Hans Walser, [20260619]

Invariant Area

Suggestion: M. K., V.

1 Parabolic Lens

The lens (Fig. 1) is bounded by two parabolas whose vertices are perpendicular to each other and are a constant distance apart.

Fig. 1: Invariant Area

2 Invariant Area

The yellow area remains invariant.

3 Proofs

Calculation.

Affine distortion.

Cavalieri's Principle (Fig. 3).

Fig. 2: Cavalieri's Principle