Everything about Evolute
Centers of curvature of a curve
In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that curve. The evolute of a circle is therefore a single point at its center. Equivalently, an evolute is the envelope of the normals to a curve. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: EvoluteA 5-minute orientation
- Skim a recent paper: DK‐Crush or Mini‐Crush Stenting for Complex Left Main Bifurcation Lesions: The Multicenter EVOLUTE‐CRUSH LM RegistryInfluential work since 2022
- Pick up a classic book: On the origin of species by means of natural selectionThe most-reprinted book on the subject
- Read the landmark paper: Reconfiguration of a Rolling Sphere: A Problem in Evolute-Involute GeometryCited 26 times
- Go sideways: InvoluteA closely related topic
- Go sideways: CardioidA closely related topic
📖 Definitions
Noun A curve comprising the centres of curvature of another curve.
Adjective Having or being a (mollusc) spiral shell in which the whorls touch along a surface.
Adjective Unfolded; turned back.
Verb Synonym of evolve (“cause to come into being”).
🏆 Landmark papers (most cited)
Reconfiguration of a Rolling Sphere: A Problem in Evolute-Involute Geometry
Moire fringes by evolute gratings
Cardiovascular Outcomes After Mini-Crush or Double Kissing Crush Stenting Techniques for Complex Bifurcation Lesions: The EVOLUTE-CRUSH Registry
Deep radio occultations and “evolute flashes”; their characteristics and utility for planetary studies
Spinor Representations of Involute Evolute Curves in E^3
An Extension of the Principle of the Diffraction Evolute, and some of its Structural Detail
Collimation testing with linear dual-field, spiral, and evolute gratings: a comparative study
On the involute and evolute curves of the spacelike curve with a spacelike binormal in Minkowski 3-space
🆕 Influential since 2022
DK‐Crush or Mini‐Crush Stenting for Complex Left Main Bifurcation Lesions: The Multicenter EVOLUTE‐CRUSH LM Registry
Involute evolute curve family induced by the coupled dispersionless equations
Legendrian dualities and evolute-involute curve pairs of spacelike fronts in null sphere
How did blue and green water resource evolute spatially and temporally in the Meijiang River Basin, China?
Exploring Harmonic Evolute Geometries Derived from Tubular Surfaces in Minkowski 3-Space Using the RM Darboux Frame
📚 Books worth reading
On the origin of species by means of natural selectionCharles Darwin · 1859
Guns, Germs, and SteelJared Diamond · 1997
The Selfish GeneRichard Dawkins · 1976
Life on EarthDavid Attenborough · 1705
The God DelusionRichard Dawkins · 2001
The Blind WatchmakerRichard Dawkins · 1986
The Phenomenon of ManPierre Teilhard de Chardin, Pierre Teilhard de Chardin · 1955
The Third ChimpanzeeJared Diamond · 1991
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Involute An involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An example of the involute of a curve…
- Cardioid Look up cardioid in Wiktionary, the free dictionary. In geometry, a cardioid (from Greek καρδιά (kardiá) 'heart') is a plane curve traced by a point on…
- Nephroid In geometry, a nephroid (from Ancient Greek νεφρός (nephrós) 'kidney') is a specific plane curve. It is a type of epicycloid in which the smaller circle's…
- Semicubical parabola In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form y2−a2x3=0 (with a ≠ 0) in…
- Tschirnhausen cubic In mathematics, the Tschirnhausen cubic is a cubic plane curve defined in Cartesian coordinates (x,y) by the cubic equation 27ay2=(a−x)(8a+x)2, or in polar…
- Osculating circle An osculating circle is a circle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has…
- Parallel curve A parallel curve of a given (progenitor) curve is the envelope of a family of congruent (equal-radius) circles centered on the curve. It generalises the…
- Curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being…