# rational approximation in a sentence

1) Here are all of its best

**rational**

**approximations**.

approximation collocations

2) In fact "π" could be computed from these

**rational**

**approximations**.

3) The continued fraction representation of can be used to generate successive best

**rational**

**approximations**.

## rational **approximation** example sentences

4) These **approximations**are the best possible

**rational**

**approximations**of relative to the size of their denominators.

5) Thus to incorporate a new term into a

**rational**

**approximation**, only the two previous convergents are necessary.

6) Their

**rational**

**approximation**of the "error" for the finite sum of their series are of particular interest.

7) However, the existence or usefulness of a

**rational**

**approximation**to a quantity does not mean the quantity is irrational.

8) An infinite continued fraction representation for an irrational number is useful because its initial segments provide

**rational**

**approximations**to the number.

9) The Kerala school of astronomy and mathematics further expanded his works with various series expansions and

**rational**

**approximations**until the 16th century.

10) Each

**approximation**generated in this way is a best

**rational**

**approximation**; that is, each is closer to than any other fraction with the same or a smaller denominator.

11) We can use "ƒ" and "g" together to compute as close a

**rational**

**approximation**as we like to the real number they represent.

12) The "R""n" are

**rational**

**approximations**to "π" and two successive terms always enclose the true value of "π".

13) The last entry of the table has 355⁄113 as one of its best

**rational**

**approximations**;

14) the numerator of the best simplified

**rational**

**approximation**of pi having a denominator of four digits or fewer.

15) The simple continued fraction for __FORMULA__ generates "all" of the best

**rational**

**approximations**for __FORMULA__ according to three rules:

### example sentences with **rational** **approximation**

16) They are intimately connected with the golden ratio ; for example, the closest **rational**

**approximations**to the ratio are 2/1, 3/2, 5/3, 8/5, ... .

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