Every so often (well, ok, daily) I check my wordpress stats to see how many people have found a link pointing at my ramblings, or have unwittingly found it using a search engine. Indeed, much of the entertainment I get out of this site derives from the search terms used.

One used yesterday was “program to see if a triangle is equilateral”. Obviously I’ve never answered that question here, an omission I should put right immediately.

There are several ways to tell if a triangle is equilateral: the two most obvious ones are to check that all of the sides have the same length, or to check that all of the angles are 60º; you can also check that two sides are the same length and that the angle between them is 60º.

The easiest one to implement is the same-length check. Let’s say you have three points – we need to see if the distance between each pair of points is the same. That distance is sqrt(x^2 + y^2 + z^2). Because we’re only checking for equality, we don’t even need to take the square root. Our python code is something like:

class Point:
# Class to keep the points tidy
def __init__(self, x,y,z):
self.x = x
self.y = y
self.z = z
def distanceSquared(P, Q):
dx2 = (P.x - Q.x) ** 2
dy2 = (P.y - Q.y) ** 2
dz2 = (P.z - Q.z) ** 2
return dx2 + dy2 + dz2
def isEquilateral(A, B, C):
ab2 = distanceSquared(A, B)
ac2 = distanceSquared(B, C)
bc2 = distanceSquared(A, C)
if ab2 != ac2 or ab2 != bc2:
return 0
else:
return 1
A = Point(0.,0.,0.)
B = Point(1.,1.,0.)
C = Point(0.,1.,1.)
D = Point(1.,0.,0.)
print isEqulilateral( A, B, C)
# should return 1
print isEquilateral ( A, B, D)
# should return 0

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This entry was posted on February 16, 2008 at 7:33 pm and is filed under articles.

Tags: equilateral triangle, python code, reader requests

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