done

src/Main.elm

@@ -8,6 +8,7 @@ import Tuple exposing (first, second)
 
 type alias Memory =
     { dx : Number
+    , count : Int
     }
 
 
@@ -26,6 +27,7 @@ type alias Coords =
 init : Memory
 init =
     { dx = 0.8
+    , count = 0
     }
 
 
@@ -53,6 +55,11 @@ view computer memory =
             placeCornerAtCoords computer bounds
 
         fx x = x * x * x / 32 / 32
+        corner = case memory.count // 30 of
+            0 ->
+                TopLeft
+            1 -> TopRight
+            _ -> TopLeft
     in
     List.append
         (makeRectangles computer atCorner fx bounds memory [])
@@ -60,12 +67,59 @@ view computer memory =
             List.append
                 (makeCircles computer fx bounds memory [])
                 ([ P.words black "Welcome to my math project! Use arrow keys to adjust the width of each rectangle."
-                    |> at ( (bounds.xmax - bounds.xmin) / 2, bounds.ymax - 1)
+                    |> at ( (bounds.xmax - bounds.xmin) / 2, bounds.ymax - 0.5)
                 , P.words black ("The current dx is " ++ (String.fromFloat memory.dx))
+                    |> at ( (bounds.xmax - bounds.xmin) / 2, bounds.ymax - 1)
+                , P.words black ("The current approximation is " ++ (String.fromFloat <| (\n->n/32/32) <| getArea computer corner fx bounds memory))
+                    |> at ( (bounds.xmax - bounds.xmin) / 2, bounds.ymax - 1.5)
+                , P.words black ("The real area under the curve is thus about " ++ (String.fromFloat 898))
                     |> at ( (bounds.xmax - bounds.xmin) / 2, bounds.ymax - 2)
                 ])
 
 
+fillLeftFxs : Computer -> (Number -> Number) -> Bounds -> Memory -> List Number -> List Number
+fillLeftFxs computer fx bounds memory fxs =
+    let
+        xcoord = toFloat (List.length fxs) * memory.dx
+        ycoord = fx xcoord
+        widthOfCell = computer.screen.width / (bounds.xmax - bounds.xmin)
+        newVal = memory.dx * widthOfCell * ycoord * widthOfCell
+    in
+    if memory.dx + memory.dx * (toFloat <| List.length fxs) < bounds.xmax then
+        fillLeftFxs computer fx bounds memory <| List.append fxs <| [newVal]
+    else
+        List.append fxs <| [(bounds.xmax - memory.dx * (toFloat <| List.length fxs)) * widthOfCell * ycoord * widthOfCell]
+
+
+
+fillRightFxs : Computer -> (Number -> Number) -> Bounds -> Memory -> List Number -> List Number
+fillRightFxs computer fx bounds memory fxs =
+    let
+        xcoord = toFloat (List.length fxs) * memory.dx
+        ycoord = fx <| memory.dx + xcoord
+        widthOfCell = computer.screen.width / (bounds.xmax - bounds.xmin)
+        newVal = memory.dx * widthOfCell * ycoord * widthOfCell
+    in
+    if memory.dx + memory.dx * (toFloat <| List.length fxs) < bounds.xmax then
+        fillRightFxs computer fx bounds memory <| List.append fxs <| [newVal]
+    else
+        List.append fxs <| [(bounds.xmax - memory.dx * (toFloat <| List.length fxs)) * widthOfCell * ycoord * widthOfCell]
+
+
+getArea : Computer -> Corner -> (Number -> Number) -> Bounds -> Memory -> Number
+getArea computer corner fx bounds memory =
+    let
+        fxs0 = fillLeftFxs computer fx bounds memory []
+        fxs1 = fillRightFxs computer fx bounds memory []
+    in
+    case corner of
+        TopLeft ->
+            List.sum fxs0
+        TopRight ->
+            List.sum fxs1
+                
+        
+
 
 makeCircles : Computer -> (Number -> Number) -> Bounds -> Memory -> List Shape -> List Shape
 makeCircles computer fx bounds memory prev =
@@ -92,12 +146,19 @@ makeRectangles computer atCorner fx bounds memory prev =
         xcoord = toFloat (List.length prev) * memory.dx
         ycoord = fx xcoord
         widthOfCell = computer.screen.width / (bounds.xmax - bounds.xmin)
+        corner = case (memory.count // 30) of
+            0 ->
+                TopLeft
+            1 ->
+                TopRight
+            _ ->
+                TopLeft
         newRec = 
             rectangle red (memory.dx * widthOfCell) (ycoord * widthOfCell)
-                |> atCorner (xcoord, ycoord) TopLeft (memory.dx, ycoord)
+                |> atCorner (xcoord, ycoord) corner (memory.dx, ycoord)
     in
     if
-        xcoord < bounds.xmax
+        xcoord - memory.dx < bounds.xmax
     then
         makeRectangles computer atCorner fx bounds memory <| List.append prev [ newRec ]
 
@@ -125,6 +186,14 @@ update computer memory =
                         |> (*) step
                         |> (+) threshold
             )) / toFloat 100
+        , count =
+                if memory.count <= 0 then
+                    memory.count + 50
+                else
+                    if memory.count >= 60 then
+                        memory.count - 50
+                    else
+                        (+) memory.count <| round <| toY computer.keyboard
     }
 
 
@@ -150,7 +219,7 @@ placeAtCoords computer bounds (x, y) shape =
         shape
 
 
-type Corner = TopLeft | TopRight | BottomLeft | BottomRight
+type Corner = TopLeft | TopRight
 
 placeCornerAtCoords : Computer -> Bounds -> Coords -> Corner -> (Number, Number) -> Shape -> Shape
 placeCornerAtCoords computer bounds (x, y) corner (width, height) shape =
@@ -161,8 +230,4 @@ placeCornerAtCoords computer bounds (x, y) corner (width, height) shape =
                     (x + width / 2, y - height / 2)
                 TopRight ->
                     (x - width / 2, y - height / 2)
-                BottomLeft ->
-                    (x + width / 2, y + height / 2)
-                BottomRight ->
-                    (x - width / 2, y + height / 2)
             )