Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.

Consequently, both the rake angle of the knife as well as the friction occurring between the back of the removed coating and the front of the knife will determine in large part the detailed mechanism of the cutting removal process.

If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

In the Euclidean plane, the angle θ between two vectors u and v is related to their dot product and their lengths by the formula

This formula supplies an easy method to find the angle between two planes ( or curved surfaces ) from their normal vectors and between skew lines from their vector equations.

The latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces and spanned by the vectors and correspondingly.

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

In Riemannian geometry, the metric tensor is used to define the angle between two tangents.

The latter estimate was based on the angle between the half moon and the Sun, which he estimated as 87 ° ( the true value being close to 89. 853 °).

where is 1 au, is the phase angle, the angle between the Sun – Body and Body – Observer lines.

In predicted fire the basic geospatial data of range, angle of sight and azimuth between a fire unit and its target was produced and corrected for variations from the ' standard conditions '.

where θ is the true angle SEE ′, is the apparent angle S ′ EE ′, and is the relative speed between the presumed fixed frame of reference ( such as heliocentric ) and the observer's one.

After March it began to pass northwards, a motion quite apparent by the middle of April ; in June it passed at the same distance from the zenith as it did in December ; and in September it passed through its most northerly position, the extreme range from north to south, i. e. the angle between the March and September positions, being 40 ″.

If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O ' 1 there is a circular disk of confusion of radius O ' 1R, and in a parallel plane at O ' 2 another one of radius O ' 2R2 ; between these two is situated the disk of least confusion.

The largest opening of the pencils, which take part in the reproduction of O, i. e. the angle u, is generally determined by the margin of one of the lenses or by a hole in a thin plate placed between, before, or behind the lenses of the system.

where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.

Measuring the angle between the string-ball apparatus and the vertical gives an estimate of the wind speed.

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.

The mineral was first discovered in Saxony by August Breithaupt in 1817, and named by him from the Greek amblus, blunt, and gouia, angle, because of the obtuse angle between the cleavages.

Let S ( fig. 5 ) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O ' 1 ; and those under an angle u2 in the axis point O ' 2.

One important definition is the fourth: " Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal.

The number of rays in between the two original rays are infinite like those possible in the complementary angle.

For example, the problem of trisecting an angle with a compass and straightedge is one that naturally occurs within the theory, since the axioms refer to constructive operations that can be carried out with those tools.

In general, liquids in the Cassie – Baxter state exhibit lower slide angles and contact angle hysteresis than those in the Wenzel state.

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.

This is why present day streets on the northeast side of Cherry Street run at a slightly different angle from those to the southwest of it.

In other words, the farther from the tropics you lie, the lower the sun angle is, which causes those locations to be cooler due to the indirect sunlight.

For a given mirror ratio ( the maximum field strength divided by the minimum field strength ), particles with a pitch angle ( angle between the particle velocity and the magnetic field ) greater than a critical value will be reflected, those with a smaller pitch angle will escape.

When the angle between the sun and the horizon is less than 10 percent, as it is just after sunrise or just prior to sunset, sunlight becomes too red due to refraction for any colors other than those with a reddish hue to be seen.

In spherical geometry, the shortest distance between two points is an arc of a great circle, but the triangle inequality holds provided the restriction is made that the distance between two points on a sphere is the length of a minor spherical line segment ( that is, one with central angle in π ) with those endpoints.

* Coordinates in angle brackets such as < 100 > denote a family of directions that are equivalent due to symmetry operations, such as,, or the negative of any of those directions.

From this angle, one ’ s state of mind is an “ effect ” rather than a determinant of existence, including those aspects of existence that one is not conscious of.

Euclid uses right angles in definitions 11 and 12 to define acute angles ( those smaller than a right angle ) and obtuse angles ( those greater than a right angle ).

The design had to incorporate those parts of the building that escaped destruction, most notably Westminster Hall, the adjoining double storey cloisters of St Stephen's court and the crypt of St Stephen's Chapel, Barry's design was parallel to the River Thames, but the surviving buildings are at a slight angle to the river, thus Barry had to incorporate this awkward difference in axis into the design.

The shuttlecock shall be hit at an upward angle and in a direction parallel to the side lines.

Euler discussed a generalization of Euclidean geometry called affine geometry, which retains the fifth postulate unmodified while weakening postulates three and four in a way that eliminates the notions of angle ( whence right triangles become meaningless ) and of equality of length of line segments in general ( whence circles become meaningless ) while retaining the notions of parallelism as an equivalence relation between lines, and equality of length of parallel line segments ( so line segments continue to have a midpoint ).

Modern acrobatic kites use two or four lines to allow fine control of the kite's angle to the wind.

The conformal latitude defines a transformation from the ellipsoid to a sphere of arbitrary radius such that the angle of intersection between any two lines on the ellipsoid is the same as the corresponding angle on the sphere ( so that the shape of small elements is well preserved ).

Straight lines represent straight fingers ( these may be at an angle to indicate that they are not in line with the palm ; if they point toward or away from the signer, they have a diamond shape at the tip ); curved lines for curved ( cupped ) fingers ; hooked lines for hooked fingers ; right-angle lines, for fingers bent at only one joint ; and crossed lines, for crossed fingers, as shown in the chart at right.

* Line and Cross-court Shot: refers to whether the ball flies in a straight trajectory parallel to the side lines, or crosses through the court in an angle.

Geometrical elements took on increasing importance in both his teaching and painting — particularly the circle, half-circle, the angle, straight lines and curves.

The two lines were approaching at an angle so that the leading ships of the vans of both lines were within range of each other, while the ships at the rear were too far apart to engage.

None of the options for closing the angle between the lines presented a favourable option to the British commander: any maneouvre to bring ships closer would limit its firing ability to its bow guns, and potentially expose its decks to raking or enfilading fire from the enemy ships.

Walking the course before the event is a chance for the rider to walk the lines he or she will have to ride, in order to decide how many strides the horse will need to take between each jump and from which angle.

High-voltage direct current lines are restricted only by thermal and voltage drop limits, since the phase angle is not material to their operation.

Given two dual numbers p, and q, they determine the set of z such that the Galilean angle between the lines from z to p and q is constant.

In this case the drafter places one or more triangles of known angles on the T-square — which is itself at right angles to the edge of the table — and can then draw lines at any chosen angle to others on the page.