I finally finished a construction that has consumed much of my recent puzzling. There is little to show for it at the moment, but I thought I would make a note here as it was an elegant problem with a fairly satisfying solution. Rather than post my solution I will post the problem, which is of greater value to you, should you attempt to solve it:

I have occasionally used a calculation with the

I ought to add that I tried to do this myself and it's likely enough that while I thought it was tricky, I could have missed something that everyone else already knows about. For example, I always thought that there was no explicit formula for Fibonacci numbers, but there is and I only learned about it recently.

**Find the maximum value of a function f(x) on an interval (a, b).**I have occasionally used a calculation with the

`sgn()`

function to determine the greater of two values, but I was hoping to use iteration to work through an interval. My construction will improve with iterations, but of course it has some precision limitations with discontinuous or very steep functions; it is not calculus on smooth curves, after all.I ought to add that I tried to do this myself and it's likely enough that while I thought it was tricky, I could have missed something that everyone else already knows about. For example, I always thought that there was no explicit formula for Fibonacci numbers, but there is and I only learned about it recently.

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