diff --git a/Math/Manifold/Core/PseudoAffine.hs b/Math/Manifold/Core/PseudoAffine.hs
--- a/Math/Manifold/Core/PseudoAffine.hs
+++ b/Math/Manifold/Core/PseudoAffine.hs
@@ -215,10 +215,9 @@
 --   it can have a different topology, the prime example being 'TangentBundle', where
 --   nearby points may have differently-oriented tangent spaces.
 data FibreBundle b f = FibreBundle
-      { baseSpace :: !(Interior b)
+      { baseSpace :: !b
       , fibreSpace :: !f
-      } deriving (Generic)
-deriving instance (Show (Interior b), Show f) => Show (FibreBundle b f)
+      } deriving (Generic, Show)
 
 -- | Points on a manifold, combined with vectors in the respective tangent space.
 type TangentBundle m = FibreBundle m (Needle m)
diff --git a/Math/Manifold/Core/Types/Internal.hs b/Math/Manifold/Core/Types/Internal.hs
--- a/Math/Manifold/Core/Types/Internal.hs
+++ b/Math/Manifold/Core/Types/Internal.hs
@@ -16,6 +16,7 @@
 
 import Math.Manifold.VectorSpace.ZeroDimensional
 
+import Data.Fixed (mod')
 
 
 -- | The zero-dimensional sphere is actually just two points. Implementation might
@@ -29,8 +30,11 @@
 newtype S¹ = S¹Polar { φParamS¹ :: Double -- ^ Must be in range @[-π, π[@.
                      } deriving (Show)
 
+instance Eq S¹ where
+  S¹Polar φ == S¹Polar φ' = φ `mod'` (2*pi) == φ' `mod'` (2*pi)
 
-newtype ℝP¹ = HemisphereℝP¹Polar { φParamℝP¹ :: Double -- ^ Range @[-π/2,π/2[@.
+
+newtype ℝP¹ = HemisphereℝP¹Polar { φParamℝP¹ :: Double -- ^ Range @[-π\/2,π\/2[@.
                                  } deriving (Show)
 
 -- | The ordinary unit sphere.
@@ -38,6 +42,10 @@
                   , φParamS² :: !Double -- ^ Range @[-π, π[@.
                   } deriving (Show)
 
+instance Eq S² where
+  S²Polar θ φ == S²Polar θ' φ'
+   | θ > 0, θ < pi  = θ == θ' && φ `mod'` (2*pi) == φ' `mod'` (2*pi)
+   | otherwise      = θ == θ'
 
 -- | The two-dimensional real projective space, implemented as a disk with
 --   opposing points on the rim glued together. Image this disk as the northern hemisphere
diff --git a/manifolds-core.cabal b/manifolds-core.cabal
--- a/manifolds-core.cabal
+++ b/manifolds-core.cabal
@@ -2,7 +2,7 @@
 -- documentation, see http://haskell.org/cabal/users-guide/
 
 name:                manifolds-core
-version:             0.4.5.0
+version:             0.5.0.0
 synopsis:            The basic classes for the manifolds hierarchy.
 description:         The basic classes for the
                      <http://hackage.haskell.org/package/manifolds manifolds> hierarchy.