> ELLIPTICAL CIPHER
The idea in plain English: An ellipse is an oval shape defined by a few numbers: how wide it is (semi-major axis a), how tall it is (semi-minor axis b), how squashed it is (eccentricity e), and how much it's rotated (angle θ). Each ellipse's parameters can encode a letter or number. Read the parameter values from each ellipse, convert to ASCII, and you get the hidden message. Like reading labels off a set of differently-shaped ovals.
Why this really exists: Ellipses describe the orbits of planets (Kepler's laws), the shape of satellite dishes and radio telescopes, and the cross-section of many manufactured objects. The elliptical shape is fundamental to orbital mechanics — every satellite, moon, and planet follows an elliptical orbit. Engineers use ellipse parameters daily when designing reflective surfaces, gears, and optical systems.
▸ Concrete Example
3 ellipses with their semi-major axis values:
Ellipse 2: a=76, b=79, rot=45°
Ellipse 3: a=82, b=68, rot=90°
Read the 'a' values: 72→'H', 76→'L', 82→'R'
Read the 'b' values: 69→'E', 79→'O', 68→'D'
→ "HELLO" combined from a and b in sequence
The puzzle data tells you which parameter carries the message and in what order.
▸ How to Decode (Step by Step)
1. Get ellipse parameters from the puzzle data (a, b, eccentricity, angle)
2. Read the specified parameter from each ellipse
3. Round to nearest integer and convert to ASCII
4. Join → the answer word
word = ''.join(chr(int(round(p))) for p in params)
▸ Real-World Applications
- Planetary orbits: Kepler discovered that planets orbit in ellipses with the Sun at one focus
- Satellite dishes: Parabolic and elliptical dishes focus signals at specific points
- GPS: Satellite orbits are calculated using elliptical orbital mechanics
- Engineering: Gears, camshafts, and many mechanical parts have elliptical cross-sections