Online HP-35 Emulator - First scientific pocket calculator from 1972

[Albert Chan]

(12-30-2023 08:27 PM)Gerson W. Barbosa Wrote:  When I saw it I thought of a more slightly complex approximation and tried it on the HP-32S Solver:

LN(A×LN(B)÷LN(A×LN(B)))=\(\pi \)

When making A=16 and solving for B I got B=877.999998596

If we have lambertw, we don't need solver

Let X = A*LN(B)      → X / ln(X) = e^pi
Let Y = 1/X        → (1/Y) / -ln(Y) = e^pi      → Y ln(Y) = -1/e^pi      → Y = e^W(-1/e^pi)

Lambert W Function (hp-42s) eW

PI [E↑X] [1/X] [+/-]    → -4.321391826377224977441773717172801e-2
XEQ "eW"                   → 9.557942847885392671580346845743375e-1 // branch 0, not used
− − + × [R/S]            → 9.221489959787579635656761051607647e-3 // branch -1 = Y
[1/X]                         → 108.4423454735329303048683527540144      // = X
16 ÷ [E↑X]                 → 877.9999986484871245574784439800773      // = B, if A=16