Corner Fold - Basic
Corner Fold problems involve folding one corner of a square paper to another point (often the center or opposite corner). This creates a triangular folded region where the paper has 2 layers, while the rest remains single-layered. These problems test your ability to handle partial folds and reflection across diagonal crease lines.
What You'll Learn
Introduction to Corner Fold - Basic
Corner Fold problems involve folding one corner of a square paper to another point (often the center or opposite corner). This creates a triangular folded region where the paper has 2 layers, while the rest remains single-layered. These problems test your ability to handle partial folds and reflection across diagonal crease lines.
Prerequisites
How to Solve Corner Fold - Basic Problems
Step 1: Identify which corner is folded and where it is folded to
Step 2: The crease line is the perpendicular bisector of the segment connecting the corner and target point
Step 3: The folded region is a triangle (the corner area)
Step 4: Only the folded triangular region has 2 layers; rest has 1 layer
Step 5: If a hole is punched in the folded region, it creates 2 holes (original + reflection)
Step 6: If punched outside the folded region, it creates 1 hole
Step 7: The reflected hole appears at the original corner position
Example Problem
Example: Top-right corner folded to the center of the square. A hole is punched through the folded corner. Find the unfolded pattern. Solution: Step 1: Corner folded: top-right (100,0) to center (50,50) Step 2: Crease is perpendicular bisector - passes through (75,25) Step 3: Folded region is triangular area near the corner Step 4: Hole punched at the folded corner = at center (50,50) on folded paper Step 5: This is in the 2-layer folded region Step 6: Original hole: (50,50) Step 7: Reflection maps back to original corner (100,0) Step 8: Result: Two holes - one at center, one at top-right corner Answer: Two holes: one at center, one at original corner position
Pro Tips & Tricks
- When a corner is folded to the center, the crease goes through the midpoints of the adjacent sides
- The folded corner becomes the target point (e.g., center) in the folded state
- Hole at the folded corner in folded state → holes at target and original corner when unfolded
- The folded region is always a triangle bounded by the crease and two edges
- Outside the folded triangle, there is only 1 layer
- The reflection maps the folded region onto the opposite region
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Corner Fold - Basic. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Corner Fold - Basic is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Corner Fold - Basic?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: