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Wat (wie) is dyadic solenoid - definitie
![Real numbers with no unusually-accurate dyadic rational approximations. The red circles surround numbers that are approximated within error <math>\tfrac16/2^i</math> by <math>n/2^i</math>. For numbers in the fractal [[Cantor set]] outside the circles, all dyadic rational approximations have larger errors.](https://commons.wikimedia.org/wiki/Special:FilePath/Bad dyadic approximation.svg?width=200 "Real numbers with no unusually-accurate dyadic rational approximations. The red circles surround numbers that are approximated within error <math>\tfrac16/2^i</math> by <math>n/2^i</math>. For numbers in the fractal [[Cantor set]] outside the circles, all dyadic rational approximations have larger errors.")
![Dyadic rational approximations to the [[square root of 2]] (<math>\sqrt{2}\approx 1.4142</math>), found by rounding to the nearest smaller integer multiple of <math>1/2^i</math> for <math>i=0,1,2,\dots</math> The height of the pink region above each approximation is its error.](https://commons.wikimedia.org/wiki/Special:FilePath/Dyadic sqrt2 approximation.svg?width=200 "Dyadic rational approximations to the [[square root of 2]] (<math>\sqrt{2}\approx 1.4142</math>), found by rounding to the nearest smaller integer multiple of <math>1/2^i</math> for <math>i=0,1,2,\dots</math> The height of the pink region above each approximation is its error.")
![Ampère's law]] can be applied to the solenoid](https://commons.wikimedia.org/wiki/Special:FilePath/Solenoid and Ampere Law - 2.png?width=200 "Ampère's law]] can be applied to the solenoid")
![Ampèrian loops]] labelled ''a'', ''b'', and ''c''. Integrating over path ''c'' demonstrates that the magnetic field inside the solenoid must be radially uniform.](https://commons.wikimedia.org/wiki/Special:FilePath/Solenoid with 3 loops.svg?width=200 "Ampèrian loops]] labelled ''a'', ''b'', and ''c''. Integrating over path ''c'' demonstrates that the magnetic field inside the solenoid must be radially uniform.")
Fig. 305. EXPERIMENTAL SOLENOID.
The simple solenoid as constructed of wire, is a helical coil, of
uniform diameter, so as to represent a cylinder. After completing the
coil one end of the wire is bent back and carried through the centre of
the coil, bringing thus both ends out at the same end. The object of
doing this is to cause this straight return member to neutralize the
longitudinal component of the helical turns. This it does approximately
so as to cause the solenoid for its practical action to correspond with
the ideal solenoid.
Instead of carrying one end of the wire through the centre of the coil
as just described, both ends may be bent back and brought together at
the centre.
A solenoid should always have this neutralization of the longitudinal
component of the helices provided for; otherwise it is not a true
solenoid.
Solenoids are used in experiments to represent magnets and to study and
illustrate their laws. When a current goes through them they acquire
polarity, attract iron, develop lines of force and act in general like
magnets.
A solenoid is also defined as a coil of insulated wire whose length is
not small as compared with its diameter.
Wikipedia
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number.
The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted .
In advanced mathematics, the dyadic rational numbers are central to the constructions of the dyadic solenoid, Minkowski's question-mark function, Daubechies wavelets, Thompson's group, Prüfer 2-group, surreal numbers, and fusible numbers. These numbers are order-isomorphic to the rational numbers; they form a subsystem of the 2-adic numbers as well as of the reals, and can represent the fractional parts of 2-adic numbers. Functions from natural numbers to dyadic rationals have been used to formalize mathematical analysis in reverse mathematics.
