Can You Find the True Center?

Finding the true center (the centroid) of a visually misleading shape is harder than it looks. This game shows you an irregular or weighted shape and asks you to click its geometric center of area. Unlike click-center, the shapes here are specifically designed to deceive: heavy lobes, thin tendrils, and concave notches all tug your intuitive estimate away from the mathematically correct spot.

How to Play

1. A visually complex shape appears. Take a moment to scan all of its edges.
2. Click once where you believe the centroid (area-weighted center) falls.
3. The true centroid is revealed and your pixel error is displayed.
4. Each difficulty level introduces shapes with more pronounced visual tricks.

Why It's Hard

Humans estimate centroids by weighting visible area, but we over-emphasize salient features like protruding lobes and sharp corners. Research on visual centroid estimation shows a consistent "extremity bias". We're pulled toward the most visually striking part of the shape rather than the averaged center of its total area.

Tips

• Squint slightly to blur the shape. The center of the resulting blob is closer to the true centroid.
• Ignore thin protrusions; they carry little area and should barely shift your estimate.
• On L-shaped or C-shaped figures, the centroid is often outside the visible solid area. Click in the "gap".

FAQ

What is the difference between centroid and center of mass?

For a uniform flat shape they are identical. Centroid is a purely geometric concept; center of mass requires knowing the object's density distribution. This game uses centroid.

Can the centroid fall outside the shape?

Yes, for concave shapes like crescents or C-shapes, the centroid lands in empty space. This is one of the core "tricks" in harder levels.

How many shapes are in the rotation?

The game procedurally generates irregular polygons, so the shape set is practically unlimited and different every round.