Final answer:
A picture and the board it is mounted on are not mathematically similar because their corresponding sides do not have the same proportions, with the board generally having extra space around the picture that alters the length-to-width ratio. Additionally, artistic elements like tension and abstractness in images disrupt dimensional consistency that similarity requires.
Step-by-step explanation:
To show that a picture and the board it is mounted on are not mathematically similar, we must understand similarity in a mathematical context. For two figures to be similar, they must have the same shape but not necessarily the same size, meaning their corresponding angles are equal, and their corresponding sides are in proportion. When we mount a picture on a board, the picture itself has dimensions that are different from that of the board - the board is usually larger to provide a border or frame around the picture. Since the additional border provided by the board changes the overall dimensions, the two objects cannot be considered mathematically similar.
The concept of similarity also involves dimensional consistency. If the picture and the board were to be similar, the ratio of the length to width in the picture would have to be the same as that of the board. However, in most scenarios, a picture needs to be mounted with additional space around it, thus altering the ratio.
Additionally, from an artistic point of view, tension within a painting or an abstract representation might disrupt the dimensional consistency that mathematical similarity requires. Various factors such as perspective can create a visual illusion that skews perceived dimensions, making it impossible for the two to be similar. When a picture includes a pattern that has a specific repetition with variation, it does not satisfy the conditions of mathematical similarity when placed on a uniform board.