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Family of curves of the form r^n = a^n cos(nθ)
In algebraic geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates r n = a n cos ( n θ ) {\displaystyle
Sinusoidal_spiral
Plane curve constructed from a given curve and fixed point
forces do we have to impose on a test particle to move along it. For a sinusoidal spiral written in the form r n = a n sin ( n θ ) {\displaystyle r^{n}=a^{n}\sin(n\theta
Pedal_equation
Type of plane curve
defined as an epicycloid having a single cusp. It is also a type of sinusoidal spiral, and an inverse curve of the parabola with the focus as the center
Cardioid
Cubic plane curve
it can be drawn as a cubic Bézier curve. It is a special case of a sinusoidal spiral, of a pursuit curve, and of a Pythagorean hodograph curve. The original
Tschirnhausen_cubic
lemniscate Hurwitz surface Mandelbrot curve Polynomial lemniscate Sinusoidal spiral Superellipse Bowditch curve Brachistochrone Butterfly curve (transcendental)
Gallery_of_curves
Plane curve
(sextic of Cayley, Cayley's sextet) is a plane curve, a member of the sinusoidal spiral family, first discussed by Colin Maclaurin in 1718. Arthur Cayley
Cayley's_sextic
Scottish mathematician (1698–1746)
of Maclaurin Cayley's sextic Cramer's paradox Hesse configuration Sinusoidal spiral http://www-groups.dcs.st-and.ac.uk/Extras/Turnbull_Maclaurin_1.html
Colin_Maclaurin
Butterfly curve (algebraic) (genus 7) Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface Elkies trinomial curves Hyperelliptic
List_of_curves
Family of closed mathematical curves
{dr}{\sqrt {1-r^{n}}}}} is the arc length of the principal loop of the sinusoidal spiral r n 2 = cos ( n 2 θ ) {\textstyle r^{\frac {n}{2}}=\cos \left({\frac
Superellipse
Curve generated by the projections of a fixed point on the tangents of another curve
hyperbola Center Lemniscate of Bernoulli Logarithmic spiral Pole Logarithmic spiral Sinusoidal spiral r n = a n cos n θ {\displaystyle r^{n}=a^{n}\cos
Pedal_curve
Bolza surface Macbeath surface Polynomial lemniscate Fermat curve Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve Brachistochrone Butterfly
List_of_mathematical_shapes
Type of roulette curve
2}=(2b)^{1 \over 2}\cos {\frac {\theta }{2}},} making it a member of the sinusoidal spiral family of curves. This curve is the cardioid. In the special case
Limaçon
high-frequency oscillations, which are very close to sinusoidal. The basic principle of operation is the effect of spiral unsteadiness of electron-hole (p-n) plasmas
Oscillistor
Plane algebraic curve
Sinusoidal spirals (rn = −1n cos(nθ), θ = π/2) in polar coordinates and their equivalents in rectangular coordinates: n = −2: Equilateral hyperbola n
Lemniscate_of_Bernoulli
Plane curve: conic section
Sinusoidal spirals (rn = −1n cos(nθ), θ = π/2) in polar coordinates and their equivalents in rectangular coordinates: n = −2: Equilateral hyperbola n
Hyperbola
Moving wave that has oscillations perpendicular to the direction of the wave
Mathematically, the simplest kind of transverse wave is a plane linearly polarized sinusoidal one. "Plane" here means that the direction of propagation is unchanging
Transverse_wave
Spring attached to the balance wheel in timepieces
equation of motion for the balance is simple harmonic motion; i.e., a sinusoidal motion of constant period: θ ( t ) = A cos ( κ I t ) + B sin ( κ I
Balance_spring
groove is not a perfect spiral and contains a slight sinusoidal deviation (wobble) from a perfect spiral. The period of this sine curve corresponds to the
Wobble_frequency
Space curve that winds around a line
it spirals around, and its pitch (the height of one complete helix turn). A conic helix, also known as a conic spiral, may be defined as a spiral on a
Helix
Cylindrical conformal map projection
those countries as less important. Mercator himself used the equal-area sinusoidal projection to show relative areas. However, despite such criticisms, the
Mercator_projection
Mathematical structure
while not containing it, must be transcendental. This applies not just to sinusoidal curves, therefore; but to large classes of curves showing oscillations
Transcendental_curve
Rate of change of acceleration with time
deceleration sinusoidally with zero acceleration in between (see graphic captioned "Sinusoidal acceleration profile"), making the speed appear sinusoidal with
Jerk_(physics)
Ribosomes bound to an mRNA molecule
These double row structures generally have a "sinusoidal" (zigzag) or 3-D helical path. In the "sinusoidal" path, there are two types of contact between
Polysome
Pulse that is substantially slowed to less than the speed of light
the frequency of the (sinusoidal) light wave. The latter leads to dispersion. A human eye perceives the intensity of the sinusoidal disturbance as the brightness
Slow_light
Dynamic disturbance in a medium or field
specific direction of travel. Mathematically, the simplest wave is a sinusoidal plane wave in which at any point the field experiences simple harmonic
Wave
Information storage method
The groove on the surface of a CD-R disc is not a perfect spiral and contains slight sinusoidal deviations called wobble. Frequency modulation is used to
Absolute_Time_in_Pregroove
Passive two-terminal electrical component that stores energy in its magnetic field
i(t)~}{\mathrm {d} \;\!t}}} When there is a sinusoidal alternating current (AC) through an inductor, a sinusoidal voltage is induced. The amplitude of the
Inductor
Device that measures electric power
current coil. The wattmeter reads P = (1/T) ∫0T v(t)i(t) dt, which in sinusoidal steady-state reduces to Vrms Irms cos(φ), where T is the period of p(t)
Wattmeter
Oscillating dynamical system with nonlinear damping
(1-x^{2}){dx \over dt}+x=A\sin(\omega t),} where A is the amplitude of the sinusoidal driving function and ω is its angular frequency. Author James Gleick described
Van_der_Pol_oscillator
Type of variable star
most common type of type I Cepheid. In some cases, the smooth pseudo-sinusoidal light curve shows a "bump", a brief slowing of the decline or even a small
Classical_Cepheid_variable
Test of gravitational redshift
continuously varying Doppler shift on the gamma ray source. Superimposed on the sinusoidal motions of the transducer was the slow (typically about 0.01 mm/s) constant
Pound–Rebka_experiment
Species of fish
that clings to the gills of the fish and metamorphoses into a plump, sinusoidal, wormlike body, with a coiled mass of egg strings at the rear. Nedreaas
Merlangius
Non-diffractive wave
to produce accelerating Bessel beams included beams with helical and sinusoidal trajectories as well as the early effort for beams with piecewise straight
Bessel_beam
Optical disk technology
maintain a precise rotation speed, tracks have a slight superimposed sinusoidal excursion of 0.3 µm at a frequency of 22.05 kHz. In addition a 1 kHz frequency
CD-RW
Electrical resonant transformer circuit invented by Nikola Tesla
millisecond. Each spark across the spark gap produces a pulse of damped sinusoidal high voltage at the output terminal of the coil. Each pulse dies out before
Tesla_coil
Genus of beetles
lateral, flat and visible also in the proepisternum. Mesosternal cavity sinusoidal and a little raised behind. Metacoxal plates little enlarged inwardly
Opselater
Device or system that exhibits resonance
trip is 2 d {\displaystyle 2d\,} . To cause resonance, the phase of a sinusoidal wave after a round trip must be equal to the initial phase so the waves
Resonator
Electronic measuring instrument that combines several measurement functions in one unit
square wave, simple rectifier-type circuits can only be calibrated for sinusoidal waveforms. Other wave shapes require a different calibration factor to
Multimeter
Pregnancy monitoring test
variability, with recurrent late/variable decelerations or bradycardia; or Sinusoidal fetal heart rate. FIGO has recently modified the guidelines on intrapartum
Cardiotocography
Common name for several fish, but mainly the demersal genus Gadus
There the larva clings to the gills while it metamorphoses into a plump sinusoidal wormlike body with a coiled mass of egg strings at the rear. The front
Cod
Optical component which splits light into several beams
interference patterns. A holographic grating has sinusoidal grooves as the result of an optical sinusoidal interference pattern on the grating material during
Diffraction_grating
Dependence of the state of a system on its history
is a lag between input and output. An example is a sinusoidal input X(t) that results in a sinusoidal output Y(t), but with a phase lag φ: X ( t ) = X 0
Hysteresis
Particular mapping that projects a sphere onto a plane
"tightness" of the loxodrome. Thus, loxodromes correspond to logarithmic spirals. These spirals intersect radial lines in the plane at equal angles, just as the
Stereographic_projection
Type of radio transmitter
spark, this cycle produces a radio signal consisting of an oscillating sinusoidal wave that increases rapidly to a high amplitude and decreases exponentially
Spark-gap_transmitter
Process involved in the controlled movement of a sperm cell
viscous environment of the female reproductive tract. The trains move in a sinusoidal motion. Sperm motility is also affected by certain factors released by
Sperm_motility
Recordable optical disc specification
The groove on the surface of a CD-R disc is not a perfect spiral and contains slight sinusoidal deviations called wobble. Frequency modulation is used to
CD-R
Composite material made of a polymer matrix reinforced with fibres
of the multilayer interlock equipment is that due to the conventional sinusoidal movement of the yarn carriers to form the preform, the equipment is not
Fibre-reinforced_plastic
Type of observed X-ray astronomy pattern
as a continuum of noise together with a QPO. An oscillating shot is a sinusoidal variation that starts suddenly and decays exponentially. A scenario in
Quasi-periodic_oscillation
Constant speed wavetrain
function of space and time. Therefore, u and v, or Re(A) and Im(A), are sinusoidal functions of space and time. These exact solutions for the periodic travelling
Periodic_travelling_wave
Fish that can generate electric fields
nearly pure sine wave with few harmonics, males produce a far sharper non-sinusoidal waveform with strong harmonics. Male bluntnose knifefishes (Brachyhypopomus)
Electric_fish
Type of variable star that pulsates radially
galactic plane and the Galaxy's local spiral structure. A group of classical Cepheids with small amplitudes and sinusoidal light curves are often separated
Cepheid_variable
(1986) obtained a smooth roll-up of a vortex sheet into a double branched spiral. Since point vortices are inherently chaotic, a Fourier filter is necessary
Vortex_sheet
Planned skyscraper in New York City
Von Karman effect typical of cylindrical structures which provokes a sinusoidal whirlwind and consequently lateral pulsating forces. The helicoidal shape
Helicoidal_Skyscraper
Types of electrical transformer
an electronic oscillator circuit. Each pulse serves to drive resonant sinusoidal oscillations in the tuned winding, and due to resonance a high voltage
Transformer_types
Structural element that transmits weight from above to below
cross section throughout its length always follows a partial or composite sinusoidal curve shape, and the critical load is given by f c r ≡ π 2 E I m i n L
Column
Device to couple energy between circuits
are not typically reflected in transformer equivalent circuits. With sinusoidal supply, core flux lags the induced EMF by 90°. With open-circuited secondary
Transformer
Exactly solvable model of coupled oscillators
oscillators are identical or nearly identical, and that interactions depend sinusoidally on the phase difference between each pair of objects. In the most popular
Kuramoto_model
Behavior of some weakly electric fishes
species of Eigenmannia, which has a quasi-sinusoidal wave discharge of about 300 Hz. They found that when a sinusoidal electrical stimulus is emitted from an
Jamming_avoidance_response
French painter, illustrator and designer
"Kangaroo gun" whose "barrel is extensively studied ... to give the bullet a sinusoidal trajectory which follows the animal in its leaps", or a disposable "Plaster
Jacques_Carelman
Genus of spirocute euglenids
anterior flagellum, positioned in a curve to the right of the cell, in a sinusoidal pattern. This may also reflect the evolution of ancestral phagotrophic
Heteronema
Organ duct
liver). The inner surface of the cystic duct features spiral, crescentic mucosal folds - the spiral folds of cystic duct. The inner surface of the proximal
Cystic_duct
5483-3 Time-dependent quantities – Part 3: Complex representation of sinusoidal time-dependent quantities Active DIN 5486 Notation of matrices Withdrawn
List_of_DIN_standards
Binary star with an X-ray pulsar in the constellation Centaurus
Later, it became clear that the period variations followed a 2.09 day sinusoidal curve around the 4.84 second period. These variations in arrival time
Centaurus_X-3
List of definitions of terms and concepts used in electrical engineering and electronics
an input frequency. harmonic oscillator An oscillator which produces sinusoidal output, such as a simple RLC oscillator. harmonic A waveform that has
Glossary of electrical and electronics engineering
Glossary_of_electrical_and_electronics_engineering
Demonstration of metallic salts crystallization
(1 October 2020). "Precipitate Patterns in a Hele-Shaw Cell with Small Sinusoidal Height Variations". The Journal of Physical Chemistry C. 124 (39): 21617–21624
Chemical_garden
Medical imaging technique
single-shot EPI, all of k-space is scanned in a single shot, following either a sinusoidal or zig-zag trajectory. Since alternating lines of k-space are scanned
Physics of magnetic resonance imaging
Physics_of_magnetic_resonance_imaging
Surface containing a line through every point
Corrugated roof tiles ruled by parallel lines in one direction, and sinusoidal in the perpendicular direction Construction of a planar surface by ruling
Ruled_surface
fluctuated in intensity due to varying atmospheric conditions while tracing a sinusoidal path across the Pacific. The storm finally lost its deep convection on
2019_Pacific_hurricane_season
Medical diagnostic method
and on the presence (or absence) of internal thrombosis. During late (sinusoidal) phase, if totally "filled" with CA, hemangioma appears isoechoic to the
Ultrasonography of liver tumors
Ultrasonography_of_liver_tumors
Shape with four equal sides and angles
triangle is formable to be a rotor within a square Square wave, a non-sinusoidal periodic wavelength Tombstone (typography), a mathematical symbol involving
Square
Mongolian writing system
imperial seals and the like, was more elaborate, with squared sinusoidal lines and spirals.[citation needed] This ʼPhags-pa script is different from the
ʼPhags-pa_script
Genus of beetles
proepisternum (in males they are smaller than in females). Mesosternal cavity sinusoidal. Metacoxal plates of the same width throughout. Abdominal luminous organ
Hypsiophthalmus
pixel. Here input is an array (digital image). damped sine wave Is a sinusoidal function whose amplitude approaches zero as time increases. degree of
Glossary_of_calculus
State of matter with properties of both conventional liquids and crystals
terms are ignored since most phases can be described adequately using sinusoidal functions. For a perfect nematic ψ = 0 {\displaystyle \psi =0} and for
Liquid_crystal
Biological sound detection process
algorithms and applications. Wiley interscience. ISBN 9780471741091. For sinusoidal signals presented on the horizontal plane, spatial resolution is highest
Sound_localization
Material for building and design
façade and pitched roofs, and renovation work. Profiles available include: sinusoidal wave corrugated profiles; trapezoidal profiles with various geometries;
Copper_in_architecture
rotation of an astronomical body) or the rate of change of the phase of a sinusoidal waveform (e.g. in oscillations and waves), or as the rate of change of
Glossary_of_physics
velocity Significant wave height Sine wave Single-sideband modulation Sinusoidal plane-wave solutions of the electromagnetic wave equation Skywave Slow-wave
Index_of_wave_articles
Pressure of soil in horizontal direction
showed analytically that K0 deviates from unity with downward trend as the sinusoidal term of the internal friction angle of material increases, i.e. K 0 (
Lateral_earth_pressure
British physicist (1918–1994)
image-forming optical systems. Briefly, the contrast of the image of a sinusoidal object is defined as the difference in intensities between the peaks and
Harold_Hopkins_(physicist)
Property that an increasing voltage results in a decreasing current
the linear portion of the I–V curve, the output waveform will be nearly sinusoidal and the frequency will be most stable. In circuits in which R {\displaystyle
Negative_resistance
Star whose brightness fluctuates, as seen from Earth
was clearly detected. The light curves of these systems are often quasi-sinusoidal in shape. A comparison with the radial velocity curve will often suffice
Variable_star
Equations that describe the behavior of a physical system
{d^{2}\theta }{dt^{2}}}=-{\frac {g}{\ell }}\sin \theta \,,} and a damped, sinusoidally driven harmonic oscillator, F 0 sin ( ω t ) = m ( d 2 x d t 2 + 2 ζ
Equations_of_motion
Historic site in New South Wales, Australia
and provides water views though the curtain of native trees. The heavy sinusoidal roof mass passes over as a visually uninterrupted form from the interior
Buhrich_House_II
Representation of auditory sensation and perception in the nervous system
primarily determines the loudness with which the sound is perceived. In a sinusoidal function such as C sin ( 2 π f t ) {\displaystyle C\sin(2\pi ft)} ,
Neural_encoding_of_sound
Manufacture of electromagnetic coils
can also have a stroke adjustment and that uses the advantage of the sinusoidal movement pattern without needing a drive motor to reverse. Strokes (windings)
Coil_winding_technology
1993 video game
reflective prism. "The Spinning Song" by Felix Mendelssohn Trig Enigma Sinusoidal lines scroll down across a green background. original music by A.D. Chaplin
FlixMix
Constructed language
vowel, reflecting how Matter lasts longer than movement. Sound I [iː] A sinusoidal Sound wave: a long-held vowel, reflecting how Sound travels more slowly
AUI_(constructed_language)
Plane curve
simple equations of motion. In electronics, the relative phase of two sinusoidal signals can be compared by feeding them to the vertical and horizontal
Ellipse
Mechanisms and evolution of insect flight
than the average velocity. If we assume that the velocity oscillates (sinusoidally) along the wing path, the maximum velocity is twice as high as the average
Insect_flight
Numerical method in computational electromagnetics
subsectional basis functions include pulse, piecewise triangular, piecewise sinusoidal and rooftop functions. Triangular patches, introduced by S. Rao, D. Wilton
Method of moments (electromagnetics)
Method_of_moments_(electromagnetics)
Genus of beetles
with the color of the integument. Punctures variable. Mesosternal cavity sinusoidal. Metacoxal plates tapering outwardly. Abdominal luminous organ small,
Pyrearinus
Relativistic correction
}^{(proper)}} is the angular velocity observed by the particle. This represents sinusoidal motion with angular velocity γ ω ( p r o p e r ) {\displaystyle \gamma
Thomas_precession
Religious building in Brugherio
are linked along the axis of the shaft by a continuous sinusoidal curve, similar to a spiral. The mosaic is in reddish hues. From Jacob the branches
San_Carlo,_Brugherio
quadrupole field of intensity d E q {\displaystyle dE_{q}} that varies in a sinusoidal manner proportional to c o s ( 2 ω t ) {\displaystyle cos(2\omega t)}
Synchronous coefficient of drag alteration
Synchronous_coefficient_of_drag_alteration
Protein in the immune system
to sever F-actin. F-actin, severed and capped by pGSN, is removed by sinusoidal endothelial cells of the liver. pGSN removes 60% of actin trapped in fibrin
Plasma_gelsolin
Proposed spacecraft propulsion method
antenna coils each of radius R c {\displaystyle R_{c}} (m), each carrying a sinusoidal alternating current (AC) with the total current of I c {\displaystyle
Magnetic_sail
superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the
Glossary_of_engineering:_A–L
Mixing of fluids due to eddy currents
said that, in planetary-boundary-layer heat conduction, the source is a sinusoidal time function and so the mathematical complexity of some of these solutions
Eddy_diffusion
X-ray imaging technique
stroboscopic exposure techniques. In this way, one selected phase of a sinusoidally varying movement is selectively images as a "snapshot". First applications
Diffraction_topography
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