给定三个点的坐标，如何确定所定义的三角形是等边，等腰还是斜角？

Question

I've written the following code, but I can't make sure if it recognizes an equilateral triangle because I can't input the coordinates I need to make it (square root of 3, for example):

x1 = eval(input('x1: '))
y1 = eval(input('y1: '))
x2 = eval(input('x2: '))
y2 = eval(input('y2: '))
x3 = eval(input('x3: '))
y3 = eval(input('y3: '))
side1 = (abs(x1 - x2) + abs(y1 - y2)) ** (1/2)
side2 = (abs(x2 - x3) + abs(y2 - y3)) ** (1/2)
side3 = (abs(x3 - x1) + abs(y3 - y2)) ** (1/2)
print('side1: ', side1, 'side2: ', side2,'side3:', side3)
if side1 + side2 > side3 and side2 + side3 > side1 and side1 + side3 > side2 :
    if side1 == side2 == side3:
        print('This triangle is equilateral')
    elif side1 == side2 or side2 == side3 or side1 == side3 :
        print('This triangle is isosceles')
    else:
        print('This triangle is scalene')
else:
    print('This is not a triangle!')

EDIT: I've rewritten the code as follows

x1 = eval(input('x1: '))
y1 = eval(input('y1: '))
x2 = eval(input('x2: '))
y2 = eval(input('y2: '))
x3 = eval(input('x3: '))
y3 = eval(input('y3: '))
side1 = ((x1 - x2)**2 + (y1 - y2)**2) ** (1/2)
side2 = ((x2 - x3)**2 + (y2 - y3)**2) ** (1/2)
side3 = ((x3 - x1)**2 + (y3 - y1)**2) ** (1/2)
print('side1: ', side1, 'side2: ', side2,'side3:', side3)
if side1 + side2 > side3 and side2 + side3 > side1 and side1 + side3 > side2 :
    if side1 == side2 == side3:
        print('This triangle is equilateral')
    elif side1 == side2 or side2 == side3 or side1 == side3 :
        print('This triangle is isosceles')
    else:
        print('This triangle is scalene')
else:
    print('This is not a triangle!')

Answer 1

• Since you square the coordinate distance, you don't need abs .
• Your second y coordinate for side3 is wrong: should be y1 )).
• Your check for legal sides should include equality: sides of 2, 2, 4 give you straight line, but you classify it as an isosceles triangle.
• You can use the math package for a more readable square root.
• You can save a step or two by sorting the side lengths; this simplifies your comparisons.

Updated code:

from math import sqrt

x1 = float(raw_input('x1: '))
y1 = float(raw_input('y1: '))
x2 = float(raw_input('x2: '))
y2 = float(raw_input('y2: '))
x3 = float(raw_input('x3: '))
y3 = float(raw_input('y3: '))

side1 = sqrt((x1 - x2)**2 + (y1-y2)**2)
side2 = sqrt((x2 - x3)**2 + (y2-y3)**2)
side3 = sqrt((x3 - x1)**2 + (y3-y1)**2)

# Put the sides into a list; sort them.
tri= [side1, side2, side3]
tri.sort()

if tri[0] < tri[1]+tri[2]:
    if tri[0] == tri[2]:
        print('This triangle is equilateral')
    elif tri[1] == tri[2] or tri[1] == tri[0]:
        print('This triangle is isosceles')
    else:
        print('This triangle is scalene')
else:
    print('This is not a triangle!')

Answer 2

It sounds like the question is really about how to enter the input. You need to wrap the input in quotes because eval expects string input, not number types.

The eval function will parse that string as Python code. Thus, you use the same square root syntax as you do in your code.

So for example, let's test an equilateral triangle. I run your (edited) script from the terminal, and enter the coordinates as strings.

x1: '0'
y1: '0'
x2: '2'
y2: '12**0.5'
x3: '4'
y3: '0'
('side1: ', 1.0, 'side2: ', 1.0, 'side3:', 1.0)
This triangle is equilateral