for which bases is phi a palindrome for the first 3 digits?
If phi is truncated to 3 base-b digits, I get palindromes for bases b=4, 10, 26, at least: phi_4 = 1.21 phi_10 = 1.61 phi_26 = 1.G1 ...
participants (6)
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Allan Wechsler -
Dan Asimov -
Dan Asimov -
Gareth McCaughan -
Henry Baker -
Michael Kleber