Question

Which of the following statements CORRECTLY describe(s) a parallel fold?

• A. Inner and outer arcs of the folded layer have same curvature
• B. Dip isogons are parallel to the axial plane
• C. Orthogonal thickness of the folded layer is constant
• D. Dip isogons converge towards core of the fold

Hint:

A parallel fold keeps constant perpendicular layer thickness, with dip isogons converging toward the inner arc; a similar fold keeps constant curvature and has isogons parallel to the axial plane.

Answer 1

The Correct Option is C, D

Step 1: Start from the one rule that defines a parallel fold.
A parallel fold is built so that if you measure the layer thickness at right angles to the layer boundary, that number stays the same everywhere around the fold, limb or hinge. This single rule, constant orthogonal thickness, decides everything else about the fold's geometry.

Step 2: Work out what constant orthogonal thickness forces on the two arcs.
If the perpendicular gap between the outer and inner surface never changes, but the outer arc is longer than the inner arc (since it is the outside of the bend), the inner arc has to bend more sharply to keep pace. So the inner arc ends up with tighter curvature than the outer arc, they are not alike in shape.

Step 3: Work out what this does to dip isogons.
Dip isogons connect points of equal dip on the two arcs. Since the inner arc curves faster than the outer arc, these connecting lines are forced to lean inward and bunch up as they approach the core, so they converge towards the core rather than staying parallel to one another.

Step 4: Contrast quickly with the similar fold case, since two of the options describe that instead.
A similar fold instead keeps both arcs the same shape (same curvature) and keeps the axial plane parallel thickness fixed, and its isogons run parallel to the axial plane. Options (A) and (B) describe this similar fold behaviour, not the parallel fold asked about here, so they do not fit.

Step 5: Match the remaining options to what we derived.
Option (C), constant orthogonal thickness, is exactly the starting rule from Step 1. Option (D), isogons converging towards the core, is exactly what Step 3 worked out. Both fit a parallel fold.

Step 6: Conclude.
\[ \boxed{\text{Options C and D: constant orthogonal thickness and isogons converging towards the core}} \]