## The perfect tip

Posted by mathfail
on October 12, 2011

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That’s a dollar or so shy of 15%

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Actually thats a pretty crappy tip. A better one would’ve been 2*pi.

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Emm… what is pi in base 26.86?

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Yoav – it’s still 3.14159…

Since none of the digits need to be greater than 26.86 nothing changes. If, however, Pi were, say, 31.4159, in base 26.86 it would be 14.###something

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First of all, you can’t have a non-integer base. You can have negative integer bases, you can even have Gaussian integer bases (look it up if you’re interested), but you can’t have a non-integer real base like 26.86. As such, let’s assume that we’re dealing with base 27 (rounding the value to the nearest integer). The representation of pi actually does change. Think about it: (3.14159265…)10 means 3*100+1*10-1+4*10-2… . 100=270, so the units place would remain at 3, but for all exponents less than 0, the base representation should change. To be exact, pi base 27 is 3.3M5Q3M…, using the convention where A=10, B=11, C=12, and so on.

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Sorry, that should have been (pi) subscript 10, as in base 10, and then 3*10^0+1*10^-1+4*10^-2… and 10^0=27^0. Something must have been wrong with my HTML.

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