RE: [math-fun] batting averages
Michael Reed wrote: << . . .when i was a (younger!) kid in little league baseball, one of my friends told me that he had calculated his batting average . . . and that it was .399 . immediately i knew that this could not be correct. how did i know?
I'm gonna guess that if |2/5 - p/q| < 1/1000 then q must be greater than any reasonable number of at-bats in one Little League season. --Dan
At minimum, (c2) block([keepfloat : true],linsolve(2*n/(5*n+1) = 0.3985)) (d2) [n = 53.1321] (c3) ceiling(subst(%,5*n+1)) (d3) 267 at bats. --rwg
55/138 = .39855... --ms R. William Gosper wrote:
At minimum, (c2) block([keepfloat : true],linsolve(2*n/(5*n+1) = 0.3985))
(d2) [n = 53.1321]
(c3) ceiling(subst(%,5*n+1))
(d3) 267 at bats. --rwg
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55/138 = .39855...
--ms YIKES! R. William Gosper SHOULDA wrote: At minimum, (c74) block([keepfloat:true],linsolve((2*integer+1)/(5*integer+3)=0.3985)) (d74) [integer = 26.066] (c75) subst(ceiling(%),5*integer+3) (d75) 138 Serves me right for not using continued fractions. at bats.
From the book titled "Seminumerical Algorithms" second edition, by D. Knuth, page 363, exercice 4.5.3 number 39. says:
39. [M25] (R. W. Gosper) If a baseball player's battling average is .334, what is the fewest possible number of times he has been at bat?
round(55/138 *1000)/1000 = .399
participants (4)
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dasimov＠earthlink.net -
gfee＠cecm.sfu.ca -
Mike Speciner -
R. William Gosper