Ethan’s 29 Points by Hand 🟣
Before he knew the word “ellipse,” Ethan discovered it by construction—one point at a time.
🖐️ Hand Construction (Pencil & Compass)
When Ethan was in Grade 4, he was given a simple geometric rule: find all points whose total distance to two fixed points is constant.
Without formal terminology, he simply followed the constraint and began marking points: P₁, P₂, …, P₂₉. The result was not complete—but already suggestive.
Even in partial form, the structure began to emerge: a smooth curve forming from discrete human effort.
💻 Transition to Computation
Later, Ethan recreated the same idea in code. Instead of manually placing points, an iOS simulation generated the full set automatically.
Each point was connected back to the two fixed foci, making the defining rule visible: constant sum of distances.
🧠 What This Exhibit Shows
This is not about naming a curve. It is about discovering a constraint that generates a shape.
- Constancy becomes geometry
- Repetition becomes structure
- Discrete points become a continuous curve
Ethan experienced the same object twice—first through hand construction, then through computation.
🌙 Curator’s Note
He didn’t just learn what an ellipse is. He discovered how a rule becomes a shape.