## Issue

The following formula is used to classify points from a 2-dimensional space:

```
f(x1,x2) = np.sign(x1^2+x2^2-.6)
```

All points are in space `X = [-1,1] x [-1,1]`

with a uniform probability of picking each x.

Now I would like to visualize the circle that equals:

```
0 = x1^2+x2^2-.6
```

The values of x1 should be on the x-axis and values of x2 on the y-axis.

It must be possible but I have difficulty transforming the equation to a plot.

## Solution

You can use a contour plot, as follows (based on the examples at http://matplotlib.org/examples/pylab_examples/contour_demo.html):

```
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-1.0, 1.0, 100)
y = np.linspace(-1.0, 1.0, 100)
X, Y = np.meshgrid(x,y)
F = X**2 + Y**2 - 0.6
plt.contour(X,Y,F,[0])
plt.show()
```

This yields the following graph

Lastly, some general statements:

`x^2`

does not mean what you*think*it does in python, you have to use`x**2`

.`x1`

and`x2`

are terribly misleading (to me), especially if you state that`x2`

has to be on the y-axis.- (Thanks to Dux) You can add
`plt.gca().set_aspect('equal')`

to make the figure actually look circular, by making the axis equal.

Answered By – Bas Jansen

Answer Checked By – Cary Denson (BugsFixing Admin)