Some of them are Demographics, to forecast population growth; physicists and engineers, to work with mathematical functions that include geometric sequences; mathematicians; teachers of mathematics, science, and engineering; and farmers and ranchers, to predict crop growth and corresponding revenue growth.
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There aren't any. Geometric is an adjective and you need a noun to go with it before it is possible to consider answering the question. There are geometric sequences, geometric means, geometric theories, geometric shapes. I cannot guess what your question is about.
Although there is no precise synonym for geometric, in some cases you might use Euclidean.
By definition, yes. Any shape is a geometric shape.
no
The use of geometric shapes in painting is used in abstract art. Abstraction indicates a departure from reality in depiction of imagery in art.