Isoperimetric Area Budget
Spend an equal perimeter on different shapes and compare the enclosed areas.
Free theory articleSpend an equal perimeter on different shapes and compare the enclosed areas.
Concept & interpretation
The isoperimetric theorem states that among all planar shapes with a given perimeter, the circle encloses the maximum possible area.
Compare areas for a fixed perimeter
Open Isoperimetric Area Budget to experiment with different shapes.
- Set the Perimeter to 2 and Shape to 4 (a square). Observe the area is 0.25 and the area deficit from a circle is about 0.0683.
- Change the Shape to a Circle. Notice the area reaches the circle bound of ≈ 0.3183, and the deficit drops to 0. The quotient is exactly 1.
- Increase the Perimeter to 4 and choose Shape 6 (hexagon). The area is ≈ 1.1547 compared to a circle bound of ≈ 1.2732.