Final answer:
The question analyzes mathematical patterns formed by arranging circle-like (˚ le) and square shapes in three-place value patterns. Patterns can be listed systematically and their organization can be structured to reveal unity and variety. This concept draws parallels with patterns used in art and design where elements interact to bring cohesiveness to a composition.
Step-by-step explanation:
The question pertains to the concept of patterns and organization within those patterns, in the context of mathematical combinations of shapes. The focus is on recording all possible three-place value patterns using only two specified shapes - circle-like (˚ le) and square. To approach this systematically, one must consider all permutations of these shapes over three places. Given only two shapes to work with, we can list the patterns in a structured order by following a sequence where we first fix one shape in the first position and then alternate the second shape in the remaining positions, and then move on to fix the first shape in the second position, and so forth.
For example, starting with the circle-like shape (le), we can have patterns like le-le-le, le-le-square, le-square-le, le-square-square, and then proceed by starting with a square, such as square-le-le, square-le-square, square-square-le, square-square-square. Patterns can be organized, and by doing so, they provide a sense of unity and variety, which are important concepts in both mathematical and artistic contexts.
Patterns do vary in shape but they also can be formed in an orderly fashion which brings an element of predictability and structure to otherwise random combinations. This principle is in line with how patterns are used in art and design - they can be colorful, faded, sharp, or curved, and they work together to bring unity to the overall work. In mathematics, patterns can help to discern a sense of order and organization within what might seem like a random jumble of elements.