Nevertheless, although hedge funds go to great lengths to reduce the ratio of risk to reward, inevitably a number of risks remain.

The lengths of the parameter intervals which yield oscillations of a given length decrease rapidly ; the ratio between the lengths of two successive such bifurcation intervals approaches the Feigenbaum constant δ = 4. 669.

As the ratio of two lengths, the radian is a " pure number " that needs no unit symbol, and in mathematical writing the symbol " rad " is almost always omitted.

Corresponding sides have lengths in the same ratio:

Two sides have lengths in the same ratio, and the angles included between these sides have the same measure.

The ratio between the areas of similar figures is equal to the square of the ratio of corresponding lengths of those figures ( for example, when the the side of a square or the radius of a circle is multiplied by two, its area is multiplied by four — i. e. by two squared ).

The ratio between the volumes of similar figures is equal to the cube of the ratio of corresponding lengths of those figures ( for example, when the the edge of a cube or the radius of a sphere is multiplied by two, its volume is multiplied by eight — i. e. by two cubed ).

* The ratio of three characteristic lengths: the classical electron radius, the Bohr radius and the Compton wavelength of the electron:

The duplication scale of a striped triangle is the proportionality constant between the corresponding sides lengths of the triangles, equal to a positive ratio obliquely written within the image: or

Euclid defines a ratio to be between two quantities of the same type, so by this definition the ratios of two lengths or of two areas are defined, but not the ratio of a length and an area.

Arguing that White catches up by means of Black's ' small errors ', so that White's deficit drifts at a constant rate, it makes sense to take the ratio of game lengths as scaling factor.

The digit ratio is the ratio of the lengths of different digits or fingers typically measured from the bottom crease where the finger joins the hand to the tip of the finger.

The 2D: 4D digit ratio is sexually dimorphic: while the second digit is typically shorter in both females and males, the difference between the lengths of the two digits is greater in males than females.

At one point, however, he incorrectly resolved that the periods of oscillation of two pendulums were in the same ratio as their lengths, but he later realized and corrected the error.

Another necessary and sufficient condition is that the diagonals cut each other in mutually the same ratio ( this ratio is the same as that between the lengths of the parallel sides ).

The ratio of the areas of each pair of adjacent triangles is the same as that between the lengths of the parallel sides.

A golden rectangle is one whose side lengths are in the golden ratio, or approximately 1: 1. 618.

Angular field of view is typically specified in degrees, while linear field of view is a ratio of lengths.

With Earth held stationary at the center of a nonrotating frame, the successive inferior conjunction s of Venus over eight Earth years trace a pentagram mic pattern ( reflecting the difference between the numbers in the ratio ).

* Elliott wave principle and the golden ratio to calculate successive price movements and retracements

The ASTM B 258-02 standard defines the ratio between successive sizes to be the 39th root of 92, or approximately 1. 1229322.

Railsback, expresses the difference between normal piano tuning and an equal-tempered scale ( one in which the frequencies of successive notes are related by a constant ratio, equal to the twelfth root of two ).

In mathematics, a generalized hypergeometric series is a series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation.

in which the ratio of successive coefficients is a rational function of n. That is,

As k becomes larger, the ratio t < sub > k </ sub > / s < sub > k </ sub > approaches and the ratio of successive square triangular numbers approaches.

Pappus gives several solutions of this problem, including a method of making successive approximations to the solution, the significance of which he apparently failed to appreciate ; he adds his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one.

When the additional length of connections is taken into account, the ratio between successive lengths of rods is √ 2 / 2.

This loop forces the engine to operate both slightly lean and slightly rich on successive loops, as it attempts to maintain a mostly stoichiometric ratio on average.

In 1975, Dr. Feigenbaum, using the small HP-65 calculator he had been issued, discovered that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4. 6692 ...

Tenney has suggested the piece be " regenerated " with the distance between successive voices, the minor sixth ( 1. 6 in just intonation, 1. 587 in equal temperament ), being tuned to golden ratio phi ( 1. 618 ).

The right secondary auditory cortex processes pitch change and manipulation of fine tunes ; specifically, this region distinguishes the multiple pitches that characterize melodic tunes as contour ( pitch direction ) and interval ( frequency ratio between successive notes ) information.

This means that with each successive subdivision, the ratio of nuclear to cytoplasmic material increases.

A series x < sub > n </ sub > is called hypergeometric if the ratio of successive terms x < sub > n + 1 </ sub >/ x < sub > n </ sub > is a rational function of n. If the ratio of successive terms is a rational function of q < sup > n </ sup >, then the series is called a basic hypergeometric series.

The degree of isochronous distortion, in data transmission, is the ratio of the absolute value of the maximum measured difference between the actual and the theoretical intervals separating any two significant instants of modulation ( or demodulation ), to the unit interval.

# In asynchronous data transmission, the ratio of ( a ) the absolute value of the maximum measured difference between the actual and theoretical intervals separating any significant instant of modulation ( or demodulation ) from the significant instant of the start element immediately preceding it to ( b ) the unit interval.

Telegraphic distortion is a similar older problem, distorting the ratio between " mark " and " space " intervals.

Comparison of equal-tempered ( red ) and Pythagorean tuning | Pythagorean ( blue ) intervals showing the relationship between frequency ratio and the intervals ' values, in cents.

Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions and then extrapolating generalities in ratio or within confidence intervals.

This data helps determine the shear modulus and Poisson's ratio at intervals through the soil column for soil liquefaction analysis and low-strain soil strength analysis.

( risk ratio. 42 with statistical significant confidence intervals given the large study size, not unexpected ).

For such ratio distributions, there can be defined probabilities for intervals which can be defined either by Monte Carlo simulation, or, in some cases, by using the Geary-Hinkley transformation.

They are useful in the study of harmony: many musical intervals can be expressed as a superparticular ratio.

The Lipps – Meyer law, named for Theodor Lipps ( 1851 – 1914 ) and Max F. Meyer ( 1873 – 1967 ), hypothesizes that the closure of melodic intervals is determined by " whether or not the end tone of the interval can be represented by the number two or a power of two ", in the frequency ratio between notes ( see octave ).

As a result, as long as this ratio is fixed, recency will be observed regardless of the absolute values of intervals, so that recency can be observed at all time scales, a phenomenon known as time scale invariance.

Two different intervals are perceived to be the same when the pairs of pitches involved share the same frequency ratio.

The easiest intervals to identify, and the easiest intervals to tune, are those that are just — which have a simple whole-number ratio.

The term temperament refers to a tuning system which tempers the just intervals ( usually the perfect fifth which has the ratio 3: 2 ) in order to satisfy another mathematical property ; in equal temperament, a fifth would be tempered by narrowing it slightly, achieved by flattening its upper pitch slightly, or raising its lower pitch slightly.

Since the current is integrated over relatively longer time intervals, chronoamperometry gives a better signal to noise ratio in comparison to other amperometric technique.