PDQ Algorithm: Infinite precision best fraction within tolerance

[Joe Horn]

(01-26-2020 12:32 AM)cdmackay Wrote:  

(12-13-2013 05:09 AM)Joe Horn Wrote:  Here is a handy variable for PDQ experimentation.

PI500 (This fraction's decimal expansion has the same first 500 decimal places as pi. Remove all carriage returns):

Code:

27530008686166622188536681168621832641085194972343166639705257535483379211746872​24521381642611856603178539596529812288248903337810098177795117288227409717155741​87957420619251445521692137166819636595557228499775776315464391353285480273592327​83581546654/87630739315324660697093180818659895483560383602191807997668834668010919518358106​20316848615678705592355956178010775004819317000458201135712222333217497308440528​56473605433480720429471645084774186874516644432633187107318767999674836818181677​0785368793

sorry, this is no doubt a silly question, but, how do I get the above useful variable into my physical calculator, without having to type it all in?

I'd assumed that there must be some way of doing it with the Connectivity Kit, but after a lot of fiddling, I can't see how to do it.

I tried pasting it into the virtual Prime app, and from there I can see it in that calculator's CAS Vars entry in the CK. But I can't see to get it from there into my physical Prime, nor into the "Content" area.

thanks…

Although there must be a better way to do it than my way, here's how I do it. Create a text file on your PC called PI500.TXT which contains the following plain text (w/o carriage returns):

Code:

PI500:=2753000868616662218853668116862183264108519497234316663970525753548337921​17468722452138164261185660317853959652981228824890333781009817779511728822740971​71557418795742061925144552169213716681963659555722849977577631546439135328548027​359232783581546654/87630739315324660697093180818659895483560383602191807997668834668010919518358106​20316848615678705592355956178010775004819317000458201135712222333217497308440528​56473605433480720429471645084774186874516644432633187107318767999674836818181677​0785368793

Now create a blank Note on your Virtual Prime and/or your real Prime via the Connectivity Kit. Paste the above text file into that Note for safekeeping. Now paste it into CAS and evaluate it, which creates the desired CAS var. Any time the CAS var gets destroyed (which seems to happen to me annoyingly often) just copy that Note and paste it into CAS again. If the Note ever gets lost (happens very rarely), copy it again from PI500.TXT as before.

Ridiculously complicated, but it's how I've been doing it for years. If anybody knows of a better way of creating & saving the above PI500 as a CAS var, please share it with us.