Gradient in cylindrical coordinates

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The discussion focuses on deriving the gradient of a scalar function in cylindrical coordinates, transitioning from R^3 to R. Participants reference specific methods outlined in posts #3-4 of the linked Physics Forums thread. Key points include the importance of understanding the coordinate transformation and applying the appropriate mathematical formulas. The conversation emphasizes the need for clarity in notation and the significance of each component in the gradient. Ultimately, mastering the gradient in cylindrical coordinates is crucial for various applications in physics and engineering.
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How can you derive the gradient of a vector R^3 to R in cylindrical coordinates?
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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