find the -nth digit of Pi in a string

Forum Attachments

find the -nth digit of Pi in a string

(account deleted) 17 Sep 2018 01:10

Constraints:

• The user must type a real number indicating to find out the -nth digit of Pi
• The program must be simple as possible
• (OPTIONAL) the program can store the previous digits of Pi in a string (Begin string: "3.")
• Do not use the command summation Σ. Or any other complicated commands
• The easier the better
• Make the calculations as fast as possible
• Display the digit in Ans (obviously)
• Make it compatible for ALL graphing calculators (With the Input command and other necessary commands)
• ?<1000 bytes (extra credit <460)
• SIMPLE calculations, no formulas

---

Hewwo, my name is Achak Claw. I was formerly BioHazard.

Last edited on 18 Sep 2018 12:59 by (account deleted) Show more

Re: find the -nth digit of Pi in a string

Trenly 17 Sep 2018 21:24

Constraints:

• Do something nearly impossible
• Don't use any standard method of doing it
• Keep a very complex task, simple
• Keep it small

Last edited on 17 Sep 2018 21:25 by Trenly Show more

Re: find the -nth digit of Pi in a string

(account deleted) 17 Sep 2018 22:07

Is that supposed to be funny? I'm laughing! Seriously, I tried to looks up a program like this, w/ no success…… rip.

---

Hewwo, my name is Achak Claw. I was formerly BioHazard.

Re: find the -nth digit of Pi in a string

Trenly 17 Sep 2018 22:56

No, its supposed to be serious. Have you ever thought that the reason you haven't found one is because what you're asking for is nearly impossible?

Re: find the -nth digit of Pi in a string

Battlesquid 17 Sep 2018 23:14

Basically, Trenly is trying to say that the digits of PI are so sporadic that it's difficult to deduce a simple pattern.




However, doing some research doesn't hurt.

EDIT: Reread the post and realized that my proposed method wouldn't work.

A guideline for contests like these are to solve it yourself first. That way you know there is at least one way to solve the problem.

---

Last edited on 17 Sep 2018 23:17 by Battlesquid Show more

Re: find the -nth digit of Pi in a string

Trenly 18 Sep 2018 01:20

Another point I would like to make is that even if you calculate PI using an algorithm, Ans only recalls the first 15 digits of it (As noticed when using the number-to-string routine. Even though it stores more digits than that, for example $10 ≠ 3(10/3)$. In the same way, $3.14159265358979 ≠ π$, even though it displays the same answer whether displaying $π$ or a calulated value for pi. Therefore, some sort of algorithm has to be used to calculate the nth digit directly, or calculate all the preceding digits individually.

Because of that limitation, the program will never be simple, fast for any value over certain N's, and will likely not be under 1000 bytes. Because of that, I am almost inclined to declare this challenge impossible.

Edit: Even if you stored as many digits of pi as are available in the 1000 bytes (978), that still would not be a valid program as it doesn't solve for all n'th digits of pi within the calculators limitations

Last edited on 18 Sep 2018 01:26 by Trenly Show more

Re: find the -nth digit of Pi in a string

lirtosiast 18 Sep 2018 03:29

The constraints are a bit contradictory, but here's a routine originally from Cemetech. Details of the algorithm are in the linked thread.

• Around 300 bytes
• Optimized for speed (finance variables, precomputes things)
• Takes 320 seconds for 400 digits, runs out of memory on my 84+ when trying to compute more. Could probably run to about 1020 digits on an 84+CE.
• Compatible with the entire TI-83+ family
• I have no idea what a "complicated command" is so I can't say whether this uses any.

The problem with most Pi calculation algorithms is memory requirement— it's a long time since I last looked them up, but IIRC most algorithms' memory requirement is linear in the input. This particular algorithm could be adapted to 2000 digits or so, but that would require constantly archiving and unarchiving lists and slow it down significantly. 2000 digits would take maybe a day.

ClrHome
CLASSIC
Prompt N
startTmr->T

10->B
Repeat M*27L^^2<|E12
    B-1->B
    ~int(~N/B)+1->S //number of batches
    10^B->M
    ~int(~BS/log(13.5))+3->L //2 extra terms for accuracy
End
Disp "M=10^(",B

seq(X,X,0,L->L6
5L6+3->L1                // representation of pi
27(L6^^2+L6)+6->L2      // denominators
2(L6+1)^^2-(L6+1)->L3   // numerators
DelVar L6
Disp "INIT TIME",checkTmr(T

For(X,0,S-1
    ~int(~L+BX/log(13.5))+1->dim(L1  //we only need this many terms
    L1M->L1
    0->FV
    For([recursiven],dim(L1),1,~1
        L1([recursiven])+FV*L3([recursiven]->PV
        int(PV/L2([recursiven]->FV
        PV-FVL2([recursiven]->L1([recursiven]
    End
    int(PV/M
    //Disp Ans
    PV-MAns->L1(1
End
Disp "NTH DIGIT = ",int(10fPart(int(PV/M)10^(N-B(S-1)-1
Disp "TIME",checkTmr(T

Last edited on 18 Sep 2018 03:40 by lirtosiast Show more

Re: find the -nth digit of Pi in a string

(account deleted) 18 Sep 2018 12:58

Me: Hm…………. (5 years later)…………….. Good work!
You: Seriously?! THAT LONG?!

Meanwhile back in the ranch, great work! A+++++++

---

Hewwo, my name is Achak Claw. I was formerly BioHazard.

Re: find the -nth digit of Pi in a string

Michael2_3B 17 Sep 2018 23:22

You could use gossamer to browse the internet for the nth digit through your calculator

Re: find the -nth digit of Pi in a string

Trenly 18 Sep 2018 01:10

But that isn't "compatible for ALL graphing calculators (With the Input command and other necessary commands)"