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 angle between those lines can be measured, and is the angular separation between the two stars.

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.

Because of your forward motion relative to the falling rain, the rain now appears to be falling not straight down from directly above you, but at a slight angle from a point in the sky somewhat in front of you.

The racquet movement is typically used to suggest a straight angle but then play the stroke cross court, or vice versa.

When the rode is slack, the catenary curve presents a lower angle of pull on the anchor or mooring device than would be the case if it were nearly straight.

* angle of entry – a diver should enter the water straight, without any angle.

Those whose sum is a straight angle are supplementary.

Supplementary angles are formed when one or more rays share the same vertex and are pointed in a direction that in between the two original rays that form the straight angle ( 180 degrees ).

The sum of the angles of a triangle is equal to a straight angle ( 180 degrees ).

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.

The second is that gas piston alternatives use an off-axis operation of the piston that can introduce carrier tilt, whereby the bolt carrier fails to enter the buffer tube at a straight angle resulting in part wearing.

Geometrically two edges meeting at a corner are required to form an angle that is not straight ( 180 °); otherwise, the line segments will be considered parts of a single edge – however mathematically, such corners may sometimes be allowed.

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.

This was because the plane struck the tower from an angle, and not straight on as Flight 11 in the North Tower had done.

* 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.

This was compounded by the extended length of the card logic board ; often there was not enough room in the PC case to angle the card into the slot, requiring it to be pushed with great force straight down into the slot.

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

Horses sometimes also have to jump fences from an angle rather than straight on.

In theory, a run down the hill would consist of straight sections across the hill, followed by sharp turns to the complementary angle, as if the skier is being reflected from the edges of the run.

Those of the duikers and dwarf antelopes tend to be simple " spikes ", but differ in the angle to the head from backward curved and backward pointing ( e. g. yellow-backed duiker ) to straight and upright ( e. g. steenbok ).

However, by employing a very simple conformal mapping, the inconvenient angle is mapped to one of precisely pi radians, meaning that the corner of two planes is transformed to a straight line.

An apocryphal story claims that King Louis XVI ( an amateur locksmith ) recommended that a triangular blade with a beveled edge be used instead of a crescent blade, but it was Schmidt who suggested placing a straight blade at a 45 degree angle.

Likewise many more geometric terms derive from this same root, such as erect ( as in " upright "), rectangle ( literally " right angle "), straight and stretch.

Several other roots have similar normative and geometric descendants, such as Latin norma, whence norm, normal, and normative itself, and also geometric concepts such as normal vectors ; and likewise Greek ortho and Latin ordo, meaning either " right " or " correct " ( as in orthodox, meaning " correct opinion ") or " straight " or " perpendicular " ( as in orthogonal, meaning " perpendicular angle "), and thence order, ordinary, etc.