Final answer:
During the Renaissance, several mathematical innovations emerged, including the development of algebra. The Scientific Revolution led to the heliocentric model of the universe. The Industrial Revolution brought about significant technological innovations, such as the steam engine and the telegraph.
Step-by-step explanation:
Mathematical Innovations:
During the Renaissance, there were several mathematical innovations that emerged. One of the most important was the development of algebra by mathematicians such as Al-Khwarizmi in the 9th century. This allowed for the solving of complex equations and paved the way for further advancements in mathematics.
Scientific Innovations:
The Scientific Revolution of the 16th and 17th centuries led to numerous scientific innovations. Perhaps the most notable was the heliocentric model of the universe proposed by Nicolaus Copernicus. This challenged the prevailing belief that the Earth was the center of the universe and laid the foundation for modern astronomy.
Technological Innovations:
The Industrial Revolution of the 18th and 19th centuries brought about significant technological innovations. One example is the invention of the steam engine by James Watt, which revolutionized transportation and industry. Another is the telegraph, developed by Samuel Morse, which transformed communication and paved the way for the modern telecommunications system we have today.
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