Final answer:
Geometric shapes are mathematically named with regular lines and curves, such as in Piet Mondrian's compositions. Organic shapes, in contrast, are freeform and irregular, resembling flowing forms found in nature and do not have a mathematical name.
Step-by-step explanation:
Shapes in art are categorized as either geometric or organic. Geometric shapes are mathematically named shapes with regular lines and curves, such as circles, triangles, and squares. These shapes have precise edges and can easily be defined by mathematical terms. Examples of artwork that employs geometric shapes include that of Piet Mondrian, who used straight vertical and horizontal lines to create rectangular forms in his compositions. On the other hand, organic shapes are freeform, irregular, and resemble the flowing forms found in nature. These shapes do not have a mathematical name and are often seen as more natural and less rigid than geometric shapes. Examples of organic shapes in art can be found in the depiction of natural elements like clouds, landscapes, and living organisms.
In conclusion, geometric shapes are mathematically named and found in structured, symmetrical artwork, while organic shapes are freeform and resemble elements found in the natural world.