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.

Ethan ellipse pencil sketch 0
Ethan ellipse pencil sketch 1

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.

Ethan ellipse iOS simulation

🧠 What This Exhibit Shows

This is not about naming a curve. It is about discovering a constraint that generates a shape.

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.


LM-0009 · Ethan’s 29 Points by Hand 🟣
Living Museum of Learning