Commit 75c109c

@@ -29,10 +29,72 @@ Guaranteed constraints:
 [output] integer
 
 The maximum number of points that can be viewed from point (0, 0) with a viewing angle that is equal to 45 degrees.
+
+NOTES
+
+Vertex is always (0, 0)
+
+Pythagorean theorem.
+
+* right triangle has 90 degrees
+* sum of all angles inside a triangle = 180 degrees
+
+If we know two sides of a right triangle we can find the third side.
+
+Hypotenuse: Long side is opposite the right angle.
+
+A^2 + B^2 = C^2
+C is the hypotenuse
+
+Trigonometric Functions
+
+Soh Cah Toa
+sine(degrees) = Opposite (length) / Hypotenuse (length)
+cosine(degrees) = Adjacent (length) / Hypotenuse (length)
+tangent(degrees) = Opposite (length) / Adjacent (length)
+
+
+Inverse Trigonometric Functions
+
+sin(x) = O/H ===> x = sin-1(O/H) (inverse sine aka arcsin)
+cos(x) = A/H ===> x = cos-1(A/H) (inverse cos aka arccos)
+toa(x) = O/A ===> x = tan-1(O/A) (inverse tan aka arctan)
+
+arctan(35/65) = 28.3 degrees
+
+Math.atan(35.0/65.0) * (180 / Math::PI)
+=> 28.300755766006375
+
 DOC
 
 describe "visible points" do
+  def radians_to_degrees(radians)
+    radians * (180 / Math::PI)
+  end
+
+  def degrees_to_radians(degrees)
+    degrees * (Math::PI / 180)
+  end
+
+  # function to find third point in angle
+  def angle_for(x, y)
+    radians_to_degrees(Math.atan(y.to_f / x.to_f))
+  end
+
+  def valid_angles_for(points)
+    points.inject([]) do |angles, (x, y)|
+      return angles if x == 0 && y == 0
+      return angles if x < 0 || y < 0
+      angle = angle_for(x, y)
+      return angles if angle > 45.0
+      angles.push(angle)
+      angles
+    end
+  end
+
   def visible_points(points)
+    angles = valid_angles_for(points)
+    puts angles.inspect
   end
 
   it do