[VA] SRC #016 - Pi Day 2024 Special

[Gerson W. Barbosa]

Hello, Valentín,

Thanks for yet another SRC Pi Day Special!

Nice and interesting topics, as always, but I hope you don’t mind if I take only number 5 this time.

The easiest way to solve polynomial equations on the hp 50g is using the Polynomial Root Solver (PROOT, available also on the HP-71B). On the hp 50g:

[ 4 -22 29 2 ] PROOT 3 GET
-> 3.14159299564

[ 9 -19 28 -70 -344 ] PROOT 4 GET
-> (3.1415926538,0)

I’ll take the opportunity to present my own polynomial equation of that kind:

x^7 + 2x^6 + 3x^5 + 4x^4 + 3x^3 + 2x^2 + x - 19100/3 = 0

That’s a 7th-degree polynomial equation, but on the other hand the sizes of the coefficients of x are quite small, increasing from 1 to 4 and then down to 1 again. The closeness of the real root to π is similar to that of the previous 4th-degree polynomial equation.

[ 1 2 3 4 3 2 1 '-19100/3' ] PROOT 1 GET
-> (3.14159265373,0)

This stems from the observation that π(1 + π + π^2+ π^3)^2 ≈ 19100/3

Best regards,

Gerson