What Does the 3 in the Integral Notation \int{d^3 r} Represent?

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The notation \int{d^3 r} represents a triple integral, indicating integration over three dimensions. The "3" signifies that the integral is taken over a three-dimensional space, but it does not specify the coordinate system used. This notation is commonly used in physics and mathematics to simplify expressions involving volume integrals. It is not limited to spherical coordinates and can apply to Cartesian or other coordinate systems as well. Understanding this notation is essential for working with multi-dimensional integrals in various scientific fields.
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I saw this notation in a textbook but I'm a bit confused by it. What exactly does the 3 mean? Is it shorthand for a triple integral in spherical coordinates?

\int{d^3 r}

Thanks in advance.
 
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It means a triple integral, not necessarily in any particular coordinate system.
 

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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