(12C) Circles, Spheres, and Right Triangle
10-03-2016, 01:03 AM
Post: #1
 Eddie W. Shore Senior Member Posts: 733 Joined: Dec 2013
(12C) Circles, Spheres, and Right Triangle
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 (%)
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