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optimal leap year

Posted in Books, Kids, Mountains, pictures, R with tags , , , , , , , on November 19, 2022 by xi'an

A riddle about leap years: a solar year consists of approximately 365.24217 mean solar days, which is why there is a leap year approximately every four years. Approximately because the Gregorian calendar plans 97 and not 100 leap years over 400 years. Is this the optimal solution? No, since the Gregorian difference is 3.3 10⁻⁴ day per year, or 0.132 day per 400 years, while using 85 leap years over every 351 years leads to a difference of 4.76 10⁻⁶ day per year, or 0.002 day per 400 years… (With a further gain by a factor 4 with 116 leap years every 479 years.) This can be found by a basic R code

for(N in 10:1000)
for(L in 1:N){
  p=abs(L/N-.24217)
  if(p<T){T=p;lo=L;no=N}}

down by the lake⁴ [jatp]

Posted in pictures, Running, Travel with tags , , , , , , , , on July 21, 2022 by xi'an

down by the lake³ [jatp]

Posted in pictures, Running, Travel with tags , , , , , , , on July 18, 2022 by xi'an

down by the lake [Saint-Jean]

Posted in Statistics with tags , , , , , , , , , on July 9, 2022 by xi'an

New York New York [jatp]

Posted in pictures, Travel with tags , , , , , , , , , on April 25, 2022 by xi'an

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