Test if a random point belongs to a circumference of a circle using Python

Question

I am trying to generate a random point on the circumference of a circle using Python.

I have a circle of centre (0, 0) and of radius 50. I did the following.

import numpy as np
angle = 2 * np.pi * np.random.rand()
x = np.cos(angle) * 50
y = np.sin(angle) * 50

But when I test to see if the point is actually on the circle circumference, I did this

x ** 2 + y ** 2 == 50 ** 2

but I get

False

Why is this?

Possible duplicate of [Floating point inaccuracy examples](https://stackoverflow.com/questions/2100490/floating-point-inaccuracy-examples) — Kijewski, Jul 17 '17 at 14:09
If you want to learn how to estimate the needed epsilon then google "numerical stability floating point math". Alas, its Wikipedia article is terrible. — Kijewski, Jul 17 '17 at 14:15

Erik Godard · Accepted Answer · 2017-07-17T14:13:20.940

6

This is the result of floating point imprecision. In general, it is a bad idea to compare two floats for equality, and you should instead test to see if they are within a certain amount of each other. For example,

epsilon = 0.000001
print abs(x ** 2 + y ** 2  - 50 ** 2) <= epsilson

See also: How should I do floating point comparison?

edited Jul 17 '17 at 14:13

answered Jul 17 '17 at 14:11

Erik Godard

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score 3 · Answer 2 · answered Jul 17 '17 at 14:09

3

Floating point arithmetic is not exact, so testing for equality will not always work as would be expected with infinite precision.

answered Jul 17 '17 at 14:09

Scott Hunter

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Test if a random point belongs to a circumference of a circle using Python

2 Answers2