[superprismatic]

Can anyone determine why I celebrate

September 10^th as ln(2) day?

[Guest]

  On 4/21/2011 at 9:55 PM, superprismatic said:

Can anyone determine why I celebrate

September 10^th as ln(2) day?

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ln(2)= 0.693.....

Sept 10th is .693.... ways throu the year

[Guest]

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365 * ln (2) = 253

I suspect 9/10 is the 253rd day of the year

[Guest]

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i thought about that but they aren't exact. Sept 10 is julian 255 which is 0.66803559206023271731690622861054through the year (254 / 365.25). ln (2) = 0.69314718055994530941723212145818. if we're only talking rounding error, than i politely withdraw my comment.

[Guest]

  On 4/21/2011 at 11:02 PM, Singerbear said:

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i thought about that but they aren't exact. Sept 10 is julian 255 which is 0.66803559206023271731690622861054through the year (254 / 365.25). ln (2) = 0.69314718055994530941723212145818. if we're only talking rounding error, than i politely withdraw my comment.

odd, I get Sept 10th as the 253rd day, or 254th in a leap year. would the fact that julian dates change at noon instead of midnight cause this difference?

[superprismatic]

Well, you BrainDenners sure got onto this one quickly. I'd like to tell you why I celebrate September 10^th each year. I was debugging a subroutine which computed

rational approximations of real numbers using continued fractions. I started testing it on things like π and ln(2) when I noticed that one approximation to ln(2) was 253/365.

So, I looked up what day of the year that was. What was even more amazing is that this approximation is correct to five significant digits. It also happens that I started working

at my wonderful career on that day, September 10^th!