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The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiángjiě Jiǔzhāng Suànfǎ (詳解九章算法) [1] of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematician Jia Xian [2] who expounded it around 1100 AD, about 500 years before Pascal.
The Extended Pascal standard extends Pascal to support many things C supports, which the original standard Pascal did not, in a type safer manner. For example, schema types support (besides other uses) variable-length arrays while keeping the type-safety of mandatory carrying the array dimension with the array, allowing automatic run-time ...
Jia Xian triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD. Yang Hui referred to Jia Xian's Shi Suo Suan Shu in the Yongle Encyclopedia Jia Xian ( simplified Chinese : 贾宪 ; traditional Chinese : 賈憲 ; pinyin : Jiǎ Xiàn ; Wade–Giles : Chia Hsien ; ca. 1010–1070) was a Chinese ...
Pascal-P5, created outside the Zürich group, accepts the full Pascal language and includes ISO 7185 compatibility. Pascal-P6 is a follow on to Pascal-P5 that along with other features, aims to be a compiler for specific CPUs, including AMD64. UCSD Pascal branched off Pascal-P2, where Kenneth Bowles used it to create the interpretive UCSD p-System.
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times).
The Ramer–Douglas–Peucker algorithm, also known as the Douglas–Peucker algorithm and iterative end-point fit algorithm, is an algorithm that decimates a curve composed of line segments to a similar curve with fewer points.
In matrix theory and combinatorics, a Pascal matrix is a matrix (possibly infinite) containing the binomial coefficients as its elements. It is thus an encoding of Pascal's triangle in matrix form. There are three natural ways to achieve this: as a lower-triangular matrix , an upper-triangular matrix , or a symmetric matrix .