diff --git a/src/main/java/pythagoras/d/AbstractVector.java b/src/main/java/pythagoras/d/AbstractVector.java
index 9d595e8..9712cc2 100644
--- a/src/main/java/pythagoras/d/AbstractVector.java
+++ b/src/main/java/pythagoras/d/AbstractVector.java
@@ -48,6 +48,11 @@ public abstract class AbstractVector implements IVector
         return (x*x + y*y);
     }
 
+    @Override // from interface IVector
+    public boolean isZero () {
+        return Vectors.isZero(x(), y());
+    }
+
     @Override // from interface IVector
     public double distance (IVector other) {
         return Math.sqrt(distanceSq(other));
diff --git a/src/main/java/pythagoras/d/IVector.java b/src/main/java/pythagoras/d/IVector.java
index 2b7d40c..afecbd7 100644
--- a/src/main/java/pythagoras/d/IVector.java
+++ b/src/main/java/pythagoras/d/IVector.java
@@ -40,6 +40,9 @@ public interface IVector
     /** Returns the squared length of this vector. */
     double lengthSq ();
 
+    /** Returns true if this vector has zero magnitude. */
+    boolean isZero ();
+
     /** Returns the distance from this vector to the specified other vector. */
     double distance (IVector other);
 
diff --git a/src/main/java/pythagoras/d/Points.java b/src/main/java/pythagoras/d/Points.java
index 1604f07..1b7f43c 100644
--- a/src/main/java/pythagoras/d/Points.java
+++ b/src/main/java/pythagoras/d/Points.java
@@ -28,6 +28,22 @@ public class Points
         return Math.sqrt(distanceSq(x1, y1, x2, y2));
     }
 
+    /**
+     * Returns true if the supplied points' x and y components are equal to one another within
+     * {@link MathUtil#EPSILON}.
+     */
+    public static boolean epsilonEquals (IPoint p1, IPoint p2) {
+        return epsilonEquals(p1, p2, MathUtil.EPSILON);
+    }
+
+    /**
+     * Returns true if the supplied points' x and y components are equal to one another within
+     * {@code epsilon}.
+     */
+    public static boolean epsilonEquals (IPoint p1, IPoint p2, double epsilon) {
+        return Math.abs(p1.x() - p2.x()) < epsilon && Math.abs(p1.y() - p2.y()) < epsilon;
+    }
+
     /** Transforms a point as specified, storing the result in the point provided.
      * @return a reference to the result point, for chaining. */
     public static Point transform (double x, double y, double sx, double sy, double rotation,
diff --git a/src/main/java/pythagoras/d/Vectors.java b/src/main/java/pythagoras/d/Vectors.java
index b414314..72cd9c7 100644
--- a/src/main/java/pythagoras/d/Vectors.java
+++ b/src/main/java/pythagoras/d/Vectors.java
@@ -28,24 +28,63 @@ public class Vectors
     /**
      * Creates a new vector from polar coordinates.
      */
-    public static final Vector fromPolar (double magnitude, double angle) {
+    public static Vector fromPolar (double magnitude, double angle) {
         return new Vector(magnitude * Math.cos(angle), magnitude * Math.sin(angle));
     }
 
     /**
      * Returns the magnitude of the specified vector.
      */
-    public static final double length (double x, double y) {
+    public static double length (double x, double y) {
         return Math.sqrt(lengthSq(x, y));
     }
 
     /**
      * Returns the square of the magnitude of the specified vector.
      */
-    public static final double lengthSq (double x, double y) {
+    public static double lengthSq (double x, double y) {
         return (x*x + y*y);
     }
 
+    /**
+     * Returns true if the supplied vector has zero magnitude.
+     */
+    public static boolean isZero (double x, double y) {
+        return x == 0 && y == 0;
+    }
+
+    /**
+     * Returns true if the supplied vector's x and y components are {@link MathUtil#EPSILON} close
+     * to zero magnitude.
+     */
+    public static boolean isEpsilonZero (double x, double y) {
+        return isEpsilonZero(x, y, MathUtil.EPSILON);
+    }
+
+    /**
+     * Returns true if the supplied vector's x and y components are {@code epsilon} close to zero
+     * magnitude.
+     */
+    public static boolean isEpsilonZero (double x, double y, double epsilon) {
+        return Math.abs(x) < epsilon && Math.abs(y) < epsilon;
+    }
+
+    /**
+     * Returns true if the supplied vectors' x and y components are equal to one another within
+     * {@link MathUtil#EPSILON}.
+     */
+    public static boolean epsilonEquals (IVector v1, IVector v2) {
+        return epsilonEquals(v1, v2, MathUtil.EPSILON);
+    }
+
+    /**
+     * Returns true if the supplied vectors' x and y components are equal to one another within
+     * {@code epsilon}.
+     */
+    public static boolean epsilonEquals (IVector v1, IVector v2, double epsilon) {
+        return Math.abs(v1.x() - v2.x()) < epsilon && Math.abs(v1.y() - v2.y()) < epsilon;
+    }
+
     /**
      * Transforms a point as specified, storing the result in the point provided.
      * @return a reference to the result vector, for chaining.
diff --git a/src/main/java/pythagoras/f/AbstractVector.java b/src/main/java/pythagoras/f/AbstractVector.java
index 8dfa8a4..0d048bb 100644
--- a/src/main/java/pythagoras/f/AbstractVector.java
+++ b/src/main/java/pythagoras/f/AbstractVector.java
@@ -48,6 +48,11 @@ public abstract class AbstractVector implements IVector
         return (x*x + y*y);
     }
 
+    @Override // from interface IVector
+    public boolean isZero () {
+        return Vectors.isZero(x(), y());
+    }
+
     @Override // from interface IVector
     public float distance (IVector other) {
         return FloatMath.sqrt(distanceSq(other));
diff --git a/src/main/java/pythagoras/f/IVector.java b/src/main/java/pythagoras/f/IVector.java
index 454bb6e..0dd4fac 100644
--- a/src/main/java/pythagoras/f/IVector.java
+++ b/src/main/java/pythagoras/f/IVector.java
@@ -40,6 +40,9 @@ public interface IVector
     /** Returns the squared length of this vector. */
     float lengthSq ();
 
+    /** Returns true if this vector has zero magnitude. */
+    boolean isZero ();
+
     /** Returns the distance from this vector to the specified other vector. */
     float distance (IVector other);
 
diff --git a/src/main/java/pythagoras/f/Points.java b/src/main/java/pythagoras/f/Points.java
index 7ffe273..0cdefa7 100644
--- a/src/main/java/pythagoras/f/Points.java
+++ b/src/main/java/pythagoras/f/Points.java
@@ -28,6 +28,22 @@ public class Points
         return FloatMath.sqrt(distanceSq(x1, y1, x2, y2));
     }
 
+    /**
+     * Returns true if the supplied points' x and y components are equal to one another within
+     * {@link MathUtil#EPSILON}.
+     */
+    public static boolean epsilonEquals (IPoint p1, IPoint p2) {
+        return epsilonEquals(p1, p2, MathUtil.EPSILON);
+    }
+
+    /**
+     * Returns true if the supplied points' x and y components are equal to one another within
+     * {@code epsilon}.
+     */
+    public static boolean epsilonEquals (IPoint p1, IPoint p2, float epsilon) {
+        return Math.abs(p1.x() - p2.x()) < epsilon && Math.abs(p1.y() - p2.y()) < epsilon;
+    }
+
     /** Transforms a point as specified, storing the result in the point provided.
      * @return a reference to the result point, for chaining. */
     public static Point transform (float x, float y, float sx, float sy, float rotation,
diff --git a/src/main/java/pythagoras/f/Vectors.java b/src/main/java/pythagoras/f/Vectors.java
index 550d1a2..1cb2fbb 100644
--- a/src/main/java/pythagoras/f/Vectors.java
+++ b/src/main/java/pythagoras/f/Vectors.java
@@ -28,24 +28,63 @@ public class Vectors
     /**
      * Creates a new vector from polar coordinates.
      */
-    public static final Vector fromPolar (float magnitude, float angle) {
+    public static Vector fromPolar (float magnitude, float angle) {
         return new Vector(magnitude * FloatMath.cos(angle), magnitude * FloatMath.sin(angle));
     }
 
     /**
      * Returns the magnitude of the specified vector.
      */
-    public static final float length (float x, float y) {
+    public static float length (float x, float y) {
         return FloatMath.sqrt(lengthSq(x, y));
     }
 
     /**
      * Returns the square of the magnitude of the specified vector.
      */
-    public static final float lengthSq (float x, float y) {
+    public static float lengthSq (float x, float y) {
         return (x*x + y*y);
     }
 
+    /**
+     * Returns true if the supplied vector has zero magnitude.
+     */
+    public static boolean isZero (float x, float y) {
+        return x == 0 && y == 0;
+    }
+
+    /**
+     * Returns true if the supplied vector's x and y components are {@link MathUtil#EPSILON} close
+     * to zero magnitude.
+     */
+    public static boolean isEpsilonZero (float x, float y) {
+        return isEpsilonZero(x, y, MathUtil.EPSILON);
+    }
+
+    /**
+     * Returns true if the supplied vector's x and y components are {@code epsilon} close to zero
+     * magnitude.
+     */
+    public static boolean isEpsilonZero (float x, float y, float epsilon) {
+        return Math.abs(x) < epsilon && Math.abs(y) < epsilon;
+    }
+
+    /**
+     * Returns true if the supplied vectors' x and y components are equal to one another within
+     * {@link MathUtil#EPSILON}.
+     */
+    public static boolean epsilonEquals (IVector v1, IVector v2) {
+        return epsilonEquals(v1, v2, MathUtil.EPSILON);
+    }
+
+    /**
+     * Returns true if the supplied vectors' x and y components are equal to one another within
+     * {@code epsilon}.
+     */
+    public static boolean epsilonEquals (IVector v1, IVector v2, float epsilon) {
+        return Math.abs(v1.x() - v2.x()) < epsilon && Math.abs(v1.y() - v2.y()) < epsilon;
+    }
+
     /**
      * Transforms a point as specified, storing the result in the point provided.
      * @return a reference to the result vector, for chaining.