Comments concerning Other Calculators
Menu:
Comments on the Sharp - 9600
Comments on the TI89
Comments on the TI85
Comments on the TI82
Comments on Java Programs
Back to TI83 Calculator Programs, Part 1
Back to TI83 Calculator Programs, Part 2
Back to TI83 Calculator Programs, Part 3
Back to TI83 Calculator Programs, Part 4
Back to TI83 Calculator Programs, Part 5
Comments on the Sharp EL - 9600
Programs by Riffat Aziz
SIMPITER
y1 => x
Print x
BISECT
B => x
y1 => D
(A+B)/2 => x
y1 => Q
Print A
Print B
Print x
Print Q
If D*Q > 0 Go to THEN
x => A
End
Label THEN
x => B
End
SECANT
A => x
y1 => C
B => x
y1 => D
If D - C != 0 Go to THEN.......(Note: != means not equal. Use appropriate key.)
B => A
x => B
Print B
End
Label THEN
B - D * (B-A) / (D-C) => x
B => A
x => B
Print B
End
FALSE POSITION
A => x
y1 => C
B => x
y1 => D
B - ( D * (B-A) / (D-C) ) => x
y1 => Q
Print A
Print B
Print x
Print Q
If D * Q > 0 Go to THEN
x => A
End
Label THEN
x => B
End
STEFFENS
x => A
y1 => B
y1(B) => C
If C - 2 B + A != 0 Go to THEN.......(Note: != means not equal. Use
End........................................................appropriate key.)
Label THEN
x - ( ( B - A )2 / ( C - 2 B + A ) ) => x
Print A
Print B
Print C
Print x
End
AITKEN
x => A
y1 => B
y1(B) => C
If C - 2 B + A != 0 Go to THEN.......(Note: != means not equal. Use
End........................................................appropriate key.)
Label THEN
x - ( ( B - A )2 / ( C - 2 B + A ) ) => Z
B => x
Print A
Print Z
End
Back to Menu
--------------------------------------------
Comments on the TI-89
Comments by Lulzim Hoxha
Comments by Wai Ming Chan
Comments by Weston Hunter
Comments by Sukru Kilic
Preview of Programming Using the TI-89, by Lulzim Hoxha
1. Start a new program on the program editor: [APPS] , then [7] , then [3] , then type the NAME of the program.
Press [ENTER].
You will see the Display of "Template". The program NAME , PRGM , and EndPrgm are shown automatically.
2. To type "If" or "If ... Then" or any loop, press [F2] . The DISP command that is found under F3 displays the result on the program I/O Screen... . (So to display x you have to press [F3] , then [2] , then [x] .)
3. Very important!!!! If you want to type the variable y1 , or y2 , or ... yn in the program, you have to type y1(x) , y2(x) ... yn(x) . So to define y1 = x-2 you have to type y1(x) = x-2 .
4. Very important!!!! It is always good when you are writing a program to use parentheses in an efficient way. The same thing happens here. If you want to divide or multiply do not try to "save" parentheses. It is better to write ( x-4 ) / ( y1(x) - y2(x) ) than x-4/y1(x)-y2(x).
5. Very important . I was getting a lot of errors because instead of writing x*(y1(x) + 4 ) I was writing x (y1(x) + 4 ) . So, do not forget the (*).
6. To Run a Program:
First, go to the Homescreen and type the name of the program.
Second, do not forget ... you must always type a set of parentheses after the name.
Third, press [ENTER]. The output will be displayed on a different screen, which is the I/O screen.
To execute the program for the second time...
First press [F5]. (This will return you back to Homescreen.)
Second, press [ENTER].
Keep in mind, if you have written your program in such a way that it requires arguments, you have to include the arguments inside the set of parentheses. Most of the other commands are the same as for the TI-82, 83, 85, (such as copying, updating, and changing lines, saving...) .
Back to Menu
--------------------------------------------
Programs by Wai Ming Chan
Simple Iteration
:simpiter( )
:Prgm
:y1(x) -> x
:Disp x
:EndPrgm
Bisection Method
:bisect( )
:Prgm
:b -> x
:y1(x) -> d
:(a+b) / 2 -> x
:y1(x) -> q
:Disp a,b,x,q
:If d*q > 0 Then
:x -> b
:Else
:x -> a
:End If
:EndPrgm
Secant Method
:secant( )
:Prgm
:a -> x
:y1(x) -> c
:b -> x
:y1(x) -> d
:If d-c != 0...............(Note: we are using != to mean "not equal". You should use
:b-d*(b-a) / (d-c) -> x..........the more common symbol from the calculator menu.)
:b -> a
:x -> b
:Disp b
:EndPrgm
False Position Method
:falsepos( )
:Prgm
:a -> x
:y1(x) -> c
:b -> x
:y1(x) -> d
:b-d*(b-a) / (d-c) -> x
:y1(x) -> q
:Disp a,b,x,q
:If d*q > 0 Then
:x -> b
:Else
:x -> a
:EndIf
:EndPrgm
Steffensen's Method
:steffen( )
:Prgm
:x -> a
:y1(x) -> b
:y1(b) -> c
:If c-2*b+a != 0....................(Note: we are using != to mean "not equal". You
:x - (b-a)^2 / (c-2*b+a) -> x..................should use.the more common symbol
:Disp a,b,c,x............................................from the calculator menu.)
:EndPrgm
Aitken's Method
aitken( ):
:Prgm
:x -> a
:y1(x) -> b
:y1(b) -> c
:If c-2*b+a != 0.............(Note: we are using != to mean "not equal". You should use
:x - (b-a)^2 / (c-2*b+a) -> z.......the more common symbol from the calculator menu.)
:b -> x
:Disp a,z
:EndPrgm
Neville's Method
:neville( )
:Prgm
:dim ( bb[1] ) -> n
:Fill 0 , aa
:For i , 1 , n
:( bb[1] )[i] -> aa[ i , n+2 ]
:x - ( bb[1] )[i] -> aa[ i , n+1 ]
:( bb[2] )[i] -> aa[ i , 1 ]
:EndFor
:For j , 2 , n
:For i , j , n
:( aa[ i-1 , j-1 ] * aa[ i , n+1 ] - aa[ i , j-1 ] * aa[ i-j+1 , n+1 ] ) /
( aa[ i , n+1 ] - aa[ i-j+1 , n+1 ] ) -> aa[ i , j ]
:EndFor
:EndFor
:Disp aa
:EndPrgm
Notes Concerning the Neville Program:
1. "aa" is a matrix table. aa[i,j] refers to the element in row i and column j . "bb" is a data table. ( bb[1] )[i] refers to the ith element in the first column. The "1" refers to the first column in the data table.
2. The variable names a,b cannot be used in this program because they were reserved from previous programs, and they have different properties (integers).
3. Before executing the program, you have to set the dimension of aa beforehand. If it isn't set, or set incorrectly, it will give you a dimension error message.
Creating/Opening a Data Table
1. Press the [APPS] key.
2. Press "6:Data/Matrix Editor".
3. Press "3:New" (or "2:open" if one already exists).
4. The "Type" field remains as "Data". Go down to the "variable" field and type in "bb" .
5. A table appears with the word "DATA" in the upper left hand corner. This confirms that this is a data table.
6. Enter the x-values into the "c1" column.
7. If the f(x) values are given for the corresponding x-values, enter them into the "c2" column. If the function f(x) is given instead, go to the cell "c2", and enter the function into the cell. Remember to change the "x" in the function to "c1". For example, if f(x) = e(x/2), you should enter c2 = e^( c1 / 2 ) .
Creating/Opening a Matrix Table
1. Press the [APPS] key.
2. Press 6: Data /Matrix Editor.
3. Press 3: New (or 2: Open if one already exists).
4. The "Type" field should be changed from "Data" to "Matrix". Go down to the "Variable" field and type in "aa" . You can enter the row and column dimensions here, or you can change it later.
5. A table appears with the word " MAT " in the upper left hand corner. This confirms that this is a matrix table.
6. Next, you need to resize the matrix so the program can execute properly. To resize the matrix, Press F6 ( [2nd] + [F1] ), then press "6: Resize Matrix".
7. Then enter the correct row and column dimensions. If the data table has n values, then the matrix should have dimension n by (n+2). For example, if "bb" has 3 x-values, then you should resize the matrix into 3 rows and 5 columns.
8. Back in the matrix, you will see "3 x 5" in the upper left hand corner.
9. With the data and matrix tables set, you are ready to execute the program.
Back to Menu
--------------------------------------------
Programs by Weston Hunter
DEEULER (Euler's Method)
deeuler(y,a,b,n)
Prgm
Local h
Local t
Local w
Local i
(b-a)/n -> h
a -> t
y -> w
newMat ( n+1 , 2 ) -> dat
t -> dat [ 1 , 1 ]
w -> dat [ 1 , 2 ]
For i , 1 , n
(c) Disp i . . . . . . . . . . . . . . . . (We use the symbol (c) to represent the
w + h * f ( t , w ) -> w . . . . . . Comment Command, located in the
a + i * h -> w . . . . . . . . . . . . . Program Editor / Control Menu )
t -> dat [ i + 1 , 1 ]
w -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
DETAYLR2 (Taylor Method, Order 2)
detaylr2(y,a,b,n)
Prgm
Local h
Local t
Local w
Local i
(b-a)/n -> h
a -> t
y -> w
newMat ( n+1 , 2 ) -> dat
t -> dat [ 1 , 1 ]
w -> dat [ 1 , 2 ]
For i , 1 , n
(c) Disp i . . . . . . . . . . . . . . . . . . . . (We use the symbol (c) to represent the
w + h * tf2 ( t , w , h ) -> w . . . . . . Comment Command, located in the
a + i * h -> t . . . . . . . . . . . . . . . . . Program Editor / Control Menu )
t -> dat [ i + 1 , 1 ]
w -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
The following function is needed in the program detaylr2(y,a,b,n) :
tf2 ( t , y , h )
Func
f ( t , y ) + h / 2 * f_1 ( t , y )
EndFunc
DETAYLR4 (Taylor Method, Order 4)
detaylr4(y,a,b,n)
Prgm
(c) ClrIO . . . . . . . . . . . . . . . . (We use the symbol (c) to represent the
. . . . . . . . . . . . . . . . . . . . . . . Comment Command, located in the
Local h . . . . . . . . . . . . . . . . . Program Editor / Control Menu )
Local t
Local w
Local i
Local q
(b-a)/n -> h
a -> t
y -> w
newMat ( n+1 , 2 ) -> dat
t -> dat [ 1 , 1 ]
w -> dat [ 1 , 2 ]
For i , 1 , n
tf4 ( t , w , h ) -> q
(c) Disp t . . . . . . . . . . . . . . . . . . . . (We use the symbol (c) to represent the
w + h * q -> w . . . . . . . . . . . . . . . Comment Command, located in the
a + i * h -> t . . . . . . . . . . . . . . . . . Program Editor / Control Menu )
t -> dat [ i + 1 , 1 ]
w -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
The following function is needed in the program detaylr4(y,a,b,n) :
tf4 ( t , y , h )
Func
f ( t , y ) + h / 2 * f_1 ( t , y ) + h^2 / 6 * f_2 ( t , y ) + h^3 / 24 * f_3 ( t , y )
EndFunc
DEMIDPT ( DE Midpoint Method)
demidpt ( y , a , b , n )
Prgm
Local h
Local t
Local w
Local i
Local k
(b-a)/n -> h
a -> t
y -> w
newMat ( n+1 , 2 ) -> dat
t -> dat [ 1 , 1 ]
w -> dat [ 1 , 2 ]
For i , 1 , n
h / 2 * f ( t , w ) -> k
w + h * f ( t + h / 2 , w + k ) -> w
a + i * h -> t
t -> dat [ i + 1 , 1 ]
w -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
DEMODEUL ( DE Modified Euler Method)
demodeul ( y , a , b , n )
Prgm
Local h
Local t
Local w
Local i
Local k1
Local k2
(b-a)/n -> h
a -> t
y -> w
newMat ( n+1 , 2 ) -> dat
t -> dat [ 1 , 1 ]
w -> dat [ 1 , 2 ]
For i , 1 , n
h * f ( t , w ) -> k1
f ( t + h , w + k1 ) -> k2
w + h / 2 * ( f ( t , w ) + k2 ) -> w
a + i * h -> t
t -> dat [ i + 1 , 1 ]
w -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
DEHEUN ( DE Heun's Method)
deheun ( y , a , b , n )
Prgm
Local h
Local t
Local w
Local i
Local k1
Local k2
(b-a)/n -> h
a -> t
y -> w
newMat ( n+1 , 2 ) -> dat
t -> dat [ 1 , 1 ]
w -> dat [ 1 , 2 ]
For i , 1 , n
2 / 3 * h * f ( t , w ) -> k1
3 * f ( t + 2 / 3 * h , w + k1 ) -> k2
w + h / 4 * ( f ( t , w ) + k2 ) -> w
a + i * h -> t
t -> dat [ i + 1 , 1 ]
w -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
DERK4 ( DE Runge Kutta 4th Order Method)
derk4 ( y , a , b , n )
Prgm
Local h
Local t
Local w
Local i
Local k1
Local k2
Local k3
Local k4
(b-a)/n -> h
a -> t
y -> w
newMat ( n+1 , 2 ) -> dat
t -> dat [ 1 , 1 ]
w -> dat [ 1 , 2 ]
For i , 1 , n
h * f ( t , w ) -> k1
h * f ( t + h / 2 , w + 1 / 2 * k1 ) -> k2
h * f ( t + h / 2 , w + 1 / 2 * k2 ) -> k3
h * f ( t + h , w + k3 ) -> k4
w + 1 / 6 * ( k1 + 2 * k2 + 2 * k3 + k4 ) -> w
a + i * h -> t
t -> dat [ i + 1 , 1 ]
w -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
DEBASH2 ( Adams Bashforth 2 Step)
debash2 ( a , b , n )
Prgm
(c) ClrIO . . . . . . . . . . . . . . . . (We use the symbol (c) to represent the
. . . . . . . . . . . . . . . . . . . . . . . Comment Command, located in the
Local h . . . . . . . . . . . . . . . . . Program Editor / Control Menu )
Local t
Local t_1
Local w
Local w_1
Local i
Local rows
rowDim ( src ) -> rows
(b-a)/n -> h
newMat ( n+1 , 2 ) -> dat
For i , 1 , rows
src [ i ] -> dat [ i ]
EndFor
For i , rows , n
a + ( i - 1 ) * h -> t
t - h -> t_1
dat [ i , 2 ] -> w
dat [ i - 1 , 2 ] -> w_1
t + h -> dat [ i + 1 , 1 ]
w + h / 2 * ( 3 * f ( t , w ) - f ( t_1 , w_1 ) ) -> dat [ i + 1 , 2 ]
EndFor
EndPrgm
Back to Menu
--------------------------------------------
Programs by Sukru Kilic
More information can be found on the website of Sukru Kilic. In particular, there are images of the home screen and the input-output screen, which will appear when the program is executed. The web site can be found at:
http://sukru.com/ti89
Runge Kutta Order-4 Program for the TI-89 Calculator
The program steps are as follows:
rk4( )
Prgm
ClrIO
Dialog
Title "Runge Kutta Order-4"
Request "y'=f(t,y)=",t1
Request "a=",t2
Request "b=",t3
Request "N=",t4
Request "y(a)=a=",t5
EndDlog
expr(t1&" » f(t,y)") ....(Note: we use » to mean
expr(t2) » a .............."Store".)
expr(t3) » b
expr(t4) » n
expr(t5) » w
(b-a)/n » h
a » ti
For i,1,n
h*f(ti,w) » k1
h*f(ti+h/2,w+k1/2) » k2
h*f(ti+h/2,w+k2/2) » k3
h*f(ti+h,w+k3) » k4
w+(k1+2*k2+2*k3+k4)/6 » w
a+i*h » ti
string(w)&" » w"&shift(shift(format(i,"f0")),1) » t9
expr(t9)
Disp "w"&left(shift(shift(format(i,"f0")),1),2)&" = "&string(w)
If mod(i,6)=0 Then
Pause
ClrIO
EndIf
EndFor
EndPrgm
How to use the program
On the home screen type rk4( ) and press ENTER.
A dialog box will appear with input boxes. Fill in all the input variables. Note: By default, the dialog starts in alpha mode; press alpha to disable it. Also make sure you use * sign between variables and numbers explicitly.
i.e te^(3t)-2y becomes t*e^(3*t)-2*y
After Clicking Enter on the previous screen, the program will start calculating wi's. Once the screen gets filled, it will pause and wait for you to press ENTER for further calculations. This will go on until you reach wN.
Once you reach wN, the program will stop. At this point, press the HOME key to go back to home screen.
After you press HOME key to go back to home screen, you will see Done, which means the program finished executing.
After the program finishes, it creates variables w1 to wN with Runge Kutta Order-4 computed values. You can always type the variable name and press enter to see its value. i.e. type "w3" on home screen and press enter.
Back to Menu
--------------------------------------------
Comments on the TI-85
Comments by Gregory Hinckson
Comments by Amandeep Kaur
Programs by Gregory Hinckson
STEFFENS (Steffensen's Method)
x ---> A
y1 ---> B
B ---> x
y1 ---> C
If C - 2 B + A != 0 . . . . . (See note below.)
A - ( B - A )2 / ( C - 2 B + A ) ---> x
Disp A, B, C, x
Note: We are using != to mean "not equal". You should use
the more common symbol from the calculator menu.
NEVILLE (Neville's Method)
Instruction#1_____dimL L1 -> N..................(Note: We use the symbol "->" to
Instruction#2_____{N,N+2} -> dim A.......represent the operation "Store".)
Instruction#3_____Fill( 0 , A )
Instruction#4_____For (I,1,N)
Instruction#5_____L1(I) -> A(I,N+2)
Instruction#6_____x-L1(I) -> A(I,N+1)
Instruction#7_____L2(I) -> A(I,1)
Instruction#8_____End
Instruction#9_____For (J,2,N)
Instruction#10____For (I,J,N)
Instruction#11____( A(I-1,J-1)*A(I,N+1) - A(I,J-1)*A(I-J+1,N+1) ) /
________________( A(I,N+1) - A(I-J+1,N+1) ) -> A(I,J)
Instruction#12____End
Instruction#13____End
Instruction#14____A
NEWTDIV (Newton's Divided Difference Method)
Instruction#1_____dimL L1 -> N..................(Note: We use the symbol "->" to
Instruction#2_____{N,N+2} -> dim A.......represent the operation "Store".)
Instruction#3_____Fill( 0, A )
Instruction#4_____For(I,1,N)
Instruction#5_____L1(I) -> A(I,N+1)
Instruction#6_____L2(I) -> A(I,1)
Instruction#7_____End
Instruction#8_____For(J,2,N)
Instruction#9_____For(I,J,N)
Instruction#10____( A(I,J-1) - A(I-1,J-1) ) / ( L1(I) - L1(I-J+1) ) -> A(I,J)
Instruction#11____End
Instruction#12____End
Instruction#13____A(N,N) -> S
Instruction#14____For(I,2,N)
Instruction#15____N-I+1 -> K
Instruction#16____S * ( x - L1(K) ) + A(K,K) -> S
Instruction#17____End
Instruction#18____S -> A(1,N+2)
Instruction#19____A
NEWFORDF (Newton's Forward Difference Method)
Instruction#1_____dimL L1 -> N....................(Note: We use the symbol "->" to
Instruction#2_____{N,N+2} -> dim A........represent the operation "Store".)
Instruction#3_____Fill( 0, A )
Instruction#4_____For(I,1,N)
Instruction#5_____L1(I) -> A(I,N+1)
Instruction#6_____L2(I) -> A(I,1)
Instruction#7_____End
Instruction#8_____For(J,2,N)
Instruction#9_____For(I,J,N)
Instruction#10____( A(I,J-1) - A(I-1,J-1) ) -> A(I,J)
Instruction#11____End
Instruction#12____End
Instruction#13____L1(2) - L1(1) -> H
Instruction#14____( x - L1(1) ) / H -> S
Instruction#15____A(N,N) -> T
Instruction#16____For(I,2,N)
Instruction#17____N-I+1 -> K
Instruction#18____T * ( S - K + 1 ) / K + A(K,K) -> T
Instruction#19____End
Instruction#20____T -> A(1,N+2) : S -> A(2,N+2)
Instruction#21____A
Back to Menu
--------------------------------------------
Program by Amandeep Kaur
ICOMTRAP (Composite Trapezoid Rule)
(B-A)/N ---> H
seq ( A + I*H , I , 0 , N , 1 ) ---> L1
L1 ---> x
y1 ---> L2
seq ( (H/2) ( L2(I) + L2(I+1) ) , I , 1 , N , 1 ) ---> L3
sum L3 ---> T
fnInt ( y1 , x , A , B ) ---> S
Disp S,T,S-T
Back to Menu
------------------------------------------------
Comments on the TI-82
Program by Maria Katsaras
Program INTERP3 (3-Point Interpolation).
Instruction#1_____QuadReg L1, L2
Instruction#2_____"aX2 + bX + c" -> Y1
Instruction#3_____Disp a, b, c
Instruction#4_____Y1
Note: a, b, c are Statistics Equation Variables.
Press [VARS] [5] [right arrow] [right arrow] to find these variables.
Back to menu
------------------------------------------------
Comments on Java Programs
Java Programs by Syed Ali
Simple Iteration
The following program will iterate four times using the equation xn = g(xn-1) , where g(x) = ( 3x4 + 2x2 + 3 ) / ( 4x3 + 4x - 1 ). The initial iterate is x0 = p .
{
public static void main( String[] args )
{
double y, y1, y2, p= 1, x;
int counter = 0, n = 4; //No. Of Iteration
try
{
x = p;
System.out.println( "n . . . . g(x)");
System.out.println( "---------------------------------------------------" );
while( counter <= n)
{
y1 = 3*Math.pow( x, 4 ) + ( 2*Math.pow( x, 2 ) ) + 3;
y2 = 4*Math.pow( x, 3 ) + ( 4*Math.pow( x, 1 ) ) -1;
y = y1/y2;
System.out.print( counter +" " );
System.out.println( y);
x = y;
counter++;
}//while
}//try
catch ( Exception tooBad )
{
System.out.println( tooBad.toString() );
}
}
}
//***********OutPut May Look Like This*****************
n . . . . g( x )
--------------------------------------------------------
0 ___1.1428571428571428
1 ___1.1244816900178953
2 ___1.1241231639401488
3 ___1.124123029704334
4 ___1.1241230297043154
********************************************************//
Bisection Method
The following program will use the bisection method to obtain an approximation for the zero of the function f(x) = x3 + 4 x2 - 10 on the interval [ 1 , 2 ] . The number of bisection iterations is 13.
{
public static void main( String[] args )
{
double x, q, d, a=1, b=2, y, f;
int counter = 1, n=13;//No. Of Iteration
System.out.println(
"_______________________________________________________" );
System.out.println( "n . . a . . . . . b . . . . . x . . . . . q" );
System.out.println(
"-----------------------------------------------------------------" );
try
{
while( counter <= n)
{
x = b;
y = Math.pow( x, 3 ) + ( 4*Math.pow( x, 2 ) ) - 10;
d = y;
x =(a+b)/2 ;
y = Math.pow( x, 3 ) + ( 4*Math.pow( x, 2 ) ) - 10;
q = y ;
//System.out.print( counter + " " );
//System.out.println(a+" "+b+" "+x+" "+q);
System.out.print( counter );
System.out.print(a);
System.out.print( b );
System.out.print( x);
System.out.println( q);
f = d*q;
if ( f > 0)
{
b = x;
}
else
a = x;
counter++;
}//while
}//try
catch ( Exception tooBad )
{
System.out.println( tooBad.toString() );
}
}
}
//***********OutPut May Look Like This*****************************
___________________________________________________________
n . . a . . . . . b . . . . . x . . . . . q
---------------------------------------------------------------
1 1.0____________2.0________ 1.5______________2.375
2 1.0____________1.5________ 1.25____________-1.796875
3 1.25___________1.5________ 1.375____________0.162109375
4 1.25___________1.375______ 1.3125__________-0.848388671875
5 1.3125_________1.375______ 1.34375_________-0.350982666015625
6 1.34375________1.375______ 1.359375________-0.09640884399414062
7 1.359375_______1.375______ 1.3671875________0.03235578536987305
8 1.359375_______1.3671875__ 1.36328125______-0.03214997053146362
9 1.36328125_____1.3671875__ 1.365234375______7.202476263046265E-5
10 1.36328125____ 1.365234375 1.3642578125____-0.01604669075459242
11 1.3642578125__ 1.365234375 1.36474609375___-0.007989262812770903
12 1.36474609375_ 1.365234375 1.364990234375 _ -0.003959101522923447
13 1.364990234375 1.365234375 1.3651123046875 -0.0019436590100667672
**************************************************************//
Back to menu
------------------------------------------------