"Cycloid" Example Sentences
1) The cycloid traced out by a point on the rim of a rolling circle is a basic curve studied in calculus.
2) The cycloid curve is generated when a circle rolls along a straight line without slipping.
3) A cycloid possesses an infinite number of cusps and loops.
4) The area bound by a cycloid and the base line can be calculated using calculus.
5) The simplicity and symmetry of the cycloid make it an interesting mathematical curve to study.
6) The motion of the generating circle produces the cycloid curve.
7) The Cartesian coordinates of points on a cycloid can be expressed in terms of the generating circle's radius and angle of rotation.
8) Engineers use cycloid curves in the design of gears, cams, and other mechanical devices.
9) Simple harmonic motion often involves the motion of a particle tracing out a cycloid curve.
10) Ancient Greek mathematicians studied the geometrical properties of cycloids.
11) The perimeter and arc length of a cycloid can be approximated using calculus.
12) A cycloid is an example of a roulette, a curve generated by a curve rolling along a straight line.
13) The trough and crest radii of a cycloid can be determined from the generating radius.
14) The roulette curve traced out by the pole of a rolling circle is also a cycloid.
15) The wax seal on an ancient scroll left a cycloid impression in the softened wax.
16) Some amusement park rides involve vehicles tracing a cycloid path.
17) The inversion of a cycloid curve yields another related cycloid.
18) Analyzing a cycloid curve involves integrating a periodic function.
19) The tangent at any point on a cycloid forms a constant angle with the base line.
20) The graphical representation of the path traced by a cycloid is smooth and curved.
21) The tautochrone problem involving a cyloid curve fascinated mathematicians and physicists.
22) Construction of a cycloid with compass and straightedge requires drawing many arcs and lines.
23) The cycloid can be modeled using a parametric function.
24) The derivatives of a cycloid describe rates of change in position, velocity and acceleration.
25) The period of a simple pendulum approximates the period of a particle tracing a circular cycloid.
26) A cycloid multi-fluted milling cutter produces smooth finishes on machined surfaces.
27) A particle tracing out a cycloid curves possesses non-uniform acceleration.
28) The symmetries and self-intersections of a cycloid curve yield interesting patterns.
29) Linkages composed of rods and joints can approximate the motion of a cycloid curve.
30) The area enclosed by a cycloid and the x-axis grows nonlinearly.
31) A cycloid profile cam can control motion with uniform velocity.
32) The involute of a cycloid is a spiral curve.
33) The geometry of a cycloid curve arises from the rolling motion of a circle.
34) Pantographs designed for copying drawings often incorporate a cycloid linkage.
35) Mathematical models of cycloid motion involve solving differential equations.
36) The evolute curve of a cycloid possesses cusps corresponding to inflection points.
37) The tautochrone property led to the cycloid's importance for physics problems.
38) Engineers design cam profiles with cycloid shapes to convert rotational motion to linear motion.
39) The curve traversed by the instant center of rotation of a rolling circle is another cycloid.
40) The dual curves of a cycloid and an evolute are intimately related.
41) Constructing an automaton that traces a cycloid curve requires precise gear ratios.
42) The paramaterized equations of a cycloid involve trigonometric and exponential functions.
43) Scientists studied cycloids to gain insights into uniform acceleration and deceleration.
44) The arc length function of a cycloid yields non-polynomial expressions.
45) Constructing a cycloid curve with precise dimensional accuracy requires careful measurements.
46) Non-Euclidean geometries may reveal new properties of cycloid curves.
47) Scientists continue to uncover interesting mathematical properties of cycloid curves.
48) Representing motion using a cycloid allows for modeling phenomena involving oscillations.
49) The period of simple harmonic motion is related to the period of cycloid motion.
50) The precise geometric form of a cycloid curve requires an infinite number of points.
51) Changing parameters of the generating circle alters the size and shape of the cycloid.
52) The logarithmic spiral involute of a cycloid intersects every radial line at a constant angle.
53) Identification of a physical curve as a cycloid requires measuring radius and angle of rotation.
54) The property of a cycloid that a body takes the same time to descend different portions of its cycloid inspired numerous physical problems.
55) The curve traversed by the center of percussion of a rolling circle bouncing off frictionless edges is a cycloid.
56) Integrating functions that describe cycloid motion yields interesting hyperbolic functions.
57) Cutting a cycloid gear requires precision machining technology.
58) Deforming a cycloid curve alters its geometric and dynamic properties.
59) Constructing a device that traces an inverted cycloid is mechanically challenging.
60) The relationship between a cycloid curve and its evolute curve reveal properties of curvature.
Common Phases
cyclic curve
cyclic path
rolling circle curve
curve of constant width
roulette curve
epi
cycloid curve
hypo
cycloid curve
involute spiral curve
evolute curve
curtate curve
generatrix
cissoid curve
cissoidal curve
curve of quickest descent
tautochrone curve
pendulum curve
gear curve
cam curve
reflecting curve
multi-toothed cutter
curve of constant breadth
Common phrases related to
cycloid curves include:
area bounded by a
cycloid
arc length of a
cycloid
perimeter of a
cycloid
period of a
cycloid curve
slope at any point on a
cycloid
center of curvature of a
cycloid
point of inflection on a
cycloid
tangent line to a
cycloid
velocity of a particle on a
cycloid path
acceleration of a particle on a
cycloid path