@Christopher2222 The osculating circle is the circle tangent to a curve which most closely approximates the curve at the point of tangency (among all tangent circles). The curvature is (by definition) the reciprocal of the radius of the osculating circle.

@K5ky:When I replace the equation with a name that points to it, this returns FAIL instead.Any ideas why?

NextZero takes an operator, not an expression, as its first argument.

@K5ky:When I replace the equation with a name that points to it, this returns FAIL instead.Any ideas why?

NextZero takes an operator, not an expression, as its first argument.

@williamov It's difficult to generalize that. It will work if you write a separate top-level assignment statement for each variable. But if you try to do it in a loop or procedure, or iterating over a list of names in a set or list, it gets tricky.

@williamov It's difficult to generalize that. It will work if you write a separate top-level assignment statement for each variable. But if you try to do it in a loop or procedure, or iterating over a list of names in a set or list, it gets tricky.

One reason that the absolute-value form might be preferred over the piecewise form is that the former makes the continuity obvious. One reason that the absolute-value form might be preferred over the list-of-points form is that most symbolic computation commands will not take the latter.

@whenyourestrange Actually, my command above can be simplified slightly: One of the two zero vectors (< 0 | 0 >), it doesn't matter which one, can be removed.

@whenyourestrange Actually, my command above can be simplified slightly: One of the two zero vectors (< 0 | 0 >), it doesn't matter which one, can be removed.

@williamov To put if inside an expression, do

`if`(assigned(h251), h251, 0)

@williamov To put if inside an expression, do

`if`(assigned(h251), h251, 0)

@HDN46 There are only two ways to get out of the loop for n from 0 to 19: Either n goes above 19, or the break statement (after the then in the loop) is executed. The break is executed when we have a non-solution: either a non-integer was encountered (r<>0) or two consecutive zeroes were found. Otherwise, we have a solution, and n goes above 19, so it is 20. 

Does that answer your question?

@HDN46 There are only two ways to get out of the loop for n from 0 to 19: Either n goes above 19, or the break statement (after the then in the loop) is executed. The break is executed when we have a non-solution: either a non-integer was encountered (r<>0) or two consecutive zeroes were found. Otherwise, we have a solution, and n goes above 19, so it is 20. 

Does that answer your question?

@marc005 What trouble did you have trying to make it into a procedure?

@marc005 What trouble did you have trying to make it into a procedure?

Capital O is a protected name. I am skeptical about your attempt to use it as a variable.