Updated the typesetting for the exercises, and added cheat sheets to …

…the launcher.

content/exercises/spider1.ipynb

@@ -225,23 +225,23 @@
    "source": [
     "## Exercises\n",
     "\n",
-    "1. add a second point called point2, and render it in a different color. (Hint, select a hex number to get a color selector)\n",
-    "2. create a second line called line2, by joining (& = join) point1 to point2.\n",
-    "3. create a third point called point3 by intersecting (^ = meet) line1 and line2.\n",
-    "4. calculate line2 and point3 inside graph, so they update when you drag point1 and point2.\n",
-    "5. change line1 so that it is no longer through the origin\n",
-    "   (Hint, lines through the origin have e0 = 0)\n",
-    "6. calculate a point called point4 by reflecting point1 in line1. (>> = sandwich!)\n",
-    "7. calculate a line called line3 that is orthogonal to line1 and through point4 (| = dot)\n",
-    "8. calculate a line called line4 that is halfway between line2 and line3. (...normalize!)\n",
+    "1. add a second point called `point2`, and render it in a different color. (Integers are interpreted as hexadecimal colors.)\n",
+    "2. create a second line called `line2`, by joining (`&` = join) point1 to point2.\n",
+    "3. create a third point called `point3` by intersecting (`^` = meet) `line1` and `line2`.\n",
+    "4. calculate `line2` and `point3` inside `graph_func`, so they update when you drag `point1` and `point2`.\n",
+    "5. change `line1` so that it is no longer through the origin\n",
+    "   (Hint, lines through the origin have `e0 = 0`)\n",
+    "6. calculate a point called `point4` by reflecting `point1` in `line1`. (`>>` = group conjugation aka sandwich)\n",
+    "7. calculate a line called `line3` that is orthogonal to `line1` and through `point4` (`|` = dot)\n",
+    "8. calculate a line called `line4` that is halfway between `line2` and `line3`.\n",
     "   (Hint the normalized version of `x` is written `x.normalized()`)\n",
     "\n",
     "Self-Reflection - we've learned :\n",
     "1. how to create points and lines directly. (dual operator for points)\n",
-    "2. how to create points by meeting ^ lines and lines by joining & points.\n",
-    "3. how to find orthogonal elements with the dot | product.\n",
-    "4. how to apply >> a reflection in a line\n",
-    "5. how to use addition + to find the bisector of two (.normalized()) lines. \n",
+    "2. how to create points by meeting `^` lines and lines by joining `&` points.\n",
+    "3. how to find orthogonal elements with the dot `|` product.\n",
+    "4. how to apply `>>` a reflection in a line\n",
+    "5. how to use addition `+` to find the bisector of two (`.normalized()`) lines. \n",
     "\n",
     "BONUS\n",
     "1. Change the algebra from 2D to 3D PGA on line 10. Study what happens !"
@@ -296,7 +296,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.15"
+   "version": "3.12.8"
   }
  },
  "nbformat": 4,

content/exercises/spider2.ipynb

@@ -247,19 +247,19 @@
    "source": [
     "## Exercises\n",
     "\n",
-    "1. create and render triangle2 by reflecting triangle1 in L1\n",
+    "1. create and render `triangle2` by reflecting `triangle1` in `L1`\n",
     "   (Hint: recall that the triangle is just a list of points, so each point must be transformed seperatelly.)\n",
-    "2. create and render triangle3 by reflecting triangle2 in L2\n",
-    "3. now change the creation of triangle3 by first multiplying L2 and L1, then applying that to triangle1.\n",
-    "4. (L2*L1) is a bireflection, drag the points to see how you can use this to make :\n",
+    "2. create and render `triangle3` by reflecting `triangle2` in `L2`\n",
+    "3. now change the creation of `triangle3` by first multiplying `L2` and `L1`, then applying that to `triangle1`.\n",
+    "4. (`L2*L1`) is a bireflection, drag the points to see how you can use this to make :\n",
     "- A)  the identity operation.\n",
     "- B)  any rotation\n",
     "- C)  any translation\n",
     "- D)  Note how the resulting translation/rotation is twice that between the original reflections!\n",
-    "5. create a line L3 by normalizing the sum of (normalized) L1 and L2. (observe this is indeed always the bisector)\n",
-    "6. create triangle4 by applying (L3*L1) to triangle;\n",
-    "7. create triangle5 by applying P2 to triangle1.\n",
-    "8. How do you have to move L2 so that triangle5 and triangle3 overlap?\n",
+    "5. create a line L3 by normalizing the sum of (normalized) `L1` and `L2`. (observe this is indeed always the bisector)\n",
+    "6. create `triangle4` by applying `(L3*L1)` to triangle;\n",
+    "7. create `triangle5` by applying `P2` to `triangle1`.\n",
+    "8. How do you have to move `L2` so that `triangle5` and `triangle3` overlap?\n",
     "\n",
     "## Self-reflection: We've learned ...\n",
     "\n",
@@ -273,9 +273,9 @@
     "\n",
     "Note - this is a difficult question - we have not covered the details needed for this.\n",
     "\n",
-    "1. Change the dimensionality of the algebra from 2 to 3. Why is triangle3 still there but triangle4 isn't?\n",
-    "2. Try to fix it (hint: first render (L2|alg.blades.e012.dual())) - in 2D e012.dual(), or the dual of the pseudoscalar is\n",
-    "   just the scalar '1' - but in 3D it represents the plane we are working in - an assumption\n",
+    "1. Change the dimensionality of the algebra from 2 to 3. Why is `triangle3` still there but `triangle4` isn't?\n",
+    "2. Try to fix it (hint: first render `(L2|alg.blades.e012.dual()))` - in 2D `e012.dual()`, or the dual of the pseudoscalar is\n",
+    "   just the scalar `1` - but in 3D it represents the plane we are working in - an assumption\n",
     "   we must formalize for things to keep working unmodified."
    ]
   },
@@ -328,7 +328,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.15"
+   "version": "3.12.8"
   }
  },
  "nbformat": 4,

content/exercises/spider3.ipynb

@@ -258,15 +258,15 @@
    "source": [
     "## Exercises:\n",
     "\n",
-    "1. Create the rotor R that spins around P1 with the formula $e^{- t P_1 / 2}$, which in kingdon code is `(-0.5 * time * P1).exp()`.\n",
-    "2. Create and render triangle2 by Applying (>>) R to triangle.\n",
-    "   -> Drag point P1 around!\n",
-    "3. Create a line L2 by dotting L1 with any point (use P1 or the origin)\n",
-    "4. Create a point at infinity called P2 by intersecting 1e0 (the infinite line) with L2.normalized().\n",
+    "1. Create the rotor `R` that spins around `P1` with the formula $e^{- t P_1 / 2}$, which in kingdon code is `(-0.5 * time * P1).exp()`.\n",
+    "2. Create and render `triangle2` by Applying (`>>`) $R$ to triangle.\n",
+    "   -> Drag point `P1` around!\n",
+    "3. Create a line `L2` by dotting `L1` with any point (use `P1` or the origin)\n",
+    "4. Create a point at infinity called `P2` by intersecting `e0` (the infinite line) with `L2.normalized()`.\n",
     "   -> Note that we would find the same infinite point no matter which point we pick in step 3.\n",
-    "5. Create a translator T along L1 with the formula $e^{- t P_2 / 2}$, which in kingdon code is `(-0.5 * time * P2).exp()`\n",
+    "5. Create a translator `T` along `L1` with the formula $e^{- t P_2 / 2}$, which in kingdon code is `(-0.5 * time * P2).exp()`\n",
     "   -> translating is just like rotating, but 'around' infinite points.\n",
-    "6. Create and render triangle3 by applying T to triangle.\n",
+    "6. Create and render `triangle3` by applying `T` to triangle.\n",
     "\n",
     "## Self-reflection: we have learned \n",
     "\n",
@@ -338,7 +338,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.15"
+   "version": "3.12.8"
   }
  },
  "nbformat": 4,

jp_app_launcher_config.yaml

@@ -6,6 +6,21 @@
   type: markdown
   catalog: Other
 
+- title: 2DPGA Cheat Sheet
+  source: https://bivector.net/2DPGA.pdf
+  type: url
+  catalog: Other
+  args:
+    createNewWindow: true
+
+- title: 3DPGA Cheat Sheet
+  source: https://bivector.net/3DPGA.pdf
+  type: url
+  catalog: Other
+  args:
+    createNewWindow: true
+
+
 # 2DPGA
 
 - title: Distances and Angles