Wednesday, July 6, 2016

TI-55 III Programs Part I: Digital Root, Complex Number Multiplication, Escape Velocity

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.



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



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