How does one define a sigmoidal function

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A sigmoidal function is characterized by its S-shaped curve, typically defined by its inflection point where the curve changes concavity. To classify a curve as a sigmoid, it must exhibit specific mathematical properties, including a bounded range and a gradual approach to its asymptotes. While a skewed S-shaped curve may resemble a sigmoid, it does not meet the strict criteria unless it retains the essential properties of a standard sigmoid function. The discussion emphasizes the importance of understanding these constraints to accurately define and identify sigmoidal functions. Accurate classification is crucial for modeling purposes in various applications.
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I am trying to model a 'perturbation function' and I finally arrive at a S-shaped graph,which I later found was called a 'sigmoid'. Is a sigmoid defined based on its inflection point? How does one classify a curve as a 'sigmoid'?
Can i say that a certain function f is a sigmoid just because it has a S-shaped curve?What about skewed S-shaped curves?Are they sigmoids also?
What are the constraints?
 
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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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