Not all demand and supply curves look alike.
The reason for the savings is that fonts are stored as a set of mathematical curves.
A better test would check whether flattening curves foreshadow slowdowns, and steepening ones presage economic acceleration.
Namely, the geometer is justified in using simple curves as well as more complex curves, so long as the construction of these curves proceeds by “precise and exact” motions.
For this purpose, one of the two curves is a signal of known characteristics.
…of problems, the determination of areas and volumes and the calculation of tangents to curves.
Lissajous used a narrow stream of sand pouring from the base of a compound pendulum to produce the curves.
In mammals, however, the behavioral curves differ from the cochlear potential curves in three ways.
Bezier curves, and related curves known as B-splines, were introduced in computer-aided design programs for the modeling of automobile bodies.
Curves described by parametric equations (also called parametric curves) can range from graphs of the most basic equations to those of the most complex.
If drug X has therapeutic, toxic, and lethal dose–response curves of A, B, and C, respectively, X is a very safe drug, since there is no overlap of the curves.
Unlike behavioral curves, however, the curves obtained by plotting the sound required to produce an arbitrary amount of electrical potential of the cochlea do not represent auditory thresholds.
If one of the curves is 180° out of phase with respect to the other, another straight line is produced lying 90° away from the line produced where the curves are in phase (i.e., at 135° and 315°).
Birational transformations preserve intrinsic properties of curves, such as their genus, but provide leeway for geometers to simplify and classify curves by eliminating singularities (problematic points).
This procedure enabled him to find equations of tangents to curves and to locate maximum, minimum, and inflection points of polynomial curves, which are graphs of linear combinations of powers of the independent variable.
If a ball is sliced (a right-handed shot that curves right) off the tee, or hooked (a right-handed shot that curves left), the golfer will probably use an iron, such as a No. 5, to get his ball up quickly from the rough and still attain moderate distance.
Recall that in addition to his emphasis on the “precise and exact” motions that can be used to describe legitimately geometrical curves, Descartes also claims that these curves “can be conceived of as described by a continuous motion or by several successive motions.”
This identification allows Descartes to establish Pappus curves as “geometric” curves, but he offers no proof of the identity, and thus, there is question of whether Descartes has in fact demonstrated that the Pappus curves are “geometric” by his own standards.
The suggestion from Descartes is that when we pointwise construct a geometric curve, we can identify any possible point on the curve, and immediately after the above remarks, he proceeds to equate curves constructed in this manner with curves that could possibly be constructed by continuous motions: “this method of tracing a curve by determining a number of its points taken at random applies only to curves that can be generated by a regular and continuous motion” (G, 91).
Probably the real explanation of the refusal of ancient geometers to accept curves more complex than the conic sections lies in the fact that the first curves to which their attention was attracted happened to be the spiral, the quadratrix, and similar curves, which really do belong only to mechanics, and are not among the curves that I think should be included here, since they must be conceived of as described by two separate movements whose relation does not admit of exact determination (G, 44).
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Probably the real explanation of the refusal of ancient geometers to accept curves more complex than the conic sections lies in the fact that the first curves to which their attention was attracted happened to be the spiral the quadratrix and similar curves which really do belong only to mechanics and are not among the curves that I think should be included here since they must be conceived of as described by two separate movements whose relation does not admit of exact determination G 44