added pi example (#711)

docs/examples.md

@@ -28,6 +28,12 @@ Here are some fun programs for your @boardname@!
   "description": "Simulation in LEDs. Use button A for next stage. Button B for reset.",
   "url":"/examples/gameofLife",
   "cardType": "example"
+},
+{
+  "name": "Pi Monte Carlo",
+  "description": "Approximate the number Pi",
+  "url": "/examples/pi",
+  "cardType": "example"
 }
 ]
 ```

docs/examples/pi-montecarlo.md

@@ -0,0 +1,53 @@
+# Pi Monte Carlo
+
+Approximate the value of **pi** using your @boardname@!
+
+```blocks
+let pir = 0
+let pid = 0
+let y = 0
+let pin = 0
+let x = 0
+let r2 = 0
+let r = 0
+let inside = 0
+let n = 0
+// A simple Monte-Carlo simulation to approximate Pi.
+//
+// number of points
+//
+n = 1000000
+// radius of the circle
+r = 4000
+// radius square
+r2 = r * r
+basic.forever(() => {
+    inside = 0
+    for (let i = 0; i < n; i++) {
+        // generate a point within the square
+        x = Math.random(r + 1)
+        y = Math.random(r + 1)
+        // test if the point is within the circle
+        // sqrt(x**2 + y**2) < r ==> x**2 + y**2 < r**2
+        if (x * x + y * y < r2) {
+            inside += 1
+        }
+    }
+    // surface of a square: 4 * r * r surface of a circle:
+    // r * r * pi => inside / n ~= (r*r*pi) / (4*r*r) ~=
+    // pi / 4 pi = inside / n * 4
+    pin = inside * 4
+    // only integer arithmetic here...
+    pid = pin / n
+    pir = pin % n
+    // show results
+    basic.showLeds(`
+        # # # # #
+        . # . # .
+        . # . # .
+        . # . # .
+        . # . . #
+        `)
+    basic.showString(" " + pid + "." + pir)
+})
+```

docs/packages.md

@@ -11,6 +11,10 @@
   "name": "NeoPixel",
   "url":"/pkg/microsoft/pxt-neopixel",
   "cardType": "package"
+},{
+  "name": "micro:turtle",
+  "url":"/pkg/microsoft/pxt-microturtle",
+  "cardType": "package"
 },{
   "name": "MAX6675",
   "url":"/pkg/microsoft/pxt-max6675",