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## Continued fraction approximation for Euler's number (e):
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## Continued fraction approximation for Euler's number (e):
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cfrac(c(2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8))
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cfrac(c(2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8))
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## Iterative function application:
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## Iterative function application:
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Funcall <- function(f, ...) f(...)
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Funcall <- function(f, ...) f(...)
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## Compute log(exp(acos(cos(0))
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## Compute log(exp(acos(cos(0))))
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Reduce(Funcall, list(log, exp, acos, cos), 0, right = TRUE)
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Reduce(Funcall, list(log, exp, acos, cos), 0, right = TRUE)
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## n-fold iterate of a function, functional style:
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## n-fold iterate of a function, functional style:
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Iterate <- function(f, n = 1)
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Iterate <- function(f, n = 1)
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    function(x) Reduce(Funcall, rep.int(list(f), n), x, right = TRUE)
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    function(x) Reduce(Funcall, rep.int(list(f), n), x, right = TRUE)
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## Continued fraction approximation to the golden ratio:
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## Continued fraction approximation to the golden ratio: