Everything about Tangent
In mathematics, straight line touching a plane curve without crossing it
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is tangent to the curve y = f(x) at a point x = c if the line passes through the point (c, f(c)) on the curve and has slope f'(c), where f' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: TangentA 5-minute orientation
- Skim a recent paper: Arrhenius activation energy of tangent hyperbolic nanofluid over a cone with radiation absorptionInfluential work since 2022
- Pick up a classic book: An elementary treatise on the geometry of conicsThe most-reprinted book on the subject
- Read the landmark paper: Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle pointsCited 9,399 times
- Go sideways: SlopeA closely related topic
- Go sideways: Differential calculusA closely related topic
📖 Definitions
Noun A straight line touching a curve at a single point without crossing it there.
Noun A function of an angle that gives the ratio of the sine to the cosine, in either the real or complex numbers. Symbols: tan, tg.
Noun A course suddenly and unexpectedly divergent from one which was previously being followed (especially one embarked on before reaching the end of the previous course). A new topic of discussion unrelated to the one which came before it, arrived at due to a single (peripheral or trivial) point in common with it.
Noun A new topic of discussion unrelated to the one which came before it, arrived at due to a single (peripheral or trivial) point in common with it.
🏆 Landmark papers (most cited)
Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
When and why PINNs fail to train: A neural tangent kernel perspective
Consistent tangent operators for rate-independent elastoplasticity
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
Shape Statistics: Procrustes Superimpositions and Tangent Spaces
A tangent modulus method for rate dependent solids
A simple algebraic interface capturing scheme using hyperbolic tangent function
Cobb Method or Harrison Posterior Tangent Method
🆕 Influential since 2022
Arrhenius activation energy of tangent hyperbolic nanofluid over a cone with radiation absorption
Tangent search algorithm for solving optimization problems
Insight into Significance of Bioconvection on MHD Tangent Hyperbolic Nanofluid Flow of Irregular Thickness across a Slender Elastic Surface
An Autonomous Path Planning Method for Unmanned Aerial Vehicle Based on a Tangent Intersection and Target Guidance Strategy
Ensemble system for short term carbon dioxide emissions forecasting based on multi-objective tangent search algorithm
📚 Books worth reading
An elementary treatise on the geometry of conicsAsutosh Mookerjee · 1893- 📕Threefolds with semipositive tangent bundleDonu Arapura · 1985
- 📕Introduction to microlocal analysisMasaki Kashiwara · 1986
- 📕Generic equations for constructing smooth paths along circles and tangent lines with application to airport ground pathsL. Keith Barker · 1998
- 📕Tangent and cotangent bundlesYano, Kentarō · 1973
Tangent and cotangent bundlesKentaro Yano · 1973- 📕Eine Invariante für stabil parallelisierte MannigfaltigkeitenMatthias Kreck · 1973
Tangent Structures in Geometry and Their ApplicationsVladimir Balan, Maido Rahula · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Slope In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. It is commonly denoted by the letter m…
- Differential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. The primary objects of study in differential…
- Analytic geometry In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts…
- Derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative…
- Implicit curve In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the…
- Surface (mathematics) In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be…
- Saddle point In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions…
- Algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in…