Merge pull request #371 from RayTracing/sphere-equation-text

Sphere equation wording changes

Author: hollasch

books/RayTracingInOneWeekend.html

@@ -485,10 +485,12 @@
 <div class='together'>
 Let’s add a single object to our ray tracer. People often use spheres in ray tracers because
 calculating whether a ray hits a sphere is pretty straightforward. Recall that the equation for a
-sphere centered at the origin of radius $R$ is $x^2 + y^2 + z^2 = R^2$. The way you can read that
-equation is “for any $(x, y, z)$, if $x^2 + y^2 + z^2 = R^2$ then $(x,y,z)$ is on the sphere, and
-otherwise it is not”. It gets uglier if the sphere center is at
-$(\mathbf{c}_x, \mathbf{c}_y, \mathbf{c}_z)$:
+sphere centered at the origin of radius $R$ is $x^2 + y^2 + z^2 = R^2$. Put another way, if a given
+point $(x,y,z)$ is on the sphere, then $x^2 + y^2 + z^2 = R^2$. If the given point $(x,y,z)$ is
+_inside_ the sphere, then $x^2 + y^2 + z^2 < R^2$, and if a given point $(x,y,z)$ is _outside_ the
+sphere, then $x^2 + y^2 + z^2 > R^2$.
+
+It gets uglier if the sphere center is at $(\mathbf{c}_x, \mathbf{c}_y, \mathbf{c}_z)$:
 
   $$ (x-\mathbf{c}_x)^2 + (y-\mathbf{c}_y)^2 + (z-\mathbf{c}_z)^2 = R^2 $$
 </div>