TI55 III Programs Part III:
Area and Eccentricity of Ellipses, Determinant and Inverse of 2x2
Matrices, Speed of Sound/Principal Frequency
For Part I, click here: Digital Root, Complex Number Multiplication, Escape Velocity
For Part II, click here: Impedance of a Series RLC Circuit, Quadratic Equation, Error Function
TI55 III: Area
and Eccentricity of the Ellipse
Formulas:
Assume a>b, where a and b represent the lengths of
semidiameters, respectively
Area: A = π*a*b
Eccentricity: ϵ =
√(1 – (b/a)^2)
Program:
Partitions Allowed: 15
STEP

CODE

KEY

COMMENT

00

71

RCL

R0 = a

01

00

0


02

65

*


03

71

RCL

R1 = b

04

01

1


05

65

*


06

91

π


07

95

=


08

12

R/S

Display A

09

53

(


10

01

1


11

75




12

53

(


13

71

RCL


14

01

1


15

55

÷


16

71

RCL


17

00

0


18

54

)


19

18

X^2


20

54

)


21

95

=


22

13

√


23

12

R/S

Display ϵ

Input: a [STO] 0,
b [STO] 1, [RST] [R/S]
Result: Area,
[R/S] Eccentricity
Test: a = 7.06, b
= 3.78
Result: A ≈ 83.839055, ϵ ≈ 0.8445918
TI55 III:
Determinant and Inverse of 2 x 2 Matrices
This program will require 4 registers.
Input Matrix: M =
[[ R0, R1 ] [ R2 , R3 ]]
Output Matrix:
M^1 = [[ R3/det, R1/det ] [ R2/det, R0/det ]]
Where det = R0 * R3 – R1 * R2 (determinant).
Program:
Set 4 partitions:
[2^{nd}] [LRN] (Part) 4
STEP

CODE

KEY

COMMENT

00

71

RCL

Calculate
determinant

01

00

0


02

65

*


03

71

RCL


04

03

3


05

75




06

71

RCL


07

02

2


08

75

*


09

71

RCL


10

01

1


11

95

=


12

12

R/S

Display
determinant

13

61

STO

Calculate
inverse

14

55

÷


15

00

0


16

61

STO


17

55

÷


18

03

3


19

94

+/


20

61

STO


21

55

÷


22

01

1


23

61

STO


24

55

÷


25

02

2


26

01

1

Display 1 to
indicate “done”

27

12

R/S


Input: Store:
M(1,1) [STO] 0
M(1,2) [STO] 1
M(2,1) [STO] 2
M(2,2) [STO] 3
Press [R/S] to calculate the determinant of M. If M≠0, continue and press [R/S].
You will see a 1 in the display, this is used as an
indicator that the program is done.
Result Inverse Matrix:
M^1[1,1] stored in R3
M^1[1,2] stored in R1
M^1[2,1] stored in R2
M^1[2,2] stored in R0
Test:
M = [ [ 1.4, 3.0 ], [ 2.8, 6.4 ] ]
Determinant = 17.36
M^1 ≈ [ [
.3686635945, .1728110599 ], [ .1612903226, .0806451613 ] ]
TI55 III: Speed of Sound/Fundamental Resonant Frequency
Formulas:
Speed of Sound (m/s):
v = t*0.6 + 331.4
Where t = temperature (°C)
Fundamental Resonant Frequencies in an Open Pipe: fn = v/(2*L)
Where fn = frequency (Hz), v = speed of sound (m/s), L =
length of pipe (m)
Program:
Partitions allowed:
15
STEP

CODE

KEY

COMMENT

00

65

*


01

93

.

Decimal point

02

06

6


03

85

+


04

03

3


05

03

3


06

01

1


07

93

.

Decimal point

08

04

4


09

95

=


10

12

R/S

Display speed of
sound

11

55

÷


12

02

2


13

55

÷


14

12

R/S

Prompt for L

15

95

=


16

12

R/S

Display
frequency

Speed of Sound in Dry Air:
Input: Enter
temperature in °C [F1]
Result: Speed of
sound (m/s), press [R/S]
Fundamental Resonant Frequencies:
Store the length of the open pipe (m) then press [R/S]
Result:
Fundamental Resonant Frequency (Hz)
Test:
Open pipe of 0.45, where the temperature of the air is
39°C (102.2°F).
Input: 39 [R/S]
Result: 354.8 m/s
(speed of sound), [R/S]
394.22222 Hz (fundamental resonant frequency)
Source: Browne Ph.
D, Michael. “Schaum’s Outlines: Physics for Engineering and Science” 2^{nd} Ed. McGraw Hill: New York, 2010
I hope you are enjoying this series of programs for calculators from the 1980s. The next series, I plan to stay in the 1980s when I work with the 1988 HP 42S.
This blog is property of Edward Shore.
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