Masaaki Sasamoto, ‘Cocoro’.

Beyond the Furthest Star by Frank Frazetta

Power of the Pyramid


Brahmagupta, Indian mathematician (598 - 670), known as the “inventor of zero”. Picture from
Brahmagupta was head of the astronomical observatory at Ujjain, a holy city in the Malwa region of central India. (Ujjain has been a center of learning since ancient times, and is known in Hindu tradition as the place where Krishna went to receive his education. The observatory of Ujjain was considered the prime meridian, as Greenwich England is today, making it the baseline for all astronomical observations.)From his observations he deduced that the moon is closer to the earth than the sun is, and that the earth and heavenly bodies are all spheres. His calculation of the length of the solar year is accurate to within about half an hour! But Brahmagupta is best known for his mathematical writings, and especially for developing the concept of zero as a number.In his great work Brahmasphutasiddhanta (“The Opening of the Universe”), Brahmagupta wrote:    When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero. Previous schoars had used various symbols as placeholders to show the lack of a number or digit. Brahmagupta was the first to treat zero as a number in its own right, something that could be used in calculations along with other numbers. In doing so, he extended the rules of arithmetic from the natural numbers to what we now call the integers, including zero and negative numbers. Here’s more rules from the Brahmasphutasiddhanta:    A debt minus zero is a debt.    A fortune minus zero is a fortune.    Zero minus zero is a zero.    A debt subtracted from zero is a fortune.    A fortune subtracted from zero is a debt.    The product of zero multiplied by a debt or fortune is zero.    The product of zero multipliedby zero is zero.    The product or quotient of two fortunes is one fortune.    The product or quotient of two debts is one fortune.    The product or quotient of a debt and a fortune is a debt.    The product or quotient of a fortune and a debt is a debt.(“Fortune” and “Debt” were Brahmagupta’s quite descriptive terms for what we’d now call positive and negative numbers.)This is one of those ideas that’s so simple that, from our vantage point centuries later, it’s hard to imagine anyone not understanding it, but people had been struggling along without zero for centuries. It must have taken a stroke of genius to realize that “nothing” is something!But he didn’t stop with negative numbers! The Brahmasphutasiddhanta also contains methods for:- Finding square roots, using an algorithm that Newton would rediscover centuries later!- Solving quadratic equations!- Trigonometry, including tables of sines and cosines!- Summing series of squares and cubes- Finding the area of cyclic quadrilateralsHis work holds up extremely well today. His approximation of Pi was correct to within a few hundredths. About the only place where modern mathematicians would disagree with Brahmagupta is his statement that 0 divided by 0 is 0, where today we leave division by zero undefined.Sources:

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