## Thursday, October 23, 2014

### Fun with the HP 12C

I used the classic HP 12C, with the 99 step capacity.  Even without the trig functions, we can do a lot.

Eddie

Calculating f(x) = p * ∑(a^k, k=1 to n) using the TVM Keys

Input:
[ n ] = n
R0 = a
R1 = p

Program:

 STEP KEY CODE 01 BEGIN 43 7 02 RCL 0 45 0 03 1 1 04 - 30 05 EEX 26 06 2 2 07 * 20 08 [i] 12 09 RCL 1 45 1 10 CHS 16 11 [PMT] 14 12 [FV] 15 13 END 43 8 14 GTO 00 43 33 00

Examples:

n = 60, R0 = 1.01, R1 = 350.  Result:  28,870.2283

n = 5, R0 = 2, R1 = 10.05.   Result:  623.1

Heron’s Formula

Area of a Triangle with side lengths a, b, and c.

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

Input:
R1 = a
R2 = b
R3 = c

Program:

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

Example:   a = 5, b = 5, c = 6.  Result:  12

Projectile Motion without Air Resistance:  With the projectile being launched at 45° at velocity V.  The maximum distance will be achieved at these conditions.

Theoretical Maximum Distance:
R_max = v^2/g (in feet)

Theoretical Height of the Projectile (at x = R_max/2)
H = v^2/(4g)  (in feet)

Where g = 32.17404 ft/s^2

If you desire meters, substitute g = 9.80665 m/s^2 instead.

Run the program with V in the display.  The velocity is assumed to be feet/second.  The maximum distance is calculated, then the projectile’s theoretical height.

Program:

 STEP KEY CODE 01 2 2 02 Y^X 21 03 3 3 04 2 2 05 . 48 06 1 1 07 7 7 08 4 4 09 0 0 10 4 4 11 ÷ 40 12 R/S 31  (display R) 13 4 4 14 ÷ 40 15 GTO 00 43 33 00 (display H)

Example:  V = 40  ft/s
Results:  R = 49.7295 ft,  H = 12.4324 ft

Factorials of Large Integers

N! =  N * (N-1) * (N-2) * … * 1

**For large n, this program will take time if you have an HP 12C that was manufactured in the 1980s.

Input n, press R/S.
The mantissa is displayed.  Press R/S
The exponent is displayed (10^exponent).

Program:

 STEP KEY CODE 01 STO 0 44 0 02 0 0 03 STO 1 44 1 04 RCL 0 45 0 05 LN 43 23   // loop begins 06 STO+ 1 44 40 1 07 1 1 08 STO- 0 44 30 0 09 RCL 0 45 0 10 1 1 11 - 30 12 X=0 43 35 13 GTO 15 43 33 15   // end of loop 14 GTO 04 43 33 04 15 RCL 1 45 1 16 1 1 17 0 0 18 LN 43 23 19 ÷ 10 20 STO 1 44 1 21 ENTER 36 22 FRAC 43 24 23 1 1 24 0 0 25 X<>Y 34 26 Y^X 21 27 R/S 31  // mantissa 28 X<>Y 34 29 INTG 43 25 // exponent 30 GTO 00 43 33 00

Example:

50! » 3.0414 * 10^64
50 R/S
Result:  3.0414 R/S 64

76! » 1.8855 * 10^111
76 R/S
Result:  1.8855 R/S 111

Degrees Minutes Seconds to Decimal Degrees

2°51’32.4” -> 2.859

Type input as DD.MMSSSS (degrees, minutes, seconds). For our example, the input would be 2.51324.

Program:

 STEP KEY CODE 01 STO 0 44 0 02 INTG 43 25 03 STO 1 44 1 04 RCL 0 45 0 05 FRAC 43 24 06 EEX 26 07 2 2 08 * 20 09 INTG 43 25 10 6 6 11 0 0 12 ÷ 10 13 STO+ 1 44 40 1 14 RCL 0 45 0 15 EEX 26 16 2 2 17 * 20 18 FRAC 43 24 19 3 3 20 6 6 21 ÷ 10 22 STO+ 1 44 40 1 23 RCL 1 45 1 24 GTO 00 43 33 00

Decimal Degrees to Degrees Minutes Seconds

2.859 -> 2°51’32.4”

Answer displayed as DD.MMSSSS (degrees minutes seconds)

Program:

 01 STO 0 44 0 02 INTG 43 25 03 STO 1 44 1 04 RCL 0 45 0 05 FRAC 43 24 06 6 6 07 0 0 08 * 20 09 ENTER 36 10 INTG 43 25 11 EEX 26 12 2 2 13 ÷ 10 14 STO+ 1 44 40 1 15 R-Down 33 16 FRAC 43 24 17 6 6 18 0 0 19 * 20 20 EEX 26 21 4 4 22 ÷ 10 23 STO+ 1 44 40 1 24 RCL 1 45 1 25 GTO 00 43 33 00

This blog is property of Edward Shore - 2014