feat(fourier): add epicycles algorithm demo

Draw a shape or pick a preset, then rebuild it with a direct DFT.
Each frequency becomes one circle. Circles are sorted by radius, and
the circles slider keeps the biggest N. Also tick the ROADMAP item and
add the FOURIER SEO key.

src/assets/i18n/en.json

@@ -618,6 +618,10 @@
       "TITLE": "Four Color Theorem",
       "DESCRIPTION": "The four color theorem states that any map in a plane can be colored using at most four colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color."
     },
+    "FOURIER": {
+      "TITLE": "Fourier Epicycles",
+      "DESCRIPTION": "Any closed shape is drawn by a chain of rotating circles. Draw your own shape and watch the circles rebuild it with a discrete Fourier transform."
+    },
     "FRACTAL": {
       "TITLE": "Fractals",
       "DESCRIPTION": "Visualisation of complex geometric patterns that resemble each other on increasingly smaller scales (self-similarity)."
@@ -669,6 +673,26 @@
       "NO_SOLUTION": "No solution found (this should not happen for a planar map!)."
     }
   },
+  "FOURIER": {
+    "TITLE": "Fourier Epicycles",
+    "DRAW_HINT": "Draw a closed shape on the canvas or pick a preset",
+    "PRESET_HEART": "Heart",
+    "PRESET_STAR": "Star",
+    "PRESET_SQUARE": "Square",
+    "CIRCLES": "Circles",
+    "SPEED": "Speed",
+    "SHOW_CIRCLES": "Show circles",
+    "HIDE_CIRCLES": "Hide circles",
+    "EXPLANATION": {
+      "TITLE": "Fourier Series",
+      "EXPLANATION": "A Fourier series says that any periodic curve is a sum of rotating circles. Each circle has its own radius, speed and start angle.",
+      "DISCLAIMER": "This demo does it in three steps.",
+      "DISCLAIMER_1": "Your shape is resampled to 256 equally spaced points.",
+      "DISCLAIMER_2": "Each point is a complex number x + iy. A direct discrete Fourier transform gives one circle per frequency.",
+      "DISCLAIMER_3": "The circles are sorted by radius. The slider keeps only the biggest N circles.",
+      "DISCLAIMER_BOTTOM": "Fewer circles give a smoother approximation. With all circles the curve passes exactly through all 256 points."
+    }
+  },
   "STOPWATCH": {
     "TITLE": "Stopwatch",
     "START": "Start",
@@ -705,6 +729,10 @@
       "TITLE": "Algorithms – Andreas Dahm",
       "DESCRIPTION": "Interactive visualizations of algorithms and simulations: pathfinding, sorting, fractals, cloth and pendulum physics, running in the browser."
     },
+    "FOURIER": {
+      "TITLE": "Fourier Epicycles – Andreas Dahm",
+      "DESCRIPTION": "Interactive Fourier epicycles: draw a closed shape and watch a chain of rotating circles trace it with a discrete Fourier transform."
+    },
     "IMPRINT": {
       "TITLE": "Imprint – Andreas Dahm",
       "DESCRIPTION": "Legal information and contact details for the Andreas Dahm Playground website."