Sunday, October 2, 2016

HP 12C Programming: Circles, Spheres, and Right Triangle

HP 12C Programming:  Circles, Spheres, and Right Triangle

Links to other HP 12C Programs:

HP 12C Programming Part I:  Modulus, GCD, PITI:

HP 12C Programming Part II:  Weekday Number, Gross Up Calculation:

HP 12C Programming III: Refinancing, Advance Payments in a Lease, NPV, NFV, NUS

HP 12C:  Combination/Binomial Distribution/Negative Binomial Distribution

If you want on to calculate the date of Easter and you have the expanded HP 12C Platinum Edition:

HP 12C Platinum:  Finding the Day of Easter

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.

 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.

 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

 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)

 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 (%)

I hope you find this helpful.  Can you believe it is already October?  How fast time flies,

Eddie

This blog is property of Edward Shore, 2016.

1 comment:

1. I must say it's a very nice work. The trick you covered is very useful. Generally, I use calculator and converter for the fastest result; but Your trick is simply easy to use. Thank you for sharing.

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