HP Prime not Computing Correctly

[pschlie]

(02-25-2023 04:15 PM)Nigel (UK) Wrote:  don't agree that the formulae \(A = \pi r^2\) (or \(C = \pi d\)) assume anything about angular units. In the first, \(\pi\) is the ratio of two areas;

Please see:

https://math.stackexchange.com/questions...f-a-circle

(The area of a circle can the thought of as the sum of an infinite number of triangles with two of its sides equal to the radius of the circle, with the third representing an infinitely small segment of the circumference of the circle integrated from 0 to 2*pi as the angular variable of integration; similarly pi is an angular value which corresponds to the length of the arc traversing across 1/2 the circumference of a unit (r=1) circle; arcs are measured in terms of its distance (radius) from some point, and an angular extent, which together defines some fraction of a circle's circumference having said radius; where for a unit circle, the angular values is defined to be equivalent to the length of the arc it projects, i.e. that's how the angular value of radians is defined. But do agree that the presence of pi in a computed value doesn't mean its an angular value, but it does imply it was alternatively likely derived from angular integration, just as C= 2*pi*r and A = 2*pi*(r^2)/2 are.)

As a somewhat related aside:

https://tauday.com/tau-manifesto

And in further conclusion, upon a bit more thought; if HP/Moravia ever considers refining the Prime; and if it was considered feasible to preserve the symbolic representation of pi in intermediate calculations, including Home mode; then the existence of pi in an intermediate expression could be use to imply the value of that expression is in radians (as most such expressions would naturally when specified as some fraction of pi); and in its absence, degrees or a dimensionless value can be presumed.

Similarly based on the angular mode specified, inverse trigonometric functions can represent their results as a fraction of pi if radians is preferred, or degrees otherwise. I.e:

cos(pi) => -1 (regardless of mode, pi implies radians)
cos(180) => -1 (regardless of mode, absence of pi implies degrees)

acos(-1) => pi (if mode = rad)
acos(-1) => 180 (if mode = deg)

cos(acos(-1)) => -1 (regardless of mode)

acos(cos(pi)) => pi (if mode = rad)
acos(cos(pi)) => 180 (if mode = deg)
acos(cos(180)) => pi (if mode = rad)
acos(cos(180)) => 180 (if mode = deg)

As just a thought/wish, along with a hope the same refinements would be supported in RPN mode.