HP 12C Programming: Circles, Spheres, and Right Triangle
Links to other HP 12C
Programs:
HP 12C Programming Part I: Modulus, GCD, PITI: http://edspi31415.blogspot.com/2016/07/hp12cprogrammingpartimodulusgcd.html
HP 12C Programming Part II:
Weekday Number, Gross Up Calculation:
http://edspi31415.blogspot.com/2016/07/hp12cprogrammingpartiiweekday.html
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 HP12C 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 wellknown 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.
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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