Step 1: Understanding the Question:
We need to identify which of the four designs for eyeglasses could be constructed from a single, continuous piece of wire without any breaks. This involves tracing the path of the wire to see if it's possible to form the entire shape in one continuous line. The key is to look for smooth, continuous bends versus sharp junctions that imply separate, welded pieces.
Step 2: Detailed Analysis of Each Option:
A: This design shows a top bar (brow bar and arms) to which two separate circular lens frames are attached. The junctions where the circles meet the top bar are T-junctions, indicating that this is an assembly of at least three pieces. It cannot be made from a single wire.
B: In this design, the arms appear to join the lens frames at sharp angles, suggesting a weld or joint rather than a continuous bend of the wire. The connections look like T-junctions, making it unlikely to be a single piece of wire.
C: This design can be traced as a single continuous path. For example: Start at the left earpiece, the wire moves forward to form the complete loop of the left lens frame, continues from the inner side of the loop to form the nose bridge, then forms the complete loop of the right lens frame, and finally extends from the outer edge to become the right earpiece. The transitions are smooth curves, making it plausible as a single wire construction.
D: This design can also be formed by a single wire. A possible path is: Start at the left earpiece, the wire forms the top brow bar, curves down to form the outer edge, bottom, and inner edge of the left lens frame, continues across to form the nose bridge, then forms the inner edge, bottom, and outer edge of the right lens frame, curves up to form the top right brow bar, and then continues to form the right earpiece. The corners can be interpreted as continuous bends, making a single-wire construction feasible.
Step 3: Final Answer:
Based on the analysis of the wire path and the nature of the connections, the glasses in options (C) and (D) can be created using a single continuous wire. The designs in (A) and (B) appear to be assembled from multiple pieces.