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6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.
By applying the fundamental recurrence formulas we may easily compute the successive convergents of this continued fraction to be 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, ..., where each successive convergent is formed by taking the numerator plus the denominator of the preceding term as the denominator in the next term, then adding in the ...
For the folded general continued fractions of both expressions, the rate convergence μ = (3 − √ 8) 2 = 17 − √ 288 ≈ 0.02943725, hence 1 / μ = (3 + √ 8) 2 = 17 + √ 288 ≈ 33.97056, whose common logarithm is 1.531... ≈ 26 / 17 > 3 / 2 , thus adding at least three digits per two terms. This is because the ...
Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n. It is the multiplicative inverse (reciprocal) ...
While not normally taught as a standard method for multiplying fractions, the grid method can readily be applied to simple cases where it is easier to find a product by breaking it down. For example, the calculation 2 1 / 2 × 1 1 / 2 can be set out using the grid method
"The length of the period of the simple continued fraction expansion of d 1/2 ". Pacific J. Math. 71: 21– 32. doi: 10.2140/pjm.1977.71.21. Davenport, H. (December 1982). The Higher Arithmetic. Cambridge University Press. ISBN 0-521-28678-6. Gliga, Alexandra Ioana (17 March 2006). On continued fractions of the square root of prime numbers (PDF).
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