A folding fan shown in the image is made of bamboo and paper painted on one side. Which option is the closest representation of the same fan in the folded position? (dotted lines indicate the folds)
Show Hint
In folding problems, always identify which surface or edge will be visible in the final state. Trace the pattern on that specific part of the unfolded object to determine the appearance of the folded object.
Step 1: Understanding the Concept:
This question requires visualizing the process of folding a fan and determining what the resulting compressed object looks like from the side. The final view will be a stack of the folded segments, and the visible pattern will be determined by the pattern on the outermost segment.
Step 2: Key Formula or Approach:
1. Identify the direction of the folds. A fan typically folds like an accordion.
2. Identify which segment will be on the "top" of the folded stack. This will be the rightmost segment in this depiction.
3. Analyze the pattern on this top segment. This pattern will be what is visible on the side of the folded fan.
4. Consider the overall shape and how the colors would appear in a compressed stack.
Step 3: Detailed Explanation:
Let's analyze the pattern on the fan, segment by segment, from right to left, as the rightmost segment will be on top when folded.
The fan is painted with several concentric bands of color and patterns. Let's focus on the rightmost fold section.
The outermost band is dark purple with white circles.
The next band is a lighter magenta color.
The next band is a pattern of white semi-circles on a dark purple background.
This is followed by a plain magenta band.
The pattern continues towards the pivot.
When the fan is folded, all these segments are stacked on top of each other. The side view will show a cross-section of this stack. The visible edge of the paper will show these colored bands as stripes.
Let's trace the pattern from the outside edge inwards on the folded view:
1. The very edge should be the dark purple with white circles. This will appear as a purple stripe with white dots.
2. Next should be the magenta stripe.
3. Next is the dark purple stripe with the white semi-circles pattern.
4. Next is another magenta stripe.
5. ...and so on.
Now, let's compare this expected pattern with the options:
(A) The order of colors is incorrect. It starts with magenta.
(B) This option shows the correct sequence of stripes from right to left (corresponding to the outer edge to the inner part of the fan): Dark purple with white dots, then magenta, then the purple with white semi-circles, then magenta again. This correctly represents the pattern on the outermost segment.
(C) The order of colors and patterns is incorrect.
(D) The order of colors and patterns is incorrect.
Step 4: Final Answer:
By analyzing the pattern on the outermost segment of the fan, which becomes the visible side when folded, we can conclude that option (B) is the only one that correctly represents the sequence of colored bands.
