I have started the Graham Scan Algorithm exercise. I'm getting tripped up by the sortByCotangent* function. Here's what I have so far data Direction = DStraight | DLeft | DRight deriving (Eq,Show) type PointXY = (Double,Double) calcTurn :: PointXY -> PointXY -> PointXY -> Direction calcTurn a b c | crossProduct == 0 = DStraight | crossProduct > 0 = DLeft | otherwise = DRight where crossProduct = ((fst b - fst a) * (snd c - snd a)) - ((snd b - snd a) * (fst c - fst a)) calcDirectionList :: [PointXY] -> [Direction] calcDirectionList (x:y:z:zs) = (calcTurn x y z) : (calcDirectionList (y:z:zs)) calcDirectionList _ = [] sortListByY :: [PointXY] -> [PointXY] sortListByY [] = [] sortListByY [a] = [a] sortListByY (a:as) = insert (sortListByY as) where insert [] = [a] insert (b:bs) | snd a <= snd b = a : b : bs | otherwise = b : insert bs sortListByCoTangent :: [PointXY] -> [PointXY] sortListByCoTangent [] = [] sortListByCoTangent [a] = [a] sortListByCoTangent (a:as) = a : insert (sortListByCoTangent as) where insert :: [PointXY] -> [PointXY] insert [] = [a] insert [b] = [b] insert (b:c:cs) | (myCoTan a b) >= (myCoTan a c) = b : c : cs | otherwise = c : b : insert cs where myCoTan :: PointXY -> PointXY -> Double myCoTan p1 p2 = (fst p2 - fst p1) / (snd p2 - snd p1) test data *Main> sortListByCoTangent (sortListByY [(1,2),(2,6),(3,10),(4,9),(5,10),(2,20),(6,15)]) [(1.0,2.0),(5.0,10.0),(2.0,6.0),(4.0,9.0),(6.0,15.0),(3.0,10.0),(2.0,20.0)] (1,0,2.0) is correct. That's the pivot point. It screws up from there. I suspect my insert is hosed, but I'm having difficulty analyzing the logic of the code. I'd like hints/help but with the following boundaries. (1) I want to stick with the parts of the language that's been introduced in the text so far. I know there are solutions that make this problem trivial, however using those misses the point. (2) I'd prefer going over the logic of my code, versus what is supposed to happen. I'm trying to learn how to troubleshoot haskell code, more than implement the graham scan algorithm. I appreciate any help/hints Michael Litchard *It seems the wikipedia page on the graham scan algorithm is wrong concerning the following part of the algorithm. "...instead, it suffices to calculate the tangent of this angle, which can be done with simple arithmetic." Someone from #haskell said that it's the cotangent I want, and my math tutor confirmed. If this is the case, I suppose we should submit a correction.