A square inscribed in a curve C means a square with its four corner points on the curve, though it may not lie entirely in the interior of C.

For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

If the vertex is at Af, and if the interior of C is on the left as one moves in the direction of increasing t, then every such corner can be found from the curve obtained by rotating C clockwise through 90-degrees about the vertex.

The set of intersections of Af, the rotated curve, with the original curve C consists of just the set of forward corner points on C corresponding to the vertex at Af, plus the vertex itself.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

The order of this congruence is Af, since Af secants of a curve of symbol ( B ) on a quadric surface pass through an arbitrary point.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

Each generator, **yl, of Af is also exceptional, for each is transformed into the entire congruence of secants of the curve into which that generator is transformed by the point involution on Q.

This curve is of symbol Af since it meets **yl, and hence every line of Af in the Af invariant points on **yl and since it obviously meets every line of Af in a single point.

A conic, C, being a ( 1, 1 ) curve on Q, meets the image of any line of Af, which we have already found to be a Af curve on Q, in Af points.

Hence C' is a Af curve on Q.

But if no two lines of the regulus of multiple secants of **zg can intersect, then the regulus must be quadratic, or in other words, **zg must be either a Af or a Af curve on a nonsingular quadric surface.

We now observe that the case in which **zg is a Af curve on a quadric is impossible if the complex of singular lines consists exclusively of the lines which meet Aj.

This contradicts the preceding observations, and so, under the assumption of this paper, we must reject the possibility that **zg is a Af curve on a quadric surface.

Continuing with the case in which **zg is a Af curve on a quadric Q, we first observe that the second regulus of Q consists precisely of the lines which join the two free intersections of **zg and the planes through any one of the multiple secants.

An adiabat is a curve of constant entropy on the P-V diagram.

These return waves create the dicrotic notch displayed in the aortic pressure curve during the cardiac cycle as these reflected waves push on the aortic semilunar valve.

Usually, a single equation corresponds to a curve on the plane.

" The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.

Video sampling tends to work on a completely different scale altogether thanks to the highly nonlinear response both of cathode ray tubes ( for which the vast majority of digital video foundation work was targeted ) and the human eye, using a " gamma curve " to provide an appearance of evenly distributed brightness steps across the display's full dynamic range-hence the need to use RAMDACs in computer video applications with deep enough colour resolution to make engineering a hardcoded value into the DAC for each output level of each channel impractical ( e. g. an Atari ST or Sega Genesis would require 24 such values ; a 24-bit video card would need 768 ...).

Stereoscopy | Stereo card of a train rounding the curve, circa 1907

Still, that Java Card uses a precise subset of the Java language speeds up the learning curve, and enables using a Java environment to develop and debug a Java Card program ( caveat: even if debugging occurs with Java bytecode, make sure that the class file fits the limitation of Java Card language by converting it to Java Card bytecode ; and test in a real Java Card smart card early on to get an idea of the performance ); further, one can run and debug both the Java Card code for the application to be embedded in a smart card, and a Java application that will be in the host using the smart card, all working jointly in the same environment.

The representations of a line and a curve as marks on a piece of paper or as pixels on a computer screen have a positive width.

A Bézier curve is a parametric curve frequently used in computer graphics and related fields.

The ZAMS curve can be calculated using computer models of stellar properties at the point when stars begin hydrogen fusion.

In the computer science subfields of computer-aided design and computer graphics, the term B-spline frequently refers to a spline curve parametrized by spline functions that are expressed as linear combinations of B-splines ( in the mathematical sense above ).

* Patch, a 3-D Bézier curve used in computer graphics, or a primitive in some 3-D software packages

Because of their generally faster-paced nature ( and in some cases a smaller learning curve ), real-time strategy games have surpassed the popularity of turn-based strategy computer games.

In the mathematical field of numerical analysis and in computer graphics, a Bézier spline is a spline curve where each polynomial of the spline is in Bézier form.

* Morton order a. k. a. Z-order, a space filling curve, often used in computer science

But because Bézier published the results of his work, the average computer graphics user today recognizes splines — which are represented with control points lying off the curve itself — as Bézier splines, while de Casteljau ’ s name is only known and used for the algorithms he developed to evaluate parametric surfaces.

Some computer graphic systems make use of Bézier splines, which allow a curve to be bent in real time on a display screen to follow a set of coordinates, much in the way a French curve would be placed on a set of three or four points on paper.

* William Phillips ( economist ) ( 1914 – 1975 ), New Zealander known for the Phillips curve and Moniac hydraulic computer

In computer graphics splines are popular curves because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design.

He hired a computer expert to determine the exact shape of the reflector's curve, making it one of the first architectural elements ever to be designed with computer technology.

The term " offset curve " is used, e. g., in numerically controlled machining ( and in other computer graphics applications ), where it describes the shape of the cut made by a round cutting piece, which is " offset " from the trajectory of the cutter by a constant distance in the direction normal to the cutter trajectory at every point.

Fontographer, developed by von Ehr for the Mac and released in January 1986 — before Adobe Illustrator — was the first commercially available Bézier curve editing software for a personal computer.

Many consumer products strongly reflect the bathtub curve, such as computer processors.

By attaching both the injector site and the ventricular thermistor to a small computer, the thermodilution curve can be plotted.

A goal was to extend the range of solarisation effects possible to a computer specified curve.

Upright handlebars, the norm in Europe and elsewhere until the 1970s, curve gently back toward the rider, offering a natural grip and comfortable upright position.

They have eight legs and are easily recognized by the pair of grasping claws and the narrow, segmented tail, often carried in a characteristic forward curve over the back, ending with a venomous stinger.

It is necessary to flip back the horizon mirror shade to be able to see the horizon, and then the fine adjustment screw on the end of the index bar is turned until the bottom curve ( the lower limb ) of the sun just touches the horizon.

The horns of blue wildebeest protrude to the side then curve downwards before curving up back towards the skull, while the horns of the black wildebeest curve forward then downward before curving at the upwards at the tips.

In 2004 a new calibration curve INTCAL04 was internationally ratified for calibrated dates back to 26, 000 Before Present ( BP ) based on an agreed worldwide data set of trees and marine sediments.

** The greater omentum ( or gastrocolic ) hangs from the greater curve of the stomach and loops down in front of the intestines before curving back upwards to attach to the transverse colon.

Now a grand curve back to the right begins, with Yosemite Falls on the north, followed by the Royal Arches, topped by North Dome.

The Mouser also fights with a pair of weapons: a " slim, curving " sword called Scalpel and a dagger called Cat's Claw, the latter usually hidden in the small of the Mouser's back, and the original of which had a very subtle curve.

Dingoes can have sabre-form tails ( typically carried erect with a curve towards the back ) or tails carried directly on the back.

From here the divide extends eastwards, culminating in the Aiguille de Scolette ( 3, 505 m ), but makes a great curve to the north-west and back to the south-east before rising in the Rocciamelone ( 3, 509 m ).

* Posterior fusion: This surgical approach is through an incision on the back and involves the use of metal instrumentation to correct the curve.

Located in the neighborhood's valley on Perry Highway / U. S. 19, this one-midway trolley park featured two beloved roller coasters: The Dips, with its unique banked turn-around curve, and the Racing Whippet, which featured two coasters on a strategically placed single track so that the train that started on the left of the loading platform came back on the right side and vice-versa.

* Around year 10-60 the plantation is now mature and ( in economic terms ) is falling off the back side of its growth curve.

The antlers of the southern pudú grow to be long and tend to curve back, somewhat like a mountain goat.

Then, to " fatten up " the outside radius of the bend, one or both arms of the bend would need to be pushed back to fill the outer radius of the curve.

They then curve anteriormedially to enter the bladder through the back, at the vesicoureteric junction, running within the wall of the bladder for a few centimeters.

In the long run, this implies that monetary policy cannot affect unemployment, which adjusts back to its " natural rate ", also called the " NAIRU " or " long-run Phillips curve ".

In addition, it is not uncommon for modern practitioners to sit zazen in a chair, often with a wedge / cushion on top of the chair seat so that one is sitting on an incline, or by placing a wedge behind the lower back to help maintain the natural curve of the spine.

Also common is scoliosis, a side-to-side curve in the back or spine, often creating a pronounced " C " or " S " shape when viewed on an x-ray of the spine.

Dao blades are moderately curved and single-edged, though often with few inches of the back edge sharpened as well ; the moderate curve allows them to be reasonably effective in the thrust.

This typically causes the blade to bend or curve during quenching, as the back contracts more than the edge.

The ureters run posteroinferiorly on the lateral walls of the pelvis and then curve anteriormedially to enter the bladder through the back, at the vesicoureteric junction, running within the wall of the bladder for a few centimetres.