Which Form 8815 Amounts 2022-2023

Music, they say, the pen is mightier than the sword, and authorities have often agreed. From outlawed religious tracts and revolutionary manifestos to censored and burned books, we know the potential power of words to overturn the social order. But as strange as it may seem, some numbers have also been considered dangerous enough to ban. - Our distant ancestors long counted objects using simple tally marks, but as they developed agriculture and began living together in larger groups, this was no longer enough. As numbers grew more complex, people began not just using them but thinking about what they are and how they work. By 600 BCE in ancient Greece, the study of numbers was well developed. The mathematician Pythagoras and his school of followers found numerical patterns in shapes, music, and the stars. For them, mathematics held the deepest secrets of the universe. - However, one Pythagorean named Hippasus discovered something disturbing. Some quantities, like the diagonal of a square with sides of length 1, couldn't be expressed by any combination of whole numbers or fractions. No matter how small, these numbers, which we call irrational numbers, were perceived as a threat to the Pythagoreans' notion of a perfect universe. They imagined a reality that could be described with rational numerical patterns. Historians write that Hippasus was exiled for publicizing his findings, while legends claim he was drowned as punishment from the gods. - While irrational numbers upset philosophers, later mathematical inventions would draw attention from political and religious authorities as well. In the Middle Ages, while Europe was still using Roman numerals, other cultures had developed positional systems that included a symbol for zero. When Arab travelers brought the system to the bustling maritime cities of Italy, its advantages for merchants and bankers were clear. But the authorities were more...