The Spiral of Theodorus on the TI-83/84 Calculator

The program SPIRALT draws the spiral of Theodorus made from 19 right triangles that have one vertex in the center of the spiral.
We first explain the program code which is to be entered into the TI-83/84 calculator, and then we show some calculator screen dumps of the spiral.

PROGRAM:SPIRALT

:PlotsOff
:AxesOff
:Func
:Degree
:ClrDraw
:-5→Xmin
:-5→Xmax
:-3.67→Ymin
:-3→Ymax

:cumSum(seq(tan^-1(√(N^-1),N,1,19) →LA

:seq(√(M),M,2,2,20) →LR

:LR*cos(LA)→L1
:LR*sin(LA)→L2
:Line(0,0,1,0)
:Line(1,0,1,1)
:Line(0,0,1,1)

:Pause
:For(T,2,19)
:Line(L1(T-1),L2(T-1),L1(T),L2(T))
:Line(0,0,L1(T),L2(T))

:Pause
:End

The setting of the program are taken from:
2NDSTATPLOT 4
2ND FORMAT
MODE FUNC
MODE DEGREE
2ND DRAW 1
VARS 1:Window

List LA is created. It holds nineteen angles,
a1, a1+a2,..., a1+a2+...+a19, where aN = arctan(1/N).
List LR is created. It holds 19 radii, from the 2nd to the 20th,
which are hypotenuses of the triangles, and where the
length of rM = √(M).
L1 holds the x-coordinates of the points on the spiral
and L2 holds their y-coordinates.
The first triangle is drawn. Its vertices are:
(0, 0), which is the center of the spiral,
(1, 0), the first point on the spiral,
and (1, 1) = (L1(1), L2(1)), the second point
on the spiral.
You see the first picture
The next three statements are repeated 18 times.
One point (L1(T), L2(T) is added to the spiral.
It is connected to the previous point on the spiral,
(L1(T-1),L2(T-1), and to the center (0, 0). So a
new triangle is formed.
You see next picture
After showing the last picture, the program stops. Now you
may return to the home screen by pressing CLEAR.