Searches , social queries for SECANT LINE
Search references for SECANT LINE. Phrases containing SECANT LINE
See searches and references containing SECANT LINE!
Search references for SECANT LINE. Phrases containing SECANT LINE
See searches and references containing SECANT LINE!SECANT LINE
Line that intersects a curve at least twice
In geometry, a secant is a line that intersects a curve at a minimum of two distinct points. The word secant comes from the Latin word secare, meaning
Secant_line
Root-finding method
the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method
Secant_method
Mathematical term
points, the slope of the curve may be approximated by the slope of the secant line between two nearby points. When the curve is given as the graph of an
Slope
Topics referred to by the same term
secant in Wiktionary, the free dictionary. Secant is a term in mathematics derived from the Latin secare ("to cut"). It may refer to: a secant line,
Secant
In mathematics, straight line touching a plane curve without crossing it
called supporting lines. The geometrical idea of the tangent line as the limit of secant lines serves as the motivation for analytical methods that are
Tangent
Theorem of convex functions
that the secant line of a convex function lies above the graph of the function, which is Jensen's inequality for two points: the secant line consists
Jensen's_inequality
Geometric line segment whose endpoints lie on a circular arc
a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow"). More generally, a chord is a line segment
Chord_(geometry)
Geometry theorem relating line segments created by a secant and tangent line
Euclidean geometry, the tangent-secant theorem describes the relation of line segments created by a secant and a tangent line with the associated circle.
Tangent–secant_theorem
Change in the shape or size of an object
with secant line at point where λ = λ Y {\displaystyle \lambda =\lambda _{Y}} . After this value, the slope becomes smaller than the secant line where
Deformation_(engineering)
Instantaneous rate of change (mathematics)
the slope of the secant line from 0 to h {\displaystyle h} is one; if h {\displaystyle h} is negative, then the slope of the secant line from 0 {\displaystyle
Derivative
Use of numerical analysis to estimate derivatives of functions
approximations. A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). Choosing a small
Numerical_differentiation
Polynomial function of degree 4
the secant line and the quartic below the secant line equals the area of the region between the secant line and the quartic above the secant line. One
Quartic_function
Theorem in mathematics
means that at some point the tangent to the graph is parallel to the secant line through the interval's endpoints. It is used in proving other general
Mean_value_theorem
Relative distance of a point from a circle
and the intersection points S 1 , S 2 {\displaystyle S_{1},S_{2}} of a secant line g {\displaystyle g} with c {\displaystyle c} the following statement
Power_of_a_point
Branch of mathematics
line through two points on a curve is called a secant line, so m is the slope of the secant line between (a, f(a)) and (a + h, f(a + h)). The secant line
Calculus
Plane curve: conic section
intersection of the secant line P 2 P 3 {\displaystyle P_{2}P_{3}} with the line x = x 1 {\displaystyle x=x_{1}} (see picture). Then the secant line P 3 P 4 {\displaystyle
Parabola
Line which touches a circle at exactly one point
line t to a circle C intersects the circle at a single point T. For comparison, secant lines intersect a circle at two points, whereas another line may
Tangent_lines_to_circles
Simple curve of Euclidean geometry
centre of the circle to which their arc belongs. Secant: an extended chord, a coplanar straight line, intersecting a circle in two points. Semicircle:
Circle
Type of plane curve
one gets for φ = θ {\displaystyle \varphi =\theta } the same line. Hence any secant line of the circle, defined above, is a tangent of the cardioid, too:
Cardioid
Functions of an angle
tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less commonly used. Each of these
Trigonometric_functions
Study of rates of change
the slope of a secant line through two nearby points on the graph. As h approaches zero, the secant line approaches the tangent line, if the limiting
Differential_calculus
Trigonometric function defined as secant minus one
The external secant function (abbreviated exsecant, symbolized exsec) is a trigonometric function defined in terms of the secant function: exsec θ =
Exsecant
Real function with secant line between points above the graph itself
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or
Convex_function
Mathematical set with some added structure
a circle determines a unique line called the secant line, and as the two points move around the circle, the secant line varies continuously. However,
Space_(mathematics)
Infinite series summable to 1/3
This curve is a parabola. The dots on the secant line AE are equally spaced. Archimedes showed that the sum of the areas of triangles ABC and CDE is 1/4
1/4_+_1/16_+_1/64_+_1/256_+_⋯
Locus of the zeros of a polynomial of degree two
exterior line, a tangent line or a secant line is mapped by the involution σ P {\displaystyle \sigma _{P}} on an exterior, tangent and secant line, respectively
Quadric
Mathematical term for squaring a plane figure
the parabola's two intersection points with the secant line and its intersection with a tangent line of the same slope). For the proofs of these results
Quadrature_(mathematics)
Circle-like pointset in a geometric plane
|l ∩ Ω| = 0 the line l is an exterior line (or passant), if |l ∩ Ω| = 1 a tangent line and if |l ∩ Ω| = 2 the line is a secant line. For finite planes
Oval_(projective_plane)
Shape formed from points common to other shapes
are two intersection points; in this case the line is called a secant line of the circle, and the line segment connecting the intersection points is called
Intersection_(geometry)
Algebraic curve in projective 3-space
and secant lines are pairwise disjoint, except at points of the variety itself. The projection of C onto a plane from a point on a tangent line of C
Twisted_cubic
Speed and direction of a motion
of as the slope of the tangent line to the curve at any point, and the average velocity as the slope of the secant line between two points with t coordinates
Velocity
Function's sensitivity to argument change
x)-f(x)}{\Delta x}}.} The last term is the difference quotient (the slope of the secant line), and taking the limit yields the derivative. Condition numbers of common
Condition_number
All points whose relative distances to two circles are same
the circles have two points in common, the radical axis is the common secant line of the circles. If point P is outside the circles, P has equal tangential
Radical_axis
In algebraic geometry, the secant variety Sect ( V ) {\displaystyle \operatorname {Sect} (V)} , or the variety of chords, of a projective variety V ⊂
Secant_variety
Line tangent to a curve at two locations
bitangent lines (Rohnert 1986). A bitangent differs from a secant line in that a secant line may cross the curve at the two points it intersects it. One
Bitangent
Algorithms for calculating square roots
a secant line spanning the arc, or a tangent line somewhere along the arc may be used as the approximation, but a least-squares regression line intersecting
Square_root_algorithms
Difference of two numbers divided by the logarithm of their quotient
interval between x and y where the derivative f ′ equals the slope of the secant line: ∃ ξ ∈ ( x , y ) : f ′ ( ξ ) = f ( x ) − f ( y ) x − y {\displaystyle
Logarithmic_mean
Change in output that results from employing an added unit of labor
product curve by drawing secants from the origin that intersect (cut) the total product curve. The slope of the secant line equals the average product
Marginal_product_of_labor
Unsolved problem about inscribing a square in a Jordan curve
considers the curves traced out by the midpoints of secant line segments to the curve, parallel to a given line. He shows that, when these curves are intersected
Inscribed_square_problem
Straight figure with zero width and depth
lines can be: tangent lines, which touch the conic at a single point; secant lines, which intersect the conic at two points and pass through its interior;
Line_(geometry)
Algebra theorem about convex functions
x ) − f ( y ) x − y {\displaystyle {\frac {f(x)-f(y)}{x-y}}} of the secant line through the points (x, f (x)) and (y, f (y)) of the graph of f is a
Karamata's_inequality
Cubic plane curve
intersection of the secant line OA and the tangent line at M. Let P be the point of intersection of a line perpendicular to OM through A, and a line parallel to
Witch_of_Agnesi
Geometry theorem relating line segments created by intersecting secants of a circle
the intersecting secants theorem or just secant theorem describes the relation of line segments created by two intersecting secants and the associated
Intersecting_secants_theorem
\end{array}}\right.} It is derived from the mean value theorem, which states that a secant line, cutting the graph of a differentiable function f {\displaystyle f} at
Stolarsky_mean
Mathematical treatise by Archimedes
the area bounded by the parabola and the secant line AB. Proof: Let D be the midpoint of AC. Construct a line segment JB through D, where the distance
The Method of Mechanical Theorems
The_Method_of_Mechanical_Theorems
Type of geometry
the pole of this line. Alternatively, the polar line of P is the set of projective harmonic conjugates of P on a variable secant line passing through P
Projective_geometry
Area bounded by a circular arc and a straight line
is "cut off" from the rest of the disk by a straight line. The complete line is known as a secant, and the section inside the disk as a chord. More formally
Circular_segment
Commonly encountered and tricky integral
The integral of secant cubed is a frequent and challenging indefinite integral of elementary calculus. Integral of sec³x is as follows: ∫ sec 3 x d x
Integral_of_secant_cubed
Overview of and topical guide to geometry
interpolation One-to-one Orthogonal Polar coordinate system Pole Real axis Secant line Circular sector or "sector" Semiperimeter Symmetry Shape Pattern Crystal
Outline_of_geometry
Antiderivative of the secant function
In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expressing the antiderivative
Integral of the secant function
Integral_of_the_secant_function
Expression in calculus
interval. Geometrically, this difference quotient measures the slope of the secant line passing through the points with coordinates (a, f(a)) and (b, f(b)).
Difference_quotient
Construction of an angle equal to one third a given angle
parallel. As the line segments OP and PA are equal, these three parallel lines delimit two equal segments on every other secant line, and in particular
Angle_trisection
Cylindrical conformal map projection
This is sometimes visualized as a projection onto a cylinder which is secant to (cuts) the sphere, though this picture is misleading insofar as the standard
Mercator_projection
Arc crossing all meridians of longitude at the same angle
points Δs, measured along a loxodrome, is simply the absolute value of the secant of the bearing (azimuth) times the north–south distance (except for circles
Rhumb_line
Sphere-like surface
and if | g ∩ O | = 2 {\displaystyle |g\cap {\mathcal {O}}|=2} the line is a secant line. (2) At any point P ∈ O {\displaystyle P\in {\mathcal {O}}} the
Ovoid_(projective_geometry)
(O1) Any line meets O {\displaystyle {\mathcal {O}}} in at most two points. ( g {\displaystyle g} is called exterior, tangent and secant line if | g ∩
Quadratic_set
Ratio of distance on a map to the corresponding distance on the ground
complicated functions of both latitude and longitude. The basic idea of a secant projection is that the sphere is projected to a cylinder which intersects
Scale_(map)
Inverse functions of sin, cos, tan, etc.
Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the
Inverse trigonometric functions
Inverse_trigonometric_functions
Topics referred to by the same term
Common chord may refer to: Common chord (geometry), the secant line that joins the intersection points of two curves Common chord (music), a chord shared
Common_chord
High-capacity public transport
Marseille, Monterrey, Montreal, Nanchang, Nuremberg, Rotterdam, Toronto Secant, e.g. Athens, Budapest, Busan, Cairo, Guadalajara, Kharkiv, Kyiv, Hyderabad
Rapid_transit
Optimization algorithm
descent direction. Grid search Learning rate Pattern search (optimization) Secant method Nemirovsky and Ben-Tal (2023). "Optimization III: Convex Optimization"
Line_search
Algorithms for zeros of functions
iterated. Interpolating two values yields a line: a polynomial of degree one. This is the basis of the secant method. Regula falsi is also an interpolation
Root-finding_algorithm
New York City Subway line
shallower between East 91st and 93rd Streets, 1.1-meter-diameter (3.6 ft) secant piles did the same work at shallower depths. Earth excavation was conducted
Second_Avenue_Subway
Mathematical functions
inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent. They are commonly denoted by the symbols
Inverse_hyperbolic_functions
Optimization method
gradient evaluations (or approximate gradient evaluations) via a generalized secant method. Since the updates of the BFGS curvature matrix do not require matrix
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Conic conformal map projection
parallels. Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both
Lambert conformal conic projection
Lambert_conformal_conic_projection
Under-construction light rail transit line in Hennepin County, Minnesota
To protect the foundation of nearby buildings, an approximately 500-foot secant wall was added to construction plans. This required new equipment, different
Metro Green Line Extension (Minnesota)
Metro_Green_Line_Extension_(Minnesota)
rates . removable discontinuity . Rolle's theorem . root test . scalar . secant line . second-degree polynomial . second derivative . second derivative test
Glossary_of_calculus
Portuguese mathematician (1914–1972)
distance–time graph as speed—and the geometric notion of slope (coefficient of a secant line approaching the tangent on a curve). Only after these concrete and symbolic
José_Sebastião_e_Silva
Adaptation of the standard Mercator projection
thereby designated the central meridian. Both projections may be modified to secant forms, which means the scale has been reduced so that the cylinder slices
Transverse Mercator projection
Transverse_Mercator_projection
Systematic representation of the surface of a sphere or ellipsoid onto a plane
visualized as secant lines where the cone intersects the globe—or, if the map maker chooses the same parallel twice, as the tangent line where the cone
Map_projection
by finding the secant line. 2) When y ′ {\displaystyle y'} is concave down: the lower bound approximation can be the secant line. The upper bound approximation
Chaplygin's Theorem and Method for Solving ODE
Chaplygin's_Theorem_and_Method_for_Solving_ODE
Nonlinear form of the Schrödinger equation
A hyperbolic secant (sech) envelope soliton for surface waves on deep water. Blue line: water waves. Red line: envelope soliton.
Nonlinear Schrödinger equation
Nonlinear_Schrödinger_equation
Ancient Greek mathematician (fl. 300 BC)
Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem of
Euclid
Suburban rail line in Perth, Western Australia
it until the railway was opened. The tunnel walls were constructed using secant piles. The close proximity of the tunnel to the Mitchell Freeway's bridge
Yanchep_line
indicates the UPS system uses a stereographic map projection, specifically a secant version based on an elliptical model of the earth. The scale factor at each
Universal polar stereographic coordinate system
Universal_polar_stereographic_coordinate_system
Theorem in projective geometry
if | g ∩ o | = 2 {\displaystyle |g\cap {\mathfrak {o}}|=2} the line is a secant line. (2) For any point P ∈ o {\displaystyle P\in {\mathfrak {o}}} there
Segre's_theorem
Concept in projective geometry
extended to a larger arc (thus, every point not on the arc is on a secant line of the arc–a line meeting the arc in two points.) Theorem: Let K be a complete
Blocking_set
Line through four points of a curve
quadrisecant is a line that intersects a curve, surface, or other set in four distinct points. It is analogous to a secant line, a line that intersects
Quadrisecant
Unique point and line of a conic section
additional three diagonal points. Given a point Z not on conic C, draw two secants from Z through C crossing at points A, B, D, and E. Then these four points
Pole_and_polar
Geometry theorem relating the line segments created by intersecting chords in a circle
the circle's center M and point S. Next to the tangent-secant theorem and the intersecting secants theorem, the intersecting chords theorem represents one
Intersecting_chords_theorem
Theorem in projective geometry
passant), if |l ∩ Ω| = 1 a tangent line and if |l ∩ Ω| = 2 the line is a secant line. For finite planes (i.e. the set of points is finite) we have a
Qvist's_theorem
Algorithm for finding roots of a function
second-order recurrence relation of the secant method. Whereas the secant method proceeds by constructing a line through two points on the graph of f corresponding
Muller's_method
The area cut off by a secant of a smooth convex oval is not an algebraic function
ovals states that the area cut off by a secant of a smooth convex oval is not an algebraic function of the secant. Isaac Newton stated it as lemma 28 of
Newton's_theorem_about_ovals
Mathematical optimization method
classical secant method. The long BB step size is the same as a linearized Cauchy step, i.e. the first estimate using a secant-method for the line search
Barzilai–Borwein_method
New York City Subway station in Manhattan
Streets, where the rock becomes shallower, 1.1-meter-diameter (3.6 ft) secant piles did the same work at shallower depths. Earth excavation was conducted
96th Street station (Second Avenue Subway)
96th_Street_station_(Second_Avenue_Subway)
Topics referred to by the same term
enterprise Line segment, part of a line bounded by two end points Circular segment, the region of a circle cut off from the rest by a secant or chord Spherical
Segment
Mathematical function relating circular and hyperbolic functions
{\textstyle -\infty <\psi <\infty } to be the integral of the hyperbolic secant ϕ = gd ψ ≡ ∫ 0 ψ sech t d t = arctan ( sinh ψ ) . {\displaystyle
Gudermannian_function
Problem of constructing equal-area shapes
decimal places of π {\displaystyle \pi } . He describes the construction of line segment OS as follows. Let AB (Fig.2) be a diameter of a circle whose centre
Squaring_the_circle
Fundamental trigonometric functions
the length of the opposite side. Similarly, the reciprocal of cosine is secant, which gives the ratio of the hypotenuse length to that of the adjacent
Sine_and_cosine
Geometrical concept
Plans (drawings) Profile gauge Section lining; representation of materials Secant plane Swokowski 1983, p. 296 in more technical language, the cross sections
Cross_section_(geometry)
Circle with radius of one
six standard trigonometric functions – sine, cosine, tangent, cotangent, secant, and cosecant, as well as archaic functions like versine and exsecant –
Unit_circle
value but infinite variance. The hyperbolic distribution The hyperbolic secant distribution The Johnson SU distribution The Landau distribution The Laplace
List of probability distributions
List_of_probability_distributions
Rapid transit system in Hyderabad, India
city of Hyderabad, Telangana, India. The three lines are arranged in a secant model and contain 57 stations. It is funded by a public–private partnership
Hyderabad_Metro
Strong form of uniform continuity
variables, this holds if and only if the absolute value of the slopes of all secant lines are bounded by K. The set of lines of slope K passing through a point
Lipschitz_continuity
Computer software
protocols, like the common POP3 and IMAP4 used for internet mail, need be on-line only during message transfer; the same applies to the NNTP protocol used
Offline_reader
Plane curve
An arbitrary line g {\displaystyle g} intersects an ellipse at 0, 1, or 2 points, respectively called an exterior line, tangent and secant. Through any
Ellipse
Three-dimensional solid
section depend on the radius of the cylinder r and the angle α between the secant plane and cylinder axis, in the following way: e = cos α , a = r sin
Cylinder
Numerical method used to approximate solutions of univariate equations
interval is (ak, bk). Construct the line through the points (ak, f (ak)) and (bk, f (bk)), as illustrated. This line is a secant or chord of the graph of the
Regula_falsi
Railway station in Maharashtra, India
300 secant piles, each to extend to a depth of 17–21 metres. The primary ongoing activity at the construction site is the installation of these secant piles
Bandra Kurla Complex high-speed railway station
Bandra_Kurla_Complex_high-speed_railway_station
travel, tourism, insurance
SECANT LINE
SECANT LINE
SECANT LINE
SECANT LINE
SECANT LINE
SECANT LINE
SECANT LINE
SECANT LINE
SECANT LINE
travel, tourism, insurance