Foucault proved Earth's rotation with a public pendulum

By the mid-19th century, that the Earth rotates was mathematically well established through two centuries of astronomical observation and theory, but it remained a claim the general public had to take on the authority of astronomers and mathematicians — nothing about it was directly observable in ordinary daily life, since everything on the Earth's surface, including any observer, moves with it. A mathematical proof convinces mathematicians; it does nothing to make an invisible, counterintuitive phenomenon feel real or checkable to anyone else.

Léon Foucault built a mechanism that let the rotation demonstrate itself directly, without requiring the audience to trust anyone's authority or follow any calculation. A pendulum, once set swinging, keeps swinging in the same fixed plane relative to the universe outside — so if the floor beneath it visibly rotates relative to that fixed plane over the course of hours, the floor (and the planet it's built on) is what's turning, not the pendulum.

Built a pendulum whose swing plane stays fixed while the floor turns beneath it, making Earth's rotation visible to anyone watching.

The pendulum's swing plane stays fixed relative to the universe, so the floor's rotation becomes visible.

Sand tracing made the slow shift accumulate into a visible pattern over hours.

The public could watch the proof directly, bypassing the need to trust experts or understand math.

When experts' claims are doubted, build a demonstration that lets the phenomenon prove itself to laypeople.

The Panthéon demonstration drew immediate and sustained public and scientific attention, effectively ending a roughly two-century search for a direct experimental proof of Earth's rotation rather than an astronomical or mathematical inference of it, and Foucault pendulums were subsequently installed in science museums, universities and public buildings worldwide, where they remain a standard permanent exhibit for exactly the same demonstrative purpose more than 170 years later.