diff --git a/src/structs/dmatrix_macros.rs b/src/structs/dmatrix_macros.rs
index 80e99761..346d40f2 100644
--- a/src/structs/dmatrix_macros.rs
+++ b/src/structs/dmatrix_macros.rs
@@ -873,13 +873,13 @@ macro_rules! dmat_impl(
 
         impl<N: ApproxEq<N>> ApproxEq<N> for $dmatrix<N> {
             #[inline]
-            fn approx_epsilon(_: Option<$dmatrix<N>>) -> N {
-                ApproxEq::approx_epsilon(None::<N>)
+            fn approx_epsilon() -> N {
+                <N as ApproxEq<N>>::approx_epsilon()
             }
 
             #[inline]
-            fn approx_ulps(_: Option<$dmatrix<N>>) -> u32 {
-                ApproxEq::approx_ulps(None::<N>)
+            fn approx_ulps() -> u32 {
+                <N as ApproxEq<N>>::approx_ulps()
             }
 
             #[inline]
diff --git a/src/structs/isometry_macros.rs b/src/structs/isometry_macros.rs
index 14cfb5fd..6000c01a 100644
--- a/src/structs/isometry_macros.rs
+++ b/src/structs/isometry_macros.rs
@@ -378,13 +378,13 @@ macro_rules! isometry_impl(
          */
         impl<N: ApproxEq<N>> ApproxEq<N> for $t<N> {
             #[inline]
-            fn approx_epsilon(_: Option<$t<N>>) -> N {
-                ApproxEq::approx_epsilon(None::<N>)
+            fn approx_epsilon() -> N {
+                <N as ApproxEq<N>>::approx_epsilon()
             }
 
             #[inline]
-            fn approx_ulps(_: Option<$t<N>>) -> u32 {
-                ApproxEq::approx_ulps(None::<N>)
+            fn approx_ulps() -> u32 {
+                <N as ApproxEq<N>>::approx_ulps()
             }
 
             #[inline]
diff --git a/src/structs/matrix_macros.rs b/src/structs/matrix_macros.rs
index acfeb2cf..4f3d12ee 100644
--- a/src/structs/matrix_macros.rs
+++ b/src/structs/matrix_macros.rs
@@ -277,13 +277,13 @@ macro_rules! matrix_impl(
          */
         impl<N: ApproxEq<N>> ApproxEq<N> for $t<N> {
             #[inline]
-            fn approx_epsilon(_: Option<$t<N>>) -> N {
-                ApproxEq::approx_epsilon(None::<N>)
+            fn approx_epsilon() -> N {
+                <N as ApproxEq<N>>::approx_epsilon()
             }
 
             #[inline]
-            fn approx_ulps(_: Option<$t<N>>) -> u32 {
-                ApproxEq::approx_ulps(None::<N>)
+            fn approx_ulps() -> u32 {
+                <N as ApproxEq<N>>::approx_ulps()
             }
 
             #[inline]
diff --git a/src/structs/quaternion.rs b/src/structs/quaternion.rs
index 3d96e51a..1656e13c 100644
--- a/src/structs/quaternion.rs
+++ b/src/structs/quaternion.rs
@@ -389,13 +389,13 @@ impl<N: Rand + BaseFloat> Rand for UnitQuaternion<N> {
 
 impl<N: ApproxEq<N>> ApproxEq<N> for UnitQuaternion<N> {
     #[inline]
-    fn approx_epsilon(_: Option<UnitQuaternion<N>>) -> N {
-        ApproxEq::approx_epsilon(None::<N>)
+    fn approx_epsilon() -> N {
+        <N as ApproxEq<N>>::approx_epsilon()
     }
 
     #[inline]
-    fn approx_ulps(_: Option<UnitQuaternion<N>>) -> u32 {
-        ApproxEq::approx_ulps(None::<N>)
+    fn approx_ulps() -> u32 {
+        <N as ApproxEq<N>>::approx_ulps()
     }
 
     #[inline]
diff --git a/src/structs/rotation_macros.rs b/src/structs/rotation_macros.rs
index dfcdd835..02981503 100644
--- a/src/structs/rotation_macros.rs
+++ b/src/structs/rotation_macros.rs
@@ -341,13 +341,13 @@ macro_rules! rotation_impl(
          */
         impl<N: ApproxEq<N>> ApproxEq<N> for $t<N> {
             #[inline]
-            fn approx_epsilon(_: Option<$t<N>>) -> N {
-                ApproxEq::approx_epsilon(None::<N>)
+            fn approx_epsilon() -> N {
+                <N as ApproxEq<N>>::approx_epsilon()
             }
 
             #[inline]
-            fn approx_ulps(_: Option<$t<N>>) -> u32 {
-                ApproxEq::approx_ulps(None::<N>)
+            fn approx_ulps() -> u32 {
+                <N as ApproxEq<N>>::approx_ulps()
             }
 
             #[inline]
diff --git a/src/structs/similarity_macros.rs b/src/structs/similarity_macros.rs
index 73e8aaf7..85903d97 100644
--- a/src/structs/similarity_macros.rs
+++ b/src/structs/similarity_macros.rs
@@ -353,13 +353,13 @@ macro_rules! similarity_impl(
          */
         impl<N: ApproxEq<N>> ApproxEq<N> for $t<N> {
             #[inline]
-            fn approx_epsilon(_: Option<$t<N>>) -> N {
-                ApproxEq::approx_epsilon(None::<N>)
+            fn approx_epsilon() -> N {
+                <N as ApproxEq<N>>::approx_epsilon()
             }
 
             #[inline]
-            fn approx_ulps(_: Option<$t<N>>) -> u32 {
-                ApproxEq::approx_ulps(None::<N>)
+            fn approx_ulps() -> u32 {
+                <N as ApproxEq<N>>::approx_ulps()
             }
 
             #[inline]
diff --git a/src/structs/vector_macros.rs b/src/structs/vector_macros.rs
index 7bd0e931..22987910 100644
--- a/src/structs/vector_macros.rs
+++ b/src/structs/vector_macros.rs
@@ -34,13 +34,13 @@ macro_rules! vectorlike_impl(
          */
         impl<N: ApproxEq<N>> ApproxEq<N> for $t<N> {
             #[inline]
-            fn approx_epsilon(_: Option<$t<N>>) -> N {
-                ApproxEq::approx_epsilon(None::<N>)
+            fn approx_epsilon() -> N {
+                <N as ApproxEq<N>>::approx_epsilon()
             }
 
             #[inline]
-            fn approx_ulps(_: Option<$t<N>>) -> u32 {
-                ApproxEq::approx_ulps(None::<N>)
+            fn approx_ulps() -> u32 {
+                <N as ApproxEq<N>>::approx_ulps()
             }
 
             #[inline]
diff --git a/src/structs/vectorn_macros.rs b/src/structs/vectorn_macros.rs
index 74749375..05046c1a 100644
--- a/src/structs/vectorn_macros.rs
+++ b/src/structs/vectorn_macros.rs
@@ -582,13 +582,13 @@ macro_rules! vecn_dvec_common_impl(
          */
         impl<N: ApproxEq<N> $(, $param : ArrayLength<N>)*> ApproxEq<N> for $vecn<N $(, $param)*> {
             #[inline]
-            fn approx_epsilon(_: Option<$vecn<N $(, $param)*>>) -> N {
-                ApproxEq::approx_epsilon(None::<N>)
+            fn approx_epsilon() -> N {
+                <N as ApproxEq<N>>::approx_epsilon()
             }
 
             #[inline]
-            fn approx_ulps(_: Option<$vecn<N $(, $param)*>>) -> u32 {
-                ApproxEq::approx_ulps(None::<N>)
+            fn approx_ulps() -> u32 {
+                <N as ApproxEq<N>>::approx_ulps()
             }
 
             #[inline]
diff --git a/src/traits/operations.rs b/src/traits/operations.rs
index 7059e30e..8a7a7066 100644
--- a/src/traits/operations.rs
+++ b/src/traits/operations.rs
@@ -152,13 +152,13 @@ pub trait PartialOrder {
 /// Trait for testing approximate equality
 pub trait ApproxEq<Eps>: Sized {
     /// Default epsilon for approximation.
-    fn approx_epsilon(unused_mut: Option<Self>) -> Eps;
+    fn approx_epsilon() -> Eps;
 
     /// Tests approximate equality using a custom epsilon.
     fn approx_eq_eps(&self, other: &Self, epsilon: &Eps) -> bool;
 
     /// Default ULPs for approximation.
-    fn approx_ulps(unused_mut: Option<Self>) -> u32;
+    fn approx_ulps() -> u32;
 
     /// Tests approximate equality using units in the last place (ULPs)
     fn approx_eq_ulps(&self, other: &Self, ulps: u32) -> bool;
@@ -166,13 +166,13 @@ pub trait ApproxEq<Eps>: Sized {
     /// Tests approximate equality.
     #[inline]
     fn approx_eq(&self, other: &Self) -> bool {
-        self.approx_eq_eps(other, &ApproxEq::approx_epsilon(None::<Self>))
+        self.approx_eq_eps(other, &Self::approx_epsilon())
     }
 }
 
 impl ApproxEq<f32> for f32 {
     #[inline]
-    fn approx_epsilon(_: Option<f32>) -> f32 {
+    fn approx_epsilon() -> f32 {
         1.0e-6
     }
 
@@ -181,7 +181,7 @@ impl ApproxEq<f32> for f32 {
         ::abs(&(*self - *other)) < *epsilon
     }
 
-    fn approx_ulps(_: Option<f32>) -> u32 {
+    fn approx_ulps() -> u32 {
         8
     }
 
@@ -203,7 +203,7 @@ impl ApproxEq<f32> for f32 {
 
 impl ApproxEq<f64> for f64 {
     #[inline]
-    fn approx_epsilon(_: Option<f64>) -> f64 {
+    fn approx_epsilon() -> f64 {
         1.0e-6
     }
 
@@ -212,7 +212,7 @@ impl ApproxEq<f64> for f64 {
         ::abs(&(*self - *other)) < *approx_epsilon
     }
 
-    fn approx_ulps(_: Option<f64>) -> u32 {
+    fn approx_ulps() -> u32 {
         8
     }
 
@@ -231,16 +231,16 @@ impl ApproxEq<f64> for f64 {
 }
 
 impl<'a, N, T: ApproxEq<N>> ApproxEq<N> for &'a T {
-    fn approx_epsilon(_: Option<&'a T>) -> N {
-        ApproxEq::approx_epsilon(None::<T>)
+    fn approx_epsilon() -> N {
+        <T as ApproxEq<N>>::approx_epsilon()
     }
 
     fn approx_eq_eps(&self, other: &&'a T, approx_epsilon: &N) -> bool {
         ApproxEq::approx_eq_eps(*self, *other, approx_epsilon)
     }
 
-    fn approx_ulps(_: Option<&'a T>) -> u32 {
-        ApproxEq::approx_ulps(None::<T>)
+    fn approx_ulps() -> u32 {
+        <T as ApproxEq<N>>::approx_ulps()
     }
 
     fn approx_eq_ulps(&self, other: &&'a T, ulps: u32) -> bool {
@@ -249,16 +249,16 @@ impl<'a, N, T: ApproxEq<N>> ApproxEq<N> for &'a T {
 }
 
 impl<'a, N, T: ApproxEq<N>> ApproxEq<N> for &'a mut T {
-    fn approx_epsilon(_: Option<&'a mut T>) -> N {
-        ApproxEq::approx_epsilon(None::<T>)
+    fn approx_epsilon() -> N {
+        <T as ApproxEq<N>>::approx_epsilon()
     }
 
     fn approx_eq_eps(&self, other: &&'a mut T, approx_epsilon: &N) -> bool {
         ApproxEq::approx_eq_eps(*self, *other, approx_epsilon)
     }
 
-    fn approx_ulps(_: Option<&'a mut T>) -> u32 {
-        ApproxEq::approx_ulps(None::<T>)
+    fn approx_ulps() -> u32 {
+        <T as ApproxEq<N>>::approx_ulps()
     }
 
     fn approx_eq_ulps(&self, other: &&'a mut T, ulps: u32) -> bool {