Multilinear Functions and Polynomials

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A function is classified as multilinear if it is linear in each variable. Any function defined on the n-dimensional hypercube with values of 0 or 1 has a unique multilinear extension to all of R. This extension is not considered a polynomial in the traditional sense, as a "linear function" is inherently a polynomial. Therefore, the term "multilinear polynomial" is redundant, as all multilinear functions are polynomials. The discussion concludes that there cannot be a multilinear function that is not a multilinear polynomial.
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A function f : \mathbf{R}^n\rightarrow\mathbf{R} is multilinear if it's linear in every variable. Is there a multilinear function that's not a multilinear polynomial?

Given a function defined on the n dimensional hypercube, values of which are 0 or 1, there is a unique multilinear extension to all of R. Is this extension a polynomial?
 
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No, a "linear function" is a polynomial, by definition, so any multilinear function is a polynomial. Saying "multilinear polynomial" is redundant.
 

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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