[VA] SRC #009 - Pi Day 2021 Special

[robve]

VA's posts are fascinating and responses are brilliant. His challenges encourages sleuthing using our advanced and vintage HP calculators and perhaps by writing some code to figure this all out.

To return the favor I hereby post two small and related challenges. These two "counter" challenges "invert" VA's common objective (if I may so): instead of writing code and (CAS) expressions, let's figure out what the given code does, find its formula and finally investigate who discovered it (online searching is permitted!). The first question of each of these two should be easy to answer.

If you do not have a HP-71B (I recently acquired mine ), then any Basic-capable machine can be used instead. This code is simple enough to easily convert to HPPL, RPN, Forth.

a. Consider the following HP-71B program:

10 P=SQR(2)
20 Q=P/2
30 DISP 2/Q
40 P=SQR(2+P)
50 Q=Q*P/2
60 IF P<2 GOTO 30


1. What constant does it compute?
2. What is the algebraic formula computed by this code for this constant?
3. Who discovered the formula?
4. Anything else that is interesting about this formula?

b. Consider the following HP-71B program:

10 P=1
20 FOR I=2 TO 1000 STEP 2
30 P=P*I/(I-1)
40 DISP 2*P*P/(I+1)
50 NEXT I

1. What constant does it compute?
2. What is the algebraic formula computed by this code for this constant?
3. Who discovered the formula?
4. Anything else that is interesting about this formula?

I will reply with the answers after VA posted his conclusions of the pi day challenge.

- Rob