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A formula for finding any power of a binomial without multiplying at length.
‘It appears that this formula may have led Gregory to the binomial theorem and more generally to the first discovery of the Taylor series expansion about forty years before Taylor.’
‘The q-analog of the binomial theorem corresponding to a negative integer power was discovered by Heine in 1847.’
‘However, he was more interested in mathematics than he was in the law and at the age of 20 Buffon (he was now calling himself Georges-Louis Leclerc De Buffon) discovered the binomial theorem.’
‘François Viète adopted modern algebraic notation; René Descartes invented coordinate geometry; while Newton among many mathematical triumphs discovered the binomial theorem.’
‘His ideas centred around the so-called polynomial theorem which was a generalisation of the binomial theorem.’
‘He used the binomial theorem to show that the limit had to lie between 2 and 3 so we could consider this to be the first approximation found to e.’
‘The paper draws an analogy between the binomial theorem and the successive derivatives of the product of functions.’
‘As an example of Aepinus' less good work, the authors of relate that in 1763 Aepinus published in Latin in the Commentaries of the St Petersburg Academy a proof of the binomial theorem for real values of the exponent.’
‘Students from sixth class to 10th class have come out with interesting applications of mathematics from Vedic mathematics to Pythagoras and binomial theorem and how one cannot do without mathematics in daily life.’
‘In Book 9 Saunderson presents the binomial theorem and the theory of logarithms.’
‘Also in this book is al-Samawal's description of the binomial theorem where the coefficients are given by the Pascal triangle.’
‘The discovery of the binomial theorem for integer exponents by al-Karaji was a major factor in the development of numerical analysis based on the decimal system.’
‘With these values, we used the binomial theorem,’
‘At the academy Gauss independently discovered Bode's law, the binomial theorem and the arithmetic - geometric mean, as well as the law of quadratic reciprocity and the prime number theorem.’
‘His interpolation used Kepler's concept of continuity, and with it he discovered methods to evaluate integrals which were later used by Newton in his work on the binomial theorem.’
‘This is a beautiful description of the binomial theorem using the Pascal triangle.’