TI-55 III Programs Part I: Digital Root, Complex Number Multiplication, Escape
Velocity
This blog begins a three part series of programs with the TI-55 III. Let's show what this calculator can do.
For Part III: Area and Eccentricity of Ellipses, Determinant and Inverse of 2x2 Matrices, Speed of Sound/Principal Frequency
TI-55 III: Digital Root
Takes the digital root of an integer. To find the digital root:
1. Add up the number’s
digits.
2. The sum is over
10, add the digits again.
3. Repeat step 2
until you get a single digit.
Or alternatively, use the formula dr(n) = 1 + ((n-1) mod 9)
= n – 9 * integer((n-1)/9)
Program:
Partitions Allowed: 1-5, 1 register required
STEP
|
CODE
|
KEY
|
COMMENT
|
00
|
61
|
STO
|
Enter integer
|
01
|
00
|
0
|
|
02
|
75
|
-
|
|
03
|
09
|
9
|
|
04
|
65
|
*
|
|
05
|
53
|
(
|
|
06
|
53
|
(
|
|
07
|
71
|
RCL
|
|
08
|
00
|
0
|
|
09
|
75
|
-
|
|
10
|
01
|
1
|
|
11
|
54
|
)
|
|
12
|
55
|
÷
|
|
13
|
09
|
9
|
|
14
|
54
|
)
|
|
15
|
88
|
Intg
|
|
16
|
95
|
=
|
|
17
|
12
|
R/S
|
Display digital
root
|
Input: integer [RST]
[R/S]
Result: digital root
Test 1: Input: 1555,
Result: 7
Test 2: Input: 38267,
Result: 8
TI-55 III: Complex Number Multiplication
(a + bi)*(c + di) = (r1*r2) * e^(i*(θ1 + θ2))
Where r1 ∠ θ1 is the polar form of a + bi
and r2 ∠
θ2 is the polar form of c + di.
Program:
Partitions Allowed:
2-4, 2 memory registers are required
STEP
|
CODE
|
KEY
|
COMMENT
|
00
|
52
|
X<>Y
|
Start with a
|
01
|
12
|
R/S
|
Prompt for b
|
02
|
41
|
INV
|
|
03
|
57
|
P-R
|
Convert to Polar
|
04
|
61
|
STO
|
|
05
|
01
|
1
|
|
06
|
52
|
X<>Y
|
|
07
|
61
|
STO
|
|
08
|
00
|
0
|
|
09
|
12
|
R/S
|
Prompt for c
|
10
|
52
|
X<>Y
|
|
11
|
12
|
R/S
|
Prompt for d
|
12
|
41
|
INV
|
|
13
|
57
|
P-R
|
Convert to Polar
|
14
|
61
|
STO
|
|
15
|
85
|
+
|
|
16
|
01
|
1
|
STO+ 1
|
17
|
52
|
X<>Y
|
|
18
|
61
|
STO
|
|
19
|
65
|
*
|
|
20
|
00
|
0
|
STO* 0
|
21
|
71
|
RCL
|
|
22
|
00
|
0
|
|
23
|
52
|
X<>Y
|
|
24
|
71
|
RCL
|
|
25
|
01
|
1
|
|
26
|
57
|
P-R
|
Convert to
Rectangular
|
27
|
12
|
R/S
|
Display imaginary
part
|
28
|
52
|
X<>Y
|
|
29
|
12
|
R/S
|
Display real part
|
Input: a [RST] [R/S],
b [R/S], c [R/S], d [R/S]
Result: imaginary
part of the product [R/S], real part of the product
Test 1: (5 – 3i)*(4 +
i)
Input: 5 [RST] [R/S], 3 [+/-] [R/S], 4 [R/S], 1 [R/S]
Result: -7 [R/S] 23
(23 – 7i)
Test 2: (-6 + 3i)*(2 + 2i)
Result: -18 – 6i
TI-55 III: Escape
Velocity
v = √(2*G*m/r)
v = escape velocity (m/s)
G = University Gravitational Constant = 6.67384 * 10^-11
m^3/(kg*s^2)
m = mass of the planet (kg)
r = radius of the planet (m)
Note that 2*G = 1.334768 * 10^-10 m^3/(kg*s^2)
Program:
Allowed Partitions: 1-5
STEP
|
CODE
|
KEY
|
COMMENT
|
00
|
47
|
Eng
|
Set Engineering
Mode
|
01
|
65
|
*
|
Start with mass
|
02
|
01
|
1
|
|
03
|
93
|
.
|
Decimal Point
|
04
|
03
|
3
|
|
05
|
03
|
3
|
|
06
|
04
|
4
|
|
07
|
07
|
7
|
|
08
|
06
|
6
|
|
09
|
08
|
8
|
|
10
|
42
|
EE
|
|
11
|
01
|
1
|
|
12
|
00
|
0
|
|
13
|
94
|
+/-
|
|
14
|
55
|
÷
|
|
15
|
12
|
R/S
|
Prompt for radius
|
16
|
95
|
=
|
|
17
|
13
|
√
|
|
18
|
12
|
R/S
|
Display escape
velocity
|
Input: mass (in kg)
[RST] [R/S] radius (in m) [R/S]
Result: escape velocity (m/s)
Test 1:
Earth: m = 5.97219 *
10^24 kg, r = 6.378 * 10^6 m
Input: 5.97219 [EE]
24 [RST] [R/S] 6.378 [EE] 6 [R/S]
Result: ≈ 11.179E3
(11,179 m/s)
Test 2:
Jupiter: m = 1.89796
* 10^27 kg, r = 71.492 * 10^6 m
Result: ≈
59.528E3 (52,528 m/s)
Eddie
This blog is property of Edward Shore, 2016