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A Nice Bit of Hex on Pi

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Pi Toast

 

3.243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C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 . . . — CalcCrypto

That’s the value of pi calculated in hexadecimal, i.e., in base 16. Which is my fave of the choices I offered in my survey in Perfect π. Although I’ll take one of each survey choice, please.

WolframAlpha is useful for determining π in base 2 (11.001001000011…, with as more digits available), or π in base 7 (3.0663651432036…, ditto), or in just about any other base one’s heart might desire (like, try pi in base e or pi in base 3.14159).

One of my favorite bases for expression of π deserves a brief introductory side note —

[Q] “What would be the significance if we found out if pi repeated?”

[A] “…It would mean that you made a mistake in whatever it was that led to that conclusion.”

Quora

Ummm, except now ask WolramAlpha for the value of “pi in base pi” and we get the simple result: 10π. That is, with a “repeating” decimal of an infinite string of zeroes.

Ummm, and that non-repeating result is supposed to mean that WolframAlpha “made a mistake in whatever it was that led to that conclusion”? That’s the same sort of restrictive thinking that would fuss “you made a mistake” if you came up with a sum of angles for a triangle that did not come out to 180º or would err claiming “you made a mistake” if you came up with a result for the square root of negative one. Coming up with a “repeating” result for π doesn’t mean we are doing it incorrectly; it merely means that we are doing it differently. In this instance, calculating it in a different base, which is quite a legitimate thing to do. After all, even the computers we use to calculate billions upon billions of distant “significant digits” (begging the meaning of significance) for π don’t do so in our familiar base 10; they do so in hexadecimal, then convert it. So might not there be some circle-based analog computer system find computation in base π more feasible, similarly converting to our base 10 in the same manner as our existing binary computing machines? With no mistake in those infinitely repeating zeroes for the value of π itself in its core value.

Eh, if nothing else, π in hex gives us another day to look forward to this month: we can look forward to March 24 as our Pi in Hex Day. For that matter, we can calculate π in whatever base would be necessary to derive a result that is exact to whatever sequential time result we wish to celebrate π! A toast, then, to π in hex offering us a window to honoring π every single moment that ever is or was or will be, no mistakes at all.

 

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Written by macheide

14 March 2015 at 7:54 pm

Posted in mathematic

Tagged with ,

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