title: How to generate uniform random points inside d-dimension ball / sphere?
body: <p>I've looked around and all solutions for generating uniform random points in/on the unit ball are designed for 2 or 3 dimensions.</p>
  
  <p><strong>What is a</strong> (tractable) <strong>way to generate uniform random points <em>inside</em> a ball in arbitrary dimension?</strong> Particularly, not just on the surface of the ball.</p>
  
  <p>To preface, generating random points in the cube and throwing out the points with norm greater than 1 is <em>not feasible</em> in high dimension. The ratio of the volume of a unit ball to the volume of a unit cube in high dimension goes to 0. Even in 10 dimensions only about 0.25% of random points in the unit cube are also inside the unit ball.</p>