10-03-2016, 01:03 AM
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.
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.
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
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)
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 (%)
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 (%)