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The Multiplication Table
Factored Integers
The Circle
Reflection
Dilation
Translation
Rotation
Complex Numbers
Stirling Numbers
Numbers as Boolean Functions
Tower of Hanoi

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The Texas Instruments TI89 Titanium Graphing Calculator is very useful for checking your answers when doing homework and preparing for your exams.
With the instant feedback provided by the TI89 Scientific Graphing Calculator you can review the accuracy of your answers and keep on finetuning your skills.
Whether you are dealing with fractions, factoring polynomials, reducing algebraic expressions, solving equations, or finding derivatives and integrals, the TI89 Programmable Graphing Calculator automatically gives you the right answer, so you can immediately find out if your answer is right or wrong, even for the evennumbered exercises in your textbook.
The TI89 has a wide variety of graphing capabilities, too.
Because the TI89 calculator is programmable, if you want to practice with a special kind of complex problems, all you have to do is find a program that solves the particular type of problem you are practicing with. Then you can enter that program into the TI89, and use it to verify your results.
Example Program #1
Distance between two points (x1,y1) and (x2,y2) in the coordinate plane.
:dst(a,b,c,d)
:√((ac)^2+(bd)^2)
Example Program #2
Coordinates for the midpoint between points (x1,y1) and (x2,y2) in the coordinate plane.
:mdpt(a,b,c,d)
:Prgm
:ClrIO
:string((a+c)/2)→m
:string((b+d)/2)→n
:"("&m&" , "&n&")"→o
:Disp "Midpoint coordinates are:",o
:Pause "Press Enter to continue"
:DispHome
:EndPrgm
Example Program #3
Slope of the line that passes through the points (x1,y1) and (x2,y2) in the coordinate plane.
:slp(a,b,c,d)
:Prgm
:ClrIO
:If a=c Then
:Disp "Line is vertical or"
:Disp "it is just a point."
:Disp "The slope is undefined"
:Else
: (db)/(ca)→s
: Disp "The slope is:",s
:EndIf
:Pause "Press Enter to continue"
:DispHome
:EndPrgm
Example Program #4
Equation of the line that passes through the points (x1,y1) and (x2,y2) in the coordinate plane.
:lineq(a,b,c,d)
:Prgm
:ClrIO
:string(db)→p
:string(ac)→q
:string(c*ba*d)→r
:p&"x+"&q&"y+"&r&"=0"→s
:Disp "Line equation is:",s
:Pause "Press Enter to continue"
:DispHome
:EndPrgm
Example Program #5
Equation of the mediatrix of the segment given by the points (x1,y1) and (x2,y2) in the coordinate plane.
This is the line perpendicular to the segment and passing through its midpoint.
:mdtx(a,b,c,d)
:Prgm
:ClrIO
:string(ac)→p
:string(bd)→q
:string((c^2+d^2a^2b^2)/2)→r
:p&"x+"&q&"y+"&r&"=0"→s
:Disp "Mediatrix equation is:",s
:Pause "Press Enter to continue"
:DispHome
:EndPrgm
Example Program #6
Equation of the circle with center at (a,b) and passing through the point (c,d) in the coordinate plane.
Note: When keying in lines 8 and 9 of this code into the TI89 calculator, make sure to press the () key at the bottom of the keypad for the negative sign in front of the number 2 in each line.
:cpcrc(a,b,c,d)
:Prgm
:ClrIO
:string(a)→k
:string(b)→l
:string(c)→m
:string(d)→n
:string(2*a)→p
:string(2*b)→q
:string(2*(a*c+b*d)c^2d^2)→r
:"x^2 + y^2 +"&p&"x+"&q&"y+"&r&"=0"→s
:Disp "Equation of the circle"
:Disp "with center ("&k&","&l&") and"
:Disp "passing through ("&m&","&n&")"
:Disp "is:",s
:Pause "Press Enter to continue"
:DispHome
:EndPrgm
Example Program #7
Equation of the circle with diameter given by endpoints (a,b) and (c,d) in the coordinate plane.
Note: When keying in line 8 of this code into the TI89 calculator, make sure to press the () key at the bottom of the keypad for the negative sign in front of "a," then press the regular subtraction key (between the multiplication and addition keys) for the negative sign before "c."
The same goes for the negative signs before "b" and "d" in line 9.
:dmcrc(a,b,c,d)
:Prgm
:ClrIO
:string(a)→k
:string(b)→l
:string(c)→m
:string(d)→n
:string(ac)→p
:string(bd)→q
:string(a*c+b*d)→r
:"x^2 + y^2 +"&p&"x+"&q&"y+"&r&"=0"→s
:Disp "Equation of the circle"
:Disp "with diameter given by"
:Disp "points ("&k&","&l&") and ("&m&","&n&")"
:Disp "is:",s
:Pause "Press Enter to continue"
:DispHome
:EndPrgm
Example Program #8
For adding up any given number of terms with feet, inches and fractions of an inch each, and getting the final sum in the same format.
:smfi()
:Prgm
:ClrIO
:setMode("Pretty Print","On")
:0→i
:0→f
:0→n
:Lbl nwtrm
:n+1→n
:""→a
:""→b
:""→c
:Dialog
:Title "Term number "&string(n)
:Request "Number of feet",a
:Request "Whole inches",b
:Request "Fraction of inch",c
:EndDlog
:If ok=1 Then
:expr(a)→d
:expr(b)→e
:expr(c)→q
:d+f→f
:q+e+i→i
:EndIf
:Dialog
:Title "Another term?"
:Text "OK to enter more values"
:Text "ESC to finish the sum"
:EndDlog
:If ok=1
:Goto nwtrm
:int(i/12)→g
:f+g→h
:ig*12→k
:Disp "Total feet = "&string(h)
:Disp "Whole inches = "&string(int(k))
:Disp "Fraction inch = "&string(kint(k))
:Pause "Press Enter to continue"
:DispHome
:EndPrgm
Question #1
"How would I solve equations using the quadratic formula? Will this calculator perform this?"
Answer:
The TI89 has a builtin instruction called "solve(,)"
For example, you type
solve( x^2  5x + 6 = 0, x )
and then hit the "enter" button, and the calculator will give you the solutions
x = 2; x = 3;
You can enter a program to make the calculator follow the steps of the quadratic formula but you don't have to.
The instruction "solve(,)" already solves equations automatically, it has the quadratic formula built into its procedures and subroutines.
Not only the quadratic formula, but many algebra theorems, and several numerical methods, like Newton's iteration method. All that is already within the instruction "solve(,)"
You can access the instruction "solve(,)" from the "Home" screen by pressing [F2], which activates the "Algebra" menu tab. "solve(,)" is the first option in that menu.
Question #2
"In the equation 2^{x} + 3^{x} = 13 obviously x=2
but how can I let my ti89 titanium show how it have been solved?"
Answer:
My TI89 takes about 23 seconds to come up with the answer.
Meanwhile, it shows a message at the bottom that reads: "Warning: More solutions may exist."
In the TI89 Manual, you will find the following information:
 The instruction solve() can take not only one, but two or more equations as input.
 In general, the instruction returns solution candidates, not necessarily actual solutions.
 The manual talks about different "goals" for different settings of the Exact/Aprox mode.
 Sometimes, iterative searches are employed.
 The solution interval can be restricted using the "" operator.
 Somehow, the results returned by solve() are always considered as Boolean ones.
 In some cases, the instruction returns infinite sets of solutions, represented by the symbol @n placed to the left of an integer between 1 and 255.
All of the above, plus the fact that there are mathematical books entirely devoted to various solution methods for different kinds of equations, make me think the TI89 instruction solve() implements a whole program designed to be as comprehensive as possible, by including several procedures and subroutines.
Now, the original idea behind a calculator is for people to get the numerical results they need without having to perform the calculations themselves.
So, I am not sure about this, I may be wrong but my guess is the TI89 designers did not include any specific way to show the detailed internal work of the device’s instructions, in particular the instruction solve().
To get an aproximate solution for an equation of the form 2^{x} + 3^{x} = n, where n is a positive number, you can start by getting lower and upper bounds for the solution set.
To this end you can separately solve the equations 3^{x} = n (for the lower bound) as well as 2^{x} = n (for the upper bound) by taking the base 3 and base 2 logarithms of n, respectively.
Then you run an iterative binary search by splitting the interval at midpoint and comparing the result of the function there with those given by the end points.
Of course the TI89 will give you the result directly and probably much faster.
Question #3
"How do I store an equation with multiple variables? For example the equation
x^{2} + y = a + b/c
How do I store this equation and then later assign values for a,b,c and y and then solve for x ?"
Answer:
The TI89 has an application called Numeric Solver, with an icon that reads "f(x)=0" in the application menu. This application stores and solves equations. It is ideal for the purpose you mention. You only need to make sure that no variable involved in your equation has a nonnumeric value stored in it before you type the equation inside the Numeric Solver window. Otherwise the application will return a "data type" error message if there is any text, or a matrix, or a list stored under one of your variables.
1)
Go to the Home screen.
2)
Give the numeric values you want to each variable. At this point you can give any incorrect "guess value" to the variable you want to solve for, as long as it is a number.
You do this by using the "Store" key (It reads STO, followed by a little arrowhead pointing to the right). For example, to store the number 5 under variable "a," you key in this sequence:
[5] [Sto > ] [A] [Enter]
3)
Once all variables in your equation have been assigned numeric values, or at least you are sure they do not have any nonnumeric value, then go to the Apps menu, and select the Numeric Solver application. The Numeric Solver's icon reads "f(x)=0"
4)
Enter your equation:
x ^ 2 + y = a + b/c
and press [Enter].
5)
At this point the Numeric Solver shows a list of all the variables, each with its currently assigned value. Then you scroll up or down the list, to whatever variable you want to solve for. The screen highlights the current value of each variable as you scroll up and down.
6)
When you get to the variable you want to solve for, press the Clear key to eliminate the shown value. Then press the F2 key. This key triggers the Solve procedure that calculates the solution for the equation.
7)
Once a value has been found for a variable, you can scroll to any other variables, change their value, select another variable of interest (or go back to the same one), clear its value, and solve again using the F2 key.
This Numeric Solver application is very convenient. However, there is little problem: it only displays one solution within the given interval bounds, even if the equation may have multiple solutions in that interval. To make it show the other solutions, you can change the interval bounds. In this sense it is better to use the Solve(equation,variable) instruction available in the Home screen, because it shows you all the solutions it calculates, not just one per interval. The convenience of the Numeric Solver application lies in the ease of changing variable values, plus the fact that it automatically "remembers" the several last equations you have worked with.
To get all the solutions calculated for a given set of values, you can also copyandpaste the equation from the Numeric Solver application, into the Solve(equation,variable) instruction in the Home screen.
Question #4
"How do I convert units, say miles to yards, for example?"
Answer:
The TI89 has a unit menu. You can access it by pressing [2nd] [3].
The units come ordered by category (length, time, acceleration, and so on).
First you type the number you are going to convert. Then you open the unit menu and select the specific unit that applies to your number. You do this by selecting the right category, and then scrolling down to the desired unit.
Once the calculator displays your number followed by the unit, you press [2nd] [Mode], which inserts the conversion operator.
Then you open the unit menu again and select your target unit.
For example to convert one mile to yards you key in:
1 [2nd]; [3]; [down]; [right]; [down] (10 rows); [Enter]; [2nd]; [Mode]; [2nd]; [3]; [down]; [right]; [up] (3 rows); [Enter]; [Enter]
After this key sequence the calculator will display the number of yards in a mile as:
1760. ·_yd
Question #5
"What I am interested in is being able to add, subtract, multiply and divide, feet, inches and fractions of inches, along with the accounting, statistical and financial applications that are built into these graphing calculators.
I haven’t seen any information on the TI83 or TI84 that shows these features even exist on the TI83 or TI84.
Would the TI89 family or Voyage 200 calculator be a better choice for my requirements and can you give me some examples of how these features work in the TI89?
I'll try to give an example:
I would like to be able to edit and recall this view and previous views as necessary:
1000' 4 1/8" + 1' 0 3/8" + 2500' 2 1/2"  11 11/16" + 2' 4" + 16" = 3505' 2 11/16"
(automatically simplify as necessary)"
Answer:
The example provided in your question involves, in the same expression, both fractions in mixed number format, as well as different measure units (feet and inches).
A)
The TI89 adds, subtracts, multiplies and divides fractions. It automatically simplifies the result and it can present it either as a fraction or as a decimal.
B)
However, I see no apparent way to input mixed number format into the calculations. For example, when trying to input the sum
(1 unit and 1/2) plus (3 units and 3/4),
the sequence of keystrokes
1 [space] 1/2 [space] + [space] 3 [space] 3/4 [enter]
is interpreted by the TI89 as if meaning
1*(1/2) + 3*(3/4)
and it gives
11/4
as a final answer, instead of any expression representing the expected mixed number
5 units and 1/4
Now, if we enter the calculation in the following form
1+1/2+3+3/4 [enter]
then we get the correct answer
21/4
but still, this fraction is not in a mixed number format.
C)
The TI89 has a [units] key, which opens a Units menu.
This menu includes a wide variety of standard physical units for length, time, volume, weight, etc.
From this menu we can select meters, yards, feet or inches to enter after each one of the numbers we are including in the calculation.
But the result is given in terms of only one standard unit, not two. For example
1000_ft + (4+1/8)_in + 1_ft + (3/8)_in [enter]
gives the following result
1001.38_ft
where the end result is given in feet and expressed as a decimal, not as a fraction.
D)
If the Unit System (option from the Mode menu, accessible through the [mode] key) happens to be set to SI (Standard International) instead of the English/US option, then the result from the same calculation above will show as
305.219_m
because the 1001.38 feet are automatically converted to meters.
E)
Here is my suggestion on how to manually work out your feetinchfractionofinch calculations.
You could input them in the following way:
 Enter the feet values as regular integers.
 Enter the inch values enclosed by parenthesis appending a “divided by 12” notation after closing the parenthesis.
 Inside the parenthesis, separate each whole inch value from the fractionofinch value with a “+” sign.
Your specific example:
1000' 4 1/8" + 1' 0 3/8" + 2500' 2 1/2"  11 11/16" + 2' 4" + 16"
would be entered like this:
1000+(4+1/8)/12+1+(3/8)/12+2500+(2+1/2)/12(11+11/16)/12+2+(4+16)/12 [enter]
producing the result
672821 / 192
in fraction form.
Then we key in [diamond] [enter] to get the equivalent result in decimal form
3504.28
(The [diamond] key is located right below the [2nd] key and it activates the yellow option for the keys that have one. In the case of the [enter] key, the effect of the [diamond] key is to show numerical results in decimal form, rather than pretty text form, without any square root symbol nor fraction bar).
So far we know the result includes 3504 feet.
Now we key in [2nd] [ans] – 3504 [enter] to get rid of the integer part and we get
0.274062
which is only an approximation for 0.274061666..., as 0.28 was in the previous step.
Next we do [2nd] [ans] * 12 [enter] to find the equivalent value in terms of inches instead of feet. We get
3.3125
So we have 3 whole inches going into the final result
Then we go [2nd] [ans] – 3 [enter] to get the decimal form of the fractionofinch value
0.3125
Finally we key in 3125/10000 [enter] to get the fraction format
5 / 16
(The TI89 automatically simplifies 3125/10000 into 5/16)
So our final result is:
3504' 3 5/16"
F)
With regards to being able to edit and store those calculations, the history area of the TI89 calculator Home screen displays up to eight entry/answer pairs. These pairs scroll off the top of the screen as new calculations are performed.
If you want to permanently store your calculations and their results, you can move the cursor into the history area, highlight your entries and answers, copy them and then paste them into a session of the Text Editor application. They will stay there unchanged until you edit them or erase the corresponding text editor variable from memory.
G)
The program shown above as Example Program #8 automaticaly performs the necessary calculations.
For each term of the sum, it takes three values as input: feet, inches and fractionofinch values.
It can take as many number of terms as necessary.
The result is simplified and expressed also in terms of feet, inches and fractionofinch values.
Question #6
"How do I do logarithms with varying bases and exponetial functions?"
Answer:
The TI89 has a "ln" function for natural logarithms (in base e). You access it by pressing [2nd] [X].
For example, let's say you want to calculate the logarithm of 65 in base 3.
To get this value you can use natural logarithms, because it equals ln(65) / ln(3)
The result is 3.799691
The sequence is this:
[2nd] [X] 65 [ ) ] [ / ] [2nd] [X] 3 [ ) ] [Diamond] [Enter]
With the TI89 you need to press the [Diamond] key before [Enter] so that it will actually show you the result's numerical value. Otherwise it may only show you a "pretty print" version of the expression you just entered.
Now let's look into entering exponents. The TI89 has a specific key for this purpose.
The [^] key is located right above the division key, to the right of the "T" key. Its alternate functions are the number pi, and the variable theta for angles.
For example, to calculate "3 to the 2.5" you key in:
3 [^] 2.5 [Enter]
and the TI89 outputs the result 15.5885
Question #7
"I am trying to Program my TI89 to solve specific engineering problems.
Good information is hard to find on programing the TI89 in BASIC. I have a little BASIC experience.
All I want to do is have the calculator prompt the user for input, store that input and then plug the stored inputs into an equation.
Then finally output an answer. Do you know of a good source for a novice to get started programing?"
Answer:
Example program # 8 below uses this prompt/input kind of interaction, through the instruction "Dialog." The syntax is as follows:
:Dialog
:Title "Term number "&string(n)
:Request "Number of feet",a
:Request "Whole inches",b
:Request "Fraction of inch",c
:EndDlog
where you can vary the number of "Request" instructions nested inside the "Dialog," as well as the text string displayed by "Title" and each "Request," plus the variables you want to use to store the values given as input by the user.
At the bottom of this page are a few links pointing to good TI89 related web sites.
The TI89 instruction manual itself is of course an indispensable reference, and very useful. I suggest following the examples given in the TI89 instruction manual, and then start experimenting with the different instructions to see what you can do with them.
This approach will probably be more productive than trying to get the TI89 to "understand BASIC."
Question #8
"How would you use the TI89 to find converting binary numbers to Octal or Hexdecimal?
For some reason I'm getting a domain error, when I use 24>Hex. What mode does the calculator have to be in?"
Answer:
The TI89 has a "Base" submenu inside the "Mode" menu. The "Base" submenu has three options: Dec, Hex, and Bin.
The easiest way to convert binary numbers to Hexadecimal is by following these steps:
 Press the "Mode" button
 Scroll down until the "Base" category is highlighted
 Scroll to the right, then down again, and select "Hex"
 Press the "Enter" button twice
 Go to the "Home" screen
 Type, without any spaces, the number 0, the letter b, then a binary number
 Press "Enter"
For example, to convert 28 from binary 11100 to Hexadecimal 1C by following the above steps, first make sure you are in mode Base = Hex, then in the "Home" screen you type 0b11100
When you hit "Enter" the TI89 returns 0h1C, which means 28 in Hexadecimal.
(To type the letter "b" you hit the white "Alpha" key plus the "Left parenthesis" key)
Unfortunately, the "Base" submenu does not have an option for Octal.
You can always convert Binary to Octal by hand, it is a little faster than converting Binary to Hexadecimal.
Working from right to left, that is, starting with the units digit, you break the Binary number in blocks of three digits each, with the possible exception of the last block (in the leftmost position), which can be of length three, two, or one, because it is the leftover from the previous blocks.
Then you translate each block of Binary digits into a single Octal digit (from 0 to 7) just like that, in the same order the blocks appear in the original Binary number. This procedure is illustrated in the following pages:
In some of the following sites you can find more examples of code for TI89 math programs
Elementary number theory with the TI89/92R  Giulio Barozzi
Programs for Graphing Calculators  Calculus Calculator Notes
TI89 Intro  Using the TI89 Calculator
Using the TIGraphing Calculator  Online tutorial, by PrenticeHall
Texas Instruments  TI89 Applications
TI89 Graphing Calculator Operations Manual, by Carolyn Meitler
ti89.com  Comprehensive Math software for TI89/Titanium/Voyage200
TI89 Math and Science Programs
TI89 Graphing Calculator For Dummies Cheat Sheet
TI89 BASIC Math Programs
ticalc.org  TI calculators programming resources
Ray Kremer  TIGraphing Calculator FAQ
Wikipedia: TI89 series
Complete disassembly of a TI89 Titanium calculator
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