[VA] Short & Sweet Math Challenge #25 "San Valentin's Special: Weird Math"

[J-F Garnier]

(02-16-2021 09:56 AM)Werner Wrote:  VA#3: integral
[..]
Making use of the fact that φ^2 = φ+1
Same observations as J-F.. though the fact that it's easy to see what the value is, does not explain (to me) why it converges so quickly.

I thought the other way around: I understood that it's so fast because each sample set used by the algorithm gives the exact value of the integral, so the algorithm terminates after just the first 2 estimations (7 samples used).
Then I thought that even one sample is enough to give the exact value, using the midpoint that contributes to 1/2, hence the result.

And yes, φ^2 = φ+1 is the key :-)

J-F