## Saturday, August 20, 2016

### HP 12C: Heron’s Formula, Ulam’s Conjecture, and Prime Factorization

HP 12C:  Heron’s Formula, Ulam’s Conjecture, and Prime Factorization

The following programs have been ported to the HP 12C from various programs presented in the 1980 book, “Programmable Pocket Calculators” by Henry Mullish and Stephen Kochan.  Please see the reference at the end of this entry.

HP 12C:  Heron’s Formula

Heron’s Formula calculates the area of a triangle with side measurements a, b, and c.

Area = √( s * (s-a) *(s-b) *(s-c)), with s = (a + b + c)/2

Based on the original program for HP 67 (pg. 170 of Source)

 STEP CODE KEY 01 44, 1 STO 1 02 31 R/S 03 44, 2 STO 2 04 31 R/S 05 44, 3 STO 3 06 45, 1 RCL 1 07 40 + 08 45, 2 RCL 2 09 40 + 10 2 2 11 10 ÷ 12 44, 4 STO 4 13 45, 1 RCL 1 14 30 - 15 45, 4 RCL 4 16 20 * 17 45, 4 RCL 4 18 45, 2 RCL 2 19 30 - 20 20 * 21 45, 4 RCL 4 22 45, 3 RCL 3 23 30 - 24 20 * 25 43, 21 √ 26 43, 33, 00 GTO 00

Instructions:

Input a, press [R/S], input b, press [R/S], input c, [R/S].  The area will be calculated.

Test 1:  a = 4.00, b = 5.00, c = 3.00  Result:  6.00

Test 2:  a = 10.00, b= 15.00, c = 20.00   Result:  72.62
Test 3:  a = 7.00, b = 8.00, c = 9.00  Result:  26.83

HP 12C:  Ulam’s Conjecture

This program counts the many steps needed to reduce a positive integer to 1, by the following rules:

If the integer is even, divide by 2.
If the integer is odd, multiply it by 3 and add 1.
If the next integer is 1, stop.

Based on the original program for HP 33E (pg. 239 of Source)

 STEP CODE KEY 01 42, 0 FIX 0 ( [ f ], 0) 02 44, 1 STO 1 03 0 0 04 44, 0 STO 0 05 1 1 06 45, 1 RCL 1 07 30 - 08 43, 35 x=0 09 43, 33, 28 GTO 28 10 45, 1 RCL 1 11 2 2 12 10 ÷ 13 43, 24 FRAC 14 43, 25 x=0 15 43, 33, 32 GTO 22 16 45, 1 RCL 1 17 3 3 18 20 * 19 1 1 20 40 + 21 43, 33, 23 GTO 23 22 43, 36 LSTx 23 43, 31 PSE 24 44, 1 STO 1 25 1 1 26 44, 40, 0 STO+ 0 27 43, 33, 05 GTO 05 28 45, 0 RCL 0 29 42, 2 FIX 2 ( [ f ], 2) 30 43, 33, 00 GTO 00

Instructions:

Enter the integer, press [R/S].  The number of steps is calculated.
Test 1:  5 takes 5 steps to get to 1 through Ulam’s Conjecture.
Test 2:  21 takes 7 steps to get to 1 through Ulam’s Conjecture.
Test 3: 39 takes 34 steps to get to 1 through Ulam’s Conjecture.

HP 12C Prime Factorization

This is the prime factorization of a prime integer.  The program ends when the original integer is returned, and FIX 2 mode is set.  Another change I made was instead of the pause command in the original program, I made it a run/stop command so that you write down the prime factors at your leisure.

Based on the original program for HP 25/25C (pg. 77 of Source)

 STEP CODE KEY 01 42, 0 FIX 0  ( [ f ], 0 ) 02 44, 2 STO 2 03 44, 0 STO 0 04 2 2 05 44, 1 STO 1 06 45, 0 RCL 0 07 45 ,1 RCL 1 08 10 ÷ 09 36 ENTER 10 43, 24 FRAC 11 43, 35 x=0 12 43, 33, 16 GTO 16 13 1 1 14 44, 40, 1 STO+ 1 15 43, 33, 06 GTO 06 16 45, 1 RCL 1 17 31 R/S 18 33 R-down, R↓ 19 33 R-down, R↓ 20 44, 0 STO 0 21 1 1 22 30 - 23 43, 35 x=0 24 43, 33, 26 GTO 26 25 43, 33, 06 GTO 06 26 45, 2 RCL 2 27 42, 2 FIX 2 ( [ f ], 2) 28 43, 33, 00 GTO 00

Instructions:  Enter the integer, press [R/S].  Each factor is displayed, while in FIX 0 mode.  Press [R/S] for each factor.  If the number is prime, then only the integer is shown.
Test 1: 100.   Results: 2, [R/S], 2, [R/S], 5, [R/S], 5, [R/S], 100.00
100 = 2^2 * 5^2

Test 2:  255.  Results:  3, [R/S], 5, [R/S], 17, [R/S], 255.00
255 = 3 * 5 * 17

Test 3:  11.  Results: 11 [R/S], 11.00
11 is prime

Source:

Mullins, Henry and Stephen Kochan.  Programmable Pocket Calculators  Hayden Book Company.  Rochelle Park, NJ  1980.

Eddie

This blog is property of Edward Shore, 2016.

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