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Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's ...
Jain mathematicians were apparently also the first to use the word shunya (literally void in Sanskrit) to refer to zero. This word is the ultimate etymological origin of the English word "zero", as it was calqued into Arabic as ṣifr and then subsequently borrowed into Medieval Latin as zephirum, finally arriving at English after passing ...
He wrote, "If zero is added to any number, the sum is the same number; if zero is subtracted from any number, the number remains unchanged; if zero is multiplied by any number, the product is zero". In the case of dividing a fraction he has found out the method of multiplying the fraction by the reciprocal of the divisor.
Because of this, Pingala is sometimes also credited with the first use of zero, as he used the Sanskrit word śūnya to explicitly refer to the number. [11] Pingala's binary representation increases towards the right, and not to the left as modern binary numbers usually do. [12] In Pingala's system, the numbers start from number one, and not zero.
Brāhmasphuṭasiddhānta is one of the first books to provide concrete ideas on positive numbers, negative numbers, and zero. [4] For example, it notes that the sum of a positive number and a negative number is their difference or, if they are equal, zero; that subtracting a negative number is equivalent to adding a positive number; that the product of two negative numbers is positive.
The concept of zero and the introduction of a notation for it are important developments in early mathematics, which predates for centuries the concept of zero as a number. It was used as a placeholder by the Babylonians and Greek Egyptians, and then as an integer by the Mayans, Indians and Arabs (see the history of zero).
The Bakhshali manuscript, MacTutor History of Mathematics archive; Ch. 6 – The Bakhshali manuscript (Ian G. Pearce, Indian Mathematics: Redressing the balance) Hoernle: On the Bakhshali Manuscript, 1887, archive.org "A Big Zero: Research uncovers the date of the Bakhshali Manuscript", YouTube video, University of Oxford
The history includes Hindu–Arabic numerals, letters from the Roman, Greek, Hebrew, and German alphabets, and a variety of symbols invented by mathematicians over the past several centuries. The historical development of mathematical notation can be divided into three stages: [ 4 ] [ 5 ]