Final answer:
The windmill, mechanical clock, and investigations of optics were three innovations that helped Europe catch up to more developed civilizations. The windmill revolutionized agriculture, the mechanical clock improved timekeeping and productivity, and the investigations of optics facilitated navigation and exploration.
Step-by-step explanation:
In the 12th and 13th centuries, Europe experienced several innovations and inventions that helped it catch up to more developed civilizations. One such innovation was the invention of the windmill, which revolutionized agriculture and allowed for increased production of food. This led to a surplus of food and population growth, which in turn contributed to economic development.
Another important invention was the mechanical clock. The use of clocks allowed for more efficient timekeeping, which was crucial for coordinating activities, trade, and labor. It helped Europeans synchronize their work and improve productivity.
Finally, the investigations of optics in Europe led to the development of new knowledge in fields such as physics and astronomy. Understanding optics helped Europeans improve their navigation techniques and explore the oceans more effectively. This led to increased trade, cultural exchange, and the discovery of new lands.