TI-55 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
TI-55 III: Area
and Eccentricity of the Ellipse
Formulas:
Assume a>b, where a and b represent the lengths of
semi-diameters, respectively
Area: A = π*a*b
Eccentricity: ϵ =
√(1 – (b/a)^2)
Program:
Partitions Allowed: 1-5
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STEP
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CODE
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KEY
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COMMENT
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00
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71
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RCL
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R0 = a
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01
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00
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0
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02
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65
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*
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03
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71
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RCL
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R1 = b
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04
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01
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1
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05
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65
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*
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06
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91
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π
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07
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95
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=
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08
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12
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R/S
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Display A
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09
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53
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(
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10
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01
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1
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11
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75
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-
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12
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53
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(
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13
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71
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RCL
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14
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01
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1
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15
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55
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÷
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16
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71
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RCL
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17
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00
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0
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18
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54
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)
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19
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18
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X^2
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20
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54
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)
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21
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95
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=
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22
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13
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√
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23
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12
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R/S
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Display ϵ
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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
TI-55 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:
[2nd] [LRN] (Part) 4
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STEP
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CODE
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KEY
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COMMENT
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00
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71
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RCL
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Calculate
determinant
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01
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00
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0
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02
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65
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*
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03
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71
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RCL
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04
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03
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3
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05
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75
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-
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06
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71
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RCL
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07
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02
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2
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08
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75
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*
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09
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71
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RCL
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10
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01
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1
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11
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95
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=
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12
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12
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R/S
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Display
determinant
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13
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61
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STO
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Calculate
inverse
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14
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55
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÷
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15
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00
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0
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16
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61
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STO
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17
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55
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÷
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18
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03
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3
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19
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94
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+/-
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20
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61
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STO
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21
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55
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÷
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22
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01
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1
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23
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61
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STO
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24
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55
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÷
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25
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02
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2
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26
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01
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1
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Display 1 to
indicate “done”
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27
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12
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R/S
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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 ] ]
TI-55 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:
1-5
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STEP
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CODE
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KEY
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COMMENT
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00
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65
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*
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01
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93
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.
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Decimal point
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02
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06
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6
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03
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85
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+
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04
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03
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3
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05
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03
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3
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06
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01
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1
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07
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93
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.
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Decimal point
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08
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04
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4
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09
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95
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=
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10
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12
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R/S
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Display speed of
sound
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11
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55
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÷
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12
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02
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2
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13
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55
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÷
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14
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12
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R/S
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Prompt for L
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15
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95
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=
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16
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12
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R/S
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Display
frequency
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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” 2nd 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.