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Curve traced by a point on a rod as one end is dragged along a line
In geometry, a tractrix (from Latin trahere 'to pull, drag'; plural: tractrices) is the curve along which an object moves, under the influence of friction
Tractrix
Loudspeaker using an acoustic horn
Frequency Transducer, yielding a 90° x 35° output pattern at 20 kHz. The tractrix horn is very similar in many respects to the exponential horn and has gained
Horn_loudspeaker
Species of moth
Antaeotricha tractrix is a moth in the family Depressariidae. It was described by Edward Meyrick in 1925. It is found in Brazil. The wingspan is about
Antaeotricha_tractrix
American audio equipment manufacturer
crossover network. In 1989, Klipsch introduced a midrange horn with a tractrix flare which was said to reduce "honkiness" and create a more open sound
Klipsch_Audio_Technologies
Curve traced by a string as it is unwrapped from another curve
t,1/\cosh t),} and is thus a tractrix. The other involutes are not tractrices, as they are parallel curves of a tractrix. The parametric representation
Involute
"Seiffert's Spherical Spiral". mathworld.wolfram.com. Retrieved 2023-01-31. "Tractrix spiral". www.mathcurve.com. Retrieved 2019-02-23. "Conical spiral of Pappus"
List_of_spirals
Curve formed by a hanging chain
point starting at the vertex when a line is rolled on a catenary, is the tractrix. Another roulette, formed by rolling a line on a catenary, is another line
Catenary
Geometric surface
Another description is a generalized helicoid constructed from the tractrix. Breather surface Kuen surface "Wolfram Mathworld: Dini's Surface". Retrieved
Dini's_surface
Geometric surface
revolving a tractrix about its asymptote. As an example, the (half) pseudosphere (with radius 1) is the surface of revolution of the tractrix parametrized
Pseudosphere
Cochleoid Cycloid Horopter Isochrone Pursuit curve Rhumb line Syntractrix Tractrix Trochoid Archimedean spiral Cornu spiral Fermat's spiral Hyperbolic spiral
Gallery_of_curves
Cubic plane curve
perpendicular to its axis of symmetry) it resembles a tractrix, but it differs from the tractrix in having a polynomial equation. Let the radius of C be
Cissoid_of_Diocles
Dutch mathematician and physicist (1629–1695)
S2CID 144406041. Yoeder, Joella (1991). "Christiaan Huygens' Great Treasure" (PDF). Tractrix. 3: 1–13. Archived (PDF) from the original on 13 April 2018. Retrieved
Christiaan_Huygens
Type of inertial force
2025-09-11. Yoder, Joella (1991). "Christiaan Huygens' Great Treasure" (PDF). Tractrix. 3: 1–13. Archived (PDF) from the original on 13 April 2018. Retrieved
Centrifugal_force
Hyperbolic spiral Lituus Logarithmic spiral Nielsen's spiral Syntractrix Tractrix Trochoid Bézier curve Loess curve Lowess Ogee Polygonal curve Maurer rose
List_of_curves
Class of curves traced by a point which follows another moving point
vertices of a regular polygon chase each other along logarithmic spirals. Tractrix Circles of Apollonius#Apollonius pursuit problem Pursuit–evasion Bouguer
Pursuit_curve
Type of bridge
520-521, footnote 5 on pages 521-522 Lockwood, E.H. (1961). "Chapter 13: The Tractrix and Catenary". A Book of Curves. Cambridge. Salmon, George (1879). Higher
Simple_suspension_bridge
spiral Lituus Logarithmic spiral Nielsen's spiral Golden spiral Syntractrix Tractrix Trochoid Bézier curve Splines B-spline Nonuniform rational B-spline Ogee
List_of_mathematical_shapes
Centers of curvature of a curve
cycloid, of a logarithmic spiral is the same logarithmic spiral, of a tractrix is a catenary. A curve with a similar definition is the radial of a given
Evolute
{b+{\sqrt {b^{2}-y^{2}}}}{y}}.} It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency
Syntractrix
Mathematician, philosopher (1688–1757)
Franssen, Maarten (1991). "The Ocular Harpsichord of Louis-Bertrand Castel". Tractrix. 3: 39. Retrieved 28 November 2016. Descriptions of an Eye-Organ or the
Louis_Bertrand_Castel
Device that produces a visual display to accompany music
science and aesthetics of an eighteenth-century cause célèbre" (PDF). Tractrix: Yearbook for the History of Science, Medicine, Technology and Mathematics
Color_organ
Mathematics of smooth surfaces
equator, that is singular). Pseudosphere can be obtained by rotating a tractrix around its asymptote. In 1868 Eugenio Beltrami showed that the geometry
Differential geometry of surfaces
Differential_geometry_of_surfaces
constructions, angle trisection, and mathematical origami The catenary and the tractrix, curves formed from physical forces, and their use in bridges and bearings
How_Round_Is_Your_Circle?
French chemist (1755–1809)
devised in 1791 by Fourcroy for the establishment of clinical laboratories". Tractrix: Yearbook for the History of Science, Medicine, Technology, and Mathematics
Antoine-François_de_Fourcroy
Representation of music in film or other art forms
Maarten Franssen, "The Ocular Harpsichord of Louis-Bertrand Castel." Tractrix: Yearbook for the History of Science, Medicine, Technology and Mathematics
Visual_music
Artistic Phrase
Castel. The Science and Aesthetics of an Eighteenth-Century Cause Célèbre." Tractrix 3 (1991): 15-77. Gage, J. "Making Sense of Colour. The Synaesthetic Dimension
Synesthesia_in_art
Dutch historian of science
Robert Boyle, and Isaac Newton. "Pascal: His Science and His Religion" Tractrix 1, 1989, pp. 115–139. (Translation of "Pascal: Zijn wetenschap en zijn
Reijer_Hooykaas
Mathematical function relating circular and hyperbolic functions
Gudermannian provides a good model for the shape of spiral galaxy arms. Tractrix Catenary § Catenary of equal strength The symbols ψ {\textstyle \psi }
Gudermannian_function
Spiral asymptotic to a line
hyperbolic spiral rolls along a straight line, its center traces out a tractrix. Johann Bernoulli and Roger Cotes also wrote about this curve, in connection
Hyperbolic_spiral
Dutch historian of mathematics (1940–2024)
became professor of history of mathematics. Bos took an interest in the tractrix as a mathematical stimulus. Bos retired in 2005. Since his retirement he
Henk_J._M._Bos
Dutch science historian
University Press, 1989. ISBN 9780521341400. Christiaan Huygens' Great Treasure, Tractrix 3 (1991), pp. 1–13 'The Archives of Christiaan Huygens and his Editors'
Joella_Yoder
tetrapetra Antaeotricha tibialis Antaeotricha tornogramma Antaeotricha tractrix Antaeotricha tricapsis Antaeotricha tripustulella Antaeotricha trisinuata
List_of_moths_of_Brazil
Mathematics book on pursuit-evasion games
including variations where the pursuer may aim ahead of the target and the tractrix curve generated by a pursuer that follows the target at constant distance
Chases_and_Escapes
English-American inventor and polymath (1871–1950)
bearings for oil lubrication to achieve a more precise fit, and using tractrix-shaped sleeves to distribute wear uniformly. In an 1896 publication in
Mark_Barr
German-born Dutch anatomist
"Squares and diopters: the drawing system of a famous anatomical atlas". Tractrix: Yearbook for the History of Science, Medicine, Technology and Mathematics
Bernhard_Siegfried_Albinus
Scientific instrument
limits of the time. van Helden, A. C. (1991). "The age of the air pump". Tractrix 3. pp. 149–172. de Clercq, P. (1997). At the sign of the Oriental Lamp
Van_Musschenbroek_vacuum_pump
Largest genus in moth subfamily Stenomatinae
tinactis (Meyrick, 1915) Antaeotricha tornogramma Meyrick, 1925 Antaeotricha tractrix Meyrick, 1925 Antaeotricha tremulella (Walker, 1864) Antaeotricha tribomias
Antaeotricha
instruments around 1700. The Musschenbroek Documents in Marburg" (PDF). Tractrix. 3: 79–120. PMID 11612624.. On page 82. de Hinojosa, Adriaen Pieter (1690)
Wolferdus_Senguerdius
witch trials develop, following 250 years of witch-hunts in Europe. The tractrix, sometimes called a tractory or equitangential curve, is first studied
1692_in_science
TRACTRIX
TRACTRIX
TRACTRIX
TRACTRIX
Male
Italian
Italian form of Latin Nicolaus, NICOLA means "victor of the people."
Boy/Male
Tamil
Kriyansh | கà¯à®°à¯€à®¯à®‚à®·
Lord Krishna
Girl/Female
Hindu
Part of a divine power
Male
Hebrew
(זְרוּבָּבֶל) Hebrew name ZERUBBABEL means "born at Babylon" or "scattered to Babylon." In the bible, this is the name of the leader of the first of the returning exiles.
Female
Native American
Native American Hopi name TIPONI means "child of importance."
Boy/Male
German
Powerful ruler.
Boy/Male
Indian
Chosen one
Girl/Female
Tamil
Beautiful woman
Boy/Male
Hindu
Girl/Female
Irish
True desire.
TRACTRIX
TRACTRIX
TRACTRIX
TRACTRIX
TRACTRIX
n.
The surface of constant negative curvature generated by the revolution of a tractrix. This surface corresponds in non-Euclidian space to the sphere in ordinary space. An important property of the surface is that any figure drawn upon it can be displaced in any way without tearing it or altering in size any of its elements.
n.
A curve such that the part of the tangent between the point of tangency and a given straight line is constant; -- so called because it was conceived as described by the motion of one end of a tangent line as the other end was drawn along the given line.
n.
A tractrix.