* Trisecting the angle: Given any angle dividing it into three smaller angles all of the same size.

Trisecting a segment with ruler and compass.

According to Philippoff, the recoverable shear S is given by Af where **yc is the angle of extinction.

If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.

The definition of the angle between one-dimensional subspaces and given by

The parallax angle is given in the box to the right, and the angular diameter is known from lunar occultation measurements ( 41. 3 ± 0. 1 mas ).

These two forces add to make a resultant at an angle φ from the vertical given by

Using the tangent vector, the angle θ of the tangent to the curve is given by:

The path difference is given by so that the minimum intensity occurs at an angle θ < sub > min </ sub > given by

* is the intensity at a given angle,

The variation in intensity with angle is given by

The path difference between two waves travelling at an angle is given by:

More generally, the arc length of a portion of the circumference, as a function of the angle subtended, is given by an incomplete elliptic integral.

The inverse function, the angle subtended as a function of the arc length, is given by the elliptic functions.

The ( non-reflex ) angle θ ( 0 ° ≤ θ ≤ 180 °) between x and y is then given by

At one particular angle for a given n < sub > 1 </ sub > and n < sub > 2 </ sub >, the value of R < sub > p </ sub > goes to zero and a p-polarised incident ray is purely refracted.

This dictum led to a deep study of possible compass and straightedge constructions, and three classic construction problems: how to use these tools to trisect an angle, to construct a cube twice the volume of a given cube, and to construct a square equal in area to a given circle.

Although the bending of light can also be derived by extending the universality of free fall to light, the angle of deflection resulting from such calculations is only half the value given by general relativity.

# A certain means of wiring an alternating current electrical generator, and AC electric motors, so that when the generator is made to turn at a given speed, or even turned to a certain angle, each motor connected to it will also turn at that speed, or at the same angle.

In the case of the double-angle tangent identity, if the tangent of an angle A is given as a / b then the tangent of 2A is the product of

A location's north-south position along a meridian is given by its latitude, which is ( not quite exactly ) the angle between the local vertical and the plane of the Equator.

It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle.

Bradley explained this effect in the context of Newton's corpuscular theory of light, by showing that the aberration angle was given by simple vector addition of the Earth's orbital velocity and the velocity of the corpuscles of light, just as vertically falling raindrops strike a moving object at an angle.

With increasing advance of the knife into the coating the shear plane extends to the coatings surface and the shear angle rapidly decreases.

Babe Ruth, as he always did in the Stadium, played right field to avoid having the sun in his eyes, and Tommy Thevenow, a rather mediocre hitter who played shortstop for the St. Louis Cardinals, knocked a ball with all his might into the sharp angle formed by the permanent stands and the wooden bleachers, where Ruth could not reach it.

At each angle of its pitch a big skylight had been fitted into the roof and all these skylights were fitted with systems of multiple screens and shades.

Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures.

In addition, a rotation axis at an angle to the magnetic axis may be spinning different bands of magnetically-sorted elements into the line of sight between Alioth and the Earth.

3D beading generally uses the techniques of bead weaving, which can be further divided into right angle weave and peyote stitch.

Captain Antoine René Thévenard used the spring on his anchor cable to angle his broadside into a raking position across the bow of Nelson's flagship, which consequently suffered over 100 casualties, including the admiral.

Above, it turns into an helical antiferromagnetic state in which all of the atomic moments in a particular basal plane layer are parallel, and oriented at a fixed angle to the moments of adjacent layers.

Farkas speculated that the horn should be held in a downward angle to allow the air stream to go straight into the mouthpiece, although his later text shows that air stream direction actually is either upstream or downstream and is dependent upon the ratio of upper or lower lip inside the mouthpiece, not the horn angle.

Rail fins evolved into being and surged into popularity as riders ( Simon Anderson, most famously ) sought a solution to two major performance issues of a central " single " fin-both related to engagement of the foil: For one, a centrally-mounted fin is tilted up out of the water as the board is leaned over, and thus it loses more and more of its lift as the lean angle increases-if the lean angle is acute enough, the fin's tip can be the only area left in the water ; the tip may then rapidly stall and, having lost its lift, become disengaged from the water, leaving the board's bottom as the only control surface still operating.

When moving from a denser medium into a less dense one ( i. e., n < sub > 1 </ sub > > n < sub > 2 </ sub >), above an incidence angle known as the critical angle, all light is reflected and R < sub > s </ sub > = R < sub > p </ sub > = 1.

From this original entrance there is a Descending Passage high and wide which goes down at an angle of 26 ° 31 ' 23 " through the masonry of the pyramid and then into the bedrock beneath it.

It is roofed by slabs of stone laid at a slightly steeper angle than the floor of the gallery, so that each stone fits into a slot cut in the top of the gallery like the teeth of a ratchet.

As ever deeper depressions were advantageous to the organism, gradually, this depression would become a pit into which light would strike certain cells depending on its angle.

The average ( also referred to as the adjoint unweighted ) prompt neutron lifetime takes into account all prompt neutrons regardless of their importance in the reactor core ; the effective prompt neutron lifetime ( referred to as the adjoint weighted over space, energy, and angle ) refers to a neutron with average importance.

The analysis so far has been two dimensional ; it turns out that an unperturbed orbit is two-dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two-dimensional plane into the required angle relative to the poles of the planetary body involved.

A simpler system, developed later, uses a concave disc ( or a pair of them ) set at a large angle to the direction of progress, that uses the concave shape to hold the disc into the soil – unless something hard strikes the circumference of the disk, causing it to roll up and over the obstruction.

He divided the paddle into eight segments to change the ball's angle of return.

As the waves travel from deep water into shallower water near the shore, they are refracted from their original direction of travel to an angle more normal to the shoreline.

A useful analogy in explaining the refraction of light would be to imagine a marching band as they march at an oblique angle from pavement ( a fast medium ) into mud ( a slower medium ).