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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 ...
For every fraction p / q (in its lowest terms) there is a Ford circle C[ p / q ], which is the circle with radius 1/(2q 2) and centre at ( p / q , 1 / 2q 2 ). Two Ford circles for different fractions are either disjoint or they are tangent to one another—two Ford circles never intersect. If 0 < p / q < 1 ...
Miquel's theorem. Miquel's theorem is a result in geometry, named after Auguste Miquel, [1] concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles in Euclidean geometry due to Miquel, whose work was published in Liouville's ...
In linguistics, ordinal numerals or ordinal number words are words representing position or rank in a sequential order; the order may be of size, importance, chronology, and so on (e.g., "third", "tertiary"). They differ from cardinal numerals, which represent quantity (e.g., "three") and other types of numerals.
A math circle is an extracurricular activity intended to enrich students' understanding of mathematics. The concept of math circle came into being in the erstwhile USSR and Bulgaria, around 1907, with the very successful mission to "discover future mathematicians and scientists and to train them from the earliest possible age". [1]
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
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