[6.24] Fast Fibonacci Numbers; [6.25] Polar And Rectangular Coordinate Conversions - Texas Instruments TI-89 Tip List

TIcalc site: http://www.ticalc.org/pub/92/basic/math/
! Solve n equations in n unknowns using Gauss-Jordan elimination: srref.zip

[6.24] Fast Fibonacci Numbers

The Fibonacci numbers are defined by this recurrence relation:
F = 1,
1
This formula can be used to find the nth Fibonacci number:
1+ 5
F n = 1
5
However, the 89/92+ cannot use this formula for large n, because the CAS cannot simplify the result.
Finding the numbers with a TI Basic program in recursion is quite slow, and limits n to about 255.
However, this function can find Fibonacci numbers for large n:
Define fib(n)=([[1,1][1,0]]^(n-1))[1,1]
(Credit to Alex Astashyn)

[6.25] Polar and rectangular coordinate conversions

The 89/92+ provide a variety of methods to convert point or vector coordinates between polar and
rectangular formats.
You can use the Vector Format setting in the Mode menu to perform conversions automatically from
the command line. If the Vector Format is set to RECTANGULAR, then coordinates entered in polar
format are converted to rectangular coordinates when the vector is entered. For example, if the mode
is RECTANGULAR and
Vector Format is set to CYLINDRICAL or SPHERICAL and [1,1] in rectangular coordinates is entered,
[√(2),∠Œ/4]
then
You can also use the conversion functions
[1,1]▶Polar
example,
▶Polar ▶Rect
that and
vector: they do not really convert the vectors.
Finally, these functions can be used to return just one part of a converted vector:
These functions can be used to write user functions which, unlike
convert the input vector. These functions are:
polar(v)
F = 1, F
2 n+2
n n
1− 5
−
2 2
[√(2),∠Œ/4]
in polar coordinates is entered, then [1,1] is returned. If the
is returned.
[√(2),∠Œ/4],
returns
are called "display-format" instructions. They only affect the display of the
P▶Rx(r,θ)
Return x-coordinate of polar vector argument
P▶Ry(r,θ)
Return y-coordinate of polar vector argument
R▶Pr(x,y)
Return magnitude r of rectangular vector argument
R▶Pθ(x,y)
Return angle
= F + F
n n+1
▶Polar ▶Rect
and to convert vector coordinates. For
[√(2),∠Œ/4]▶Rect
and
✕
of rectangular vector argument
returns [1,1]. However, note
▶Polar ▶Rect
and , do actually
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