TITLE: Project 5: Explore Distributions of Random Circles
AUTHOR: Jane Doe Email:jane.doe@cyberspace.net
DATE: Due Jan 32, 2150

# Logical name of exercise: norm
# This document contains references to a parent document (../testdoc).
# These references will work for latex (using the xr package and
# a compiled parent document (with ../testdoc.aux file), but other formats
# will have missing references.
# Externaldocuments: ../testdoc


# keywords = ipynb

The formula for a circle is given by

!bt
\begin{align}
x &= x_0 + R\cos 2\pi t,
label{circle:x}\\ 
y &= y_0 + R\sin 2\pi t,
label{circle:y}
\end{align}
!et
where $R$ is the radius of the circle, $(x_0,y_0)$ is the
center point, and $t$ is a parameter in the unit interval $[0,1]$.
For any $t$, $(x,y)$ computed from (ref{circle:x})-(ref{circle:y})
is a point on the circle.
The formula can be used to generate `n` points on a circle:

!bc pypro
import numpy as np

def circle(R, x0, y0, n=501):
    t = np.linspace(0, 1, n)
    x = x0 + R*np.cos(2*np.pi*t)
    y = y0 + R*np.sin(2*np.pi*t)
    return x, y

x, y = circle(2.0, 0, 0)
!ec

# Often in an exercise we have some comments about the solution
# which we normally want to keep where they are.

The goal of this project is to draw $N$ circles with random
center and radius. Plot each circle using the `circle` function
above.


__a)__
Let $R$ be normally distributed and $(x_0,y_0)$ uniformly distributed.


__Hint.__
Use the `numpy.random` module to draw the
$x_0$, $y_0$, and $R$ quantities.






__b)__
Let $R$ be uniformly distributed and $(x_0,y_0)$ normally distributed.


__c)__
Let $R$ and $(x_0,y_0)$ be normally distributed.




# Closing remarks for this Project

=== Remarks ===

At the very end of the exercise it may be appropriate to summarize
and give some perspectives.
