(12C) Circles, Spheres, and Right Triangle

[Eddie W. Shore]

Approximating π

The HP-12C does not have a π key. We can tackle this in one of two ways:

* We can input the full approximation of π until the display no longer accepts numbers, which is up to 10 numbers. π typed to screen capacity is 3.141592654. Since each digit entered plus the decimal point takes a step, it will require 11 steps to enter.

* We can use the approximation π ≈ 355/113. 355/113 ≈ 3.141592920. 355/113 is an accurate approximation of π to 6 digits. It will take a total of 8 steps to enter this approximation. Since most of the time the HP 12C is used at Fix 2 mode (2 decimal places), this may be for most practical purposes an adequate approximation. Just a caution: make number of calculations low and the factors should be relatively small.

The programs represented on this blog will use the 355/113 to save space. If you require a better approximation of π and have the space, feel free to replace 355/113 with the 3.141592654.

HP 12C: Circles – Circumference and Area

The program calculates an approximate circumference and area of a circle given radius r.

C = 2*π*r
A = π*r^2

Here, we take 355/113 as an approximation for π.

Code:

STEP    CODE    KEY
01    44, 0    STO 0
02    3    3
03    5    5
04    5    5
05    36    ENTER
06    1    1
07    1    1
08    3    3
09    10    ÷
10    44, 1    STO 1
11    20    *
12    2    2
13    20    *
14    31    R/S
15    45, 0    RCL 0
16    2    2
17    21    Y^X
18    45, 1    RCL 1
19    20    *
20    43, 33, 00    GTO 00

Registers used:
R0 = r, R1 = 335/113 ≈ π

Input:
Enter radius, r, and press [R/S].

Output:
Obtain the approximate circumference. Press [R/S] for the area.

Examples (FIX 2):

Radius = 2.96. Results: Circumference ≈ 18.60, Area ≈ 27.53

Radius = 5.00 Results: Circumference ≈ 31.42, Area ≈ 78.54

Alternate: This uses the following shortcuts:
Number, [ENTER], [ + ] doubles the number.
Number, [ENTER], [ * ] squares the number.
That and the use of LST X reduces the number of steps to 19 and only uses one register, R0.

Code:

STEP    CODE    KEY
01    44, 0     STO 0
02    36    ENTER
03    40    +
04    3    3
05    5    5
06    5    5
07    36    ENTER
08    1    1
09    1    1
10    3    3
11    10    ÷
12    20    *
13    31    R/S
14    43, 36    LST X
15    45, 0     RCL 0
16    36    ENTER
17    20    *
18    20    *
19    43, 33, 00    GTO 00

Fun fact: A circle of radius 2 will have the same circumference and area, approximately 12.56637.

HP 12C: Sphere – Surface Area and Volume

This program calculates the surface area and volume of a sphere give the radius r. Again we take 355/113 as an approximation for π. The well-known formulas:

S = 4*π*r^2
V = 4/3*π*r^3 = S * r/3

Code:

STEP    CODE    KEY
01    44, 0    STO 0
02    2    2
03    21    Y^X
04    4    4
05    20    *
06    3    3
07    5    5
08    5    5
09    36    ENTER
10    1    1
11    1    1
12    3    3
13    10    ÷
14    20    *
15    31    R/S
16    3    3
17    10    ÷
18    45, 0    RCL 0
19    20    *
20    43, 33, 00    GTO 00

Registers used:
R0 = r

Input:
Enter radius, r, and press [R/S].

Output:
Obtain the approximate surface area. Press [R/S] for the volume.

Examples:
Radius = 2. Surface area ≈ 50.27, Volume ≈ 33.51

Radius = 8.64. Surface area ≈ 938.07, Volume ≈ 2701.65

Fun fact: A sphere of radius 3 will have the same surface area and volume, at approximately 113.09734.

HP 12C: Right Triangles – Area, Hypotenuse, and Grade given Rise and Run

Let y be the rise (height) and x be the run (length) of a right triangle. Then:

Area = 1/2 * x * y
Hypotenuse = √(x^2 + y^2)
Grade = y/x * 100% (like slope)

Code:

STEP    CODE    KEY
01    44, 1    STO 1
02    34    X<>Y
03    44, 0    STO 0
04    20    *
05    2    2
06    10    ÷
07    31    R/S
08    45, 1    RCL 1
09    2    2
10    21    Y^X
11    45, 0    RCL 0
12    2    2
13    21    Y^X
14    40    +
15    43, 21    √
16    31    R/S
17    45, 0    RCL 0
18    45, 1    RCL 1
19    10    ÷
20    1    1
21    26    EEX
22    2    2
23    20    *
24    43, 33, 00    GTO 00

Registers Used:
R0 = rise (y), R1 = run (x)

Input: rise [ENTER] run [R/S], height [ENTER] length [R/S]

Output: area of a triangle [R/S], hypotenuse [R/S], grade

Example: rise = 430, run = 1600
Input: 430 [ENTER] 1600 [R/S]
Results: Area: 344000, Hypotenuse: 1656.77, Grade: 26.88 (%)