Q14 - Geometry

Question

Surveyors and photographers use a tripod for support.

Explain why a four-legged table may rock even if the floor is level.

Step-by-Step Solution

Answer

A four-legged table may rock even if the floor is level because, in the four-legged table, there can be a combination of the planes on which the table is stable, and due to the combinations of these different planes, the four-legged table will rock.

Step 1. Description of four legged support.

The four-legged support has four legs that touch the base plane at four points.

Step 2. Stability of four legged support.

The three-legged support is more stable than four-legged because the three-legged touches the base plane at three points which are non-collinear therefore a unique plane can pass through these three non-collinear points while in four-legged support, the four-legged support touches the base plane at four non-collinear planes, therefore, more than one plane can pass through these four non-collinear planes. Therefore, the four-legged support is unstable.

Step 3. Reason why a four-legged table may rock even if the floor is level.

A four-legged table may rock even if the floor is level because, in the four-legged table, there can be a combination of the planes on which the table is stable, and due to the combinations of these different planes, the four-legged table will rock.