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The School of Athens by Raphael in the Apostolic Palace, Vatican City. Source: YouTube.com.

The School of Athens and Geometry
The School of Athens was painted by Raphael Sanzio or Raffaello Santi (1483-1520) for Pope Julius II (1503-1513) as a part of Raphael's commission to decorate with frescoes the rooms that are now known as the Stanze di Raffaello, in the Apostolic Palace in the Vatican. In this fresco.

Geometry plays a significant role in The School of Athens beyond just its representation of the pursuit of knowledge. The architecture of the building depicted in the painting is based on the principles of classical Greek and Roman architecture, which also relied heavily on geometric forms and ratios.

For example, the arches and columns in the painting are based on precise geometric proportions, such as the Golden Ratio, which was believed to embody a sense of beauty and harmony. The use of such precise mathematical ratios and proportions in the architecture of the building is a testament to the value that was placed on geometry during the Renaissance.

In the foreground of the painting, we see several figures engaged in activities related to geometry. For example, one figure is holding a compass, while another is holding a set square. These tools were commonly used in geometry during the Renaissance, which was a period of renewed interest in classical learning and ancient philosophy.

Furthermore, many of the figures in the painting are engaged in activities related to geometry, including measuring and drawing geometric shapes. This emphasis on geometry reflects the importance that was placed on mathematical knowledge during the Renaissance, which was seen as a crucial tool for unlocking the mysteries of the natural world.

In summary, The School of Athens is a celebration of classical learning and ancient philosophy, and geometry plays a crucial role in this celebration by symbolizing the pursuit of knowledge, beauty, and harmony through rational inquiry and logical reasoning.