Final answer:
The idea for the double shell design is linked to the Renaissance's emphasis on innovation and marked a departure from Gothic styles, leading to the engineering marvel of Brunelleschi's dome in the Florence Cathedral.
Step-by-step explanation:
The author describes the idea for the double shell design of the Florence Cathedral's dome because it required innovation, an important part of the Renaissance. The double dome structure was a radical design at the time, combining Gothic architectural features like the pointed arch and ribs with the Renaissance pursuit of classical ideals. The innovative use of herringbone-patterned bricks and internal chains demonstrates how Brunelleschi's dome was engineered to be self-supporting without the need for flying buttresses, which were common in Gothic architecture but were disliked in Italy.
Brunelleschi's invention was influenced by his study of ancient Roman architecture and resulted in the largest masonry dome in the world, an indispensable element in later Renaissance architecture.