The geodesic approximately ______ the angle between the counter (or reciprocal) normal sections lying closer to the direct normal section at a given point.

The geodesic approximately ______ the angle between the counter (or reciprocal) normal sections lying closer to the direct normal section at a given point.

• A. bisects
• B. trisects
• C. is perpendicular to
• D. is parallel to

Answer: (B)

Think of a point on a smooth surface and look at all the planes that pass through the surface normal. Each such plane cuts the surface in a normal section, and the tangent directions of those normal sections fill up the tangent plane around the point. If you take the two nearest normal sections to the one that is most aligned with the geodesic’s direction (the direct normal section), the tangents of those three nearby normal sections sit in the tangent plane at roughly equal angular spacing. The geodesic direction tends to sit in the middle of that small wedge, dividing the total angle between those nearby normal sections into three nearly equal parts. So, in this local picture, the geodesic approximately trisects the angle between the nearby counter normal sections.

Think of a point on a smooth surface and look at all the planes that pass through the surface normal. Each such plane cuts the surface in a normal section, and the tangent directions of those normal sections fill up the tangent plane around the point. If you take the two nearest normal sections to the one that is most aligned with the geodesic’s direction (the direct normal section), the tangents of those three nearby normal sections sit in the tangent plane at roughly equal angular spacing. The geodesic direction tends to sit in the middle of that small wedge, dividing the total angle between those nearby normal sections into three nearly equal parts. So, in this local picture, the geodesic approximately trisects the angle between the nearby counter normal sections.