Multiplication of more than 3 factors (Associativity)?

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This is an elementary math question. How to interpret multiplication of positive integers geometrically when the number of factors exceed three?

length * width (area of a rectangle)

length * width * height It's visible that the ordering doesn't matter in the calculation of 3-dimensional volume

But what about 4 factors? How to see that?

It's harder to see the associative property.

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You can do geometry in more than three dimensions, using algebraic tools to describe structures.

To specify a point in the plane you use two numbers, traditionally named "$x$" and "$y$". Then you can describe a rectangle algebraically and calculate its area as the product of difference between corner values of $x$ (the "length") and the corresponding difference for $y$ (the "width").

For three dimensions you use one more coordinate, and call that the "height".

It's clear how to generalize this to any number of dimensions, although we don't have names for those new dimensions. You can't "see" them in the way we see three dimensional objects like boxes.

See What's new in higher dimensions? .

(Associativity is not a problem in these calculations - it's just the ordinary associativity of multiplication of numbers.)