Wednesday, July 13, 2022

[kybzoejv] button-mashing the harmonic series

on the Nth button press, 1/N gets added to the displayed sum.  displaying the sum as a floating point number is acceptable but boring; better would be something geometric to visually depict 1/N and the running sum.  is there a way to visually suggest that the sum is unbounded?

similarly, add 1/nthprime(N) for an even more slowly diverging sum: OEIS A016088.  or, Nth button press computes and displays the primality or factorization of N, then adds 1/N only if N is prime.

make it public art so that many generations of people can contribute toward infinity.  or virtual: "welcome, visitor #N!  click here to contribute 1/N to the sum."

the digamma function can probably used to evaluate a large harmonic partial sum avoiding round-off error.  how can one sum reciprocals of primes minimizing round-off error?

instead of a button, a knob that clicks.  the partial sum can be decreased.

No comments :