Undergrad Vector Functions: v(r) Explained

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In vector calculus, the function v(r) is equivalent to v(x,y,z) in Cartesian coordinates. When using spherical coordinates, the function is expressed as v(r, θ, φ). This distinction is crucial for understanding how vector functions are represented in different coordinate systems. The transformation between these coordinate systems is fundamental in fields such as physics and engineering. Proper comprehension of these representations aids in solving complex problems involving vector fields.
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Is v(r) ≡ v(x,y,z)
 
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Yes, in cartesian coordinates. In spherical coordinates it is v(r, θ, φ) and so on.
 

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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