Two Possible Positions For Point B
This animation examines a circle with center O and a fixed point A, revealing that a geometric angle of π/3 admits two valid positions, B₁ and B₂, placed symmetrically on either side of OA. Both satisfy the same angle magnitude, exposing a natural ambiguity in purely geometric angle definitions. The scene closes on the guiding question of how to select a single position, setting up the need for oriented angles. Useful for students and teachers building intuition before formally introducing signed or directed angle conventions.
16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Create a clean and rigorous mathematical animation. IMPORTANT: ALL visible text MUST be written in FRENCH. DO NOT use English anywhere. Continue exactly from the previous scene. Show the circle with center O, point A, and the two possible positions B₁ and B₂. Clearly show that both positions satisfy the same geometric angle of π/3, but they are located on opposite sides of OA. Do NOT introduce or define negative angles. Do NOT use −π/3. Do NOT define oriented angles yet. Do NOT introduce the notions of direct, indirect, positive or negative sense. The only objective of this scene is to create the following problem: « Deux positions possibles pour B… Comment choisir une seule position ? » End the animation on this question. Do not show the solution yet. Do not display coordinates or unnecessary algebraic formulas. Use precise geometry, smooth animation and a clean professional educational style.
Make the next one in this series
- Introduce the concept of oriented angles and how they resolve the B₁ versus B₂ ambiguity.
- Show how choosing a rotation direction (sens direct) determines a unique position for B.
- Compare geometric angles versus oriented angles using a rotating radius animation.
