TI-84 Plus CE Python: Diophantine Books Problem and Circles Inscribed in Squares
Introduction
The two programs presented today are Python versions from the Idea Book (Ahl – see Source), where the original programs were posted in BASIC designed for the Texas Instruments computers in the 1980s. The Python versions were programmed with the TI-84 Plus CE Python (and should work on the TI-83 Premium Python Edition). Unfortunately, the Circle and Squares program may not work on the TI-82 Advanced Python as that calculator does not have any graphics modules.
Diophantine Books Problem
A book store studies the sales of three popular books: A, B, and C, each with prices PA, PB, and PC. We have the total books sold, the sales amount, and the prices of the books. How many of each books were sold?
The program solve the Diophantine system of equations:
A + B + C = N
PA * A + PB * B + PC * C = S
N = number of books sold
S = total sales
A, B, and C are positive integers
The original BASIC program covered a specific case, where in this version has the user enter the price of up to three books, total sales, and number of books sold. The code in Python also counts the number of solutions.
Code: books.py
# Math Calculations
from math import *
# Browns Books, pg 43
# TI HOME IDEA BOOK, 1983
# Translated to Python
print("Browns Books","\na+b+c=n","\npa*a+pb*b+pc*c=s")
print("books: a, b, c","\nbook prices: pa, pb, pc")
n=int(input("# books sold? "))
s=eval(input("total sales? "))
pa=eval(input("price of book a? "))
pb=eval(input("price of book b? "))
pc=eval(input("price of book c? "))
print("Prices: ","\n",pa,"\t\t",pb,"\t\t",pc)
print("-----------------")
# prices
i=0
for a in range(1,n+1):
for b in range(1,n+1):
for c in range(1,n+1):
if a+b+c==n and pa*a+pb*b+pc*c==s:
print(a,"\t\t",b,"\t\t",c)
i+=1
print("\n",i," solutions")
Circles In Squares
The program cirsqu.py calculates four areas:
The area of a square with a side of length of 2 * r.
The area of the inscribed circle with radius r.
The trapped area, which is the area of the square not taken up by the circle.
A corner of the area of the square not taken up by the circle, which is 1 / 4 of the trapped area.
The original program only printed the trapped area and the corner area. In addition, this Python code uses TI-specific modules, ti_system and ti_draw.
The ti_system module is used to temporarily stop execution with the disp_wait() command. Execution continues with by pressing the [ clear ] key.
The ti_draw module is used to draw the square, the circle, and the axis. Both the square and circle are centered at (0,0).
The code uses a scaling routine based on the radius of the circle, so that squares look like squares and circles look like circles. The TI-84 Plus CE Python graphics screen is 320 x 220 pixels. Setting up the window (xmin, xmax, ymin, and ymax) using the ratio will accomplish this task. Here are sampling of viewing windows to try:
xmin = -8, xmax = 8, ymin = -5.25, ymax = 5.25
xmin = -16, xmax = 16, ymin = -10.5, ymax = 10.5
xmin = -32, xmax = 32, ymin = -21, ymax = 21
About the fill_rect and draw_rect commands. The syntax is (x, y, width, height). The coordinates x and y are supposed to be the upper left hand corner, however the manual is incorrect in practice. The correct corner to use is the lower left hand corner. The OS that was used is 5.8.1.0012 (same number for Python).
Code: cirsqu.py
from math import *
from ti_system import *
from ti_draw import *
print("Math Module Activated")
print("Circle inside a Square")
print("circle of radius r")
print("square of side r")
r=eval(input("r? "))
ac=pi*r**2
asq=(2*r)**2
ad=asq-ac
# ti system
disp_clr()
print("Radius: ",r)
print("Areas: \nsquare:",asq)
print("circle: ",ac)
print("trapped: ",ad)
print("1/4 trapped: ",ad/4)
print("\nPress [clear] to contiue.")
# ti module ti_system
disp_wait()
# use ti module ti_draw
clear()
# text factor
f=1
# window set up
if r<=5.25:
x=8
y=5.25
else:
y=5.25
while y<r:
y*=2
f*=2
x=y*8/5.25
set_window(-x,x,-y,y)
# draw axis
set_color(235,235,235)
set_pen("thin","dotted")
draw_line(-x,0,x,0)
draw_line(0,-y,0,y)
# draw shapes
set_color(25,125,255)
set_pen("thin","solid")
# fill_rect anchors at the LOWER-left hand corner (manual error)
fill_rect(-r,-r,2*r,2*r)
set_color(230,130,0)
fill_circle(0,0,r)
set_color(0,0,0)
draw_text(-x,y-2*f,str(y))
draw_text(x-4*f,-y,str(x))
show_draw()
Source
Ahl, David H. The Texas Instruments Home Computer Idea Book. Creative Computing Press. Morris Plains, New Jersey. 1983. pg. 34-35, 105-106 ISBN 0-916688-51-8
Enjoy!
Eddie
All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
