A cusp is the most pointed end of a curve. It often refers to

cusp (anatomy) A cusp is a pointed, projecting, or elevated feature. In animals, it is usually used to refer to raised points on the crowns of teeth. The concept is also used with regard to the leaflets of the four heart valves. The mitral valve, which has two ...

, a pointed structure on a tooth. Cusp or CUSP may also refer to:

Mathematics

Cusp (singularity) In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction. A typical example is given in the figure. A cusp is thus a type of singular point of a curve. For a plane curve def ...

, a singular point of a curve *

Cusp catastrophe In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena ch ...

, a branch of bifurcation theory in the study of dynamical systems *

Cusp form In number theory, a branch of mathematics, a cusp form is a particular kind of modular form with a zero constant coefficient in the Fourier series expansion. Introduction A cusp form is distinguished in the case of modular forms for the modular gro ...

, in modular form theory *

Cusp neighborhood In mathematics, a cusp neighborhood is defined as a set of points near a cusp singularity. Cusp neighborhood for a Riemann surface The cusp neighborhood for a hyperbolic Riemann surface can be defined in terms of its Fuchsian model. Suppose ...

, a set of points near a cusp *

Cuspidal representation In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in L^2 spaces. The term ''cuspidal'' is derived, at a certain distance, from the cusp forms of classical modular form theory. In the con ...

, a generalization of cusp forms in the theory of automorphic representations

Science and medicine

Beach cusps Beach cusps are shoreline formations made up of various grades of sediment in an arc pattern. The horns are made up of coarser material and the embayment contains finer sediment. They can be found all over the world and are most noticeable on s ...

, a pointed and regular arc pattern of the shoreline at the beach *

Behavioral cusp A behavioral cusp is any behavior change that brings an organism's behavior into contact with new contingencies that have far-reaching consequences. A behavioral cusp is a special type of behavior change because it provides the learner with opp ...

, a change in behavior with far-reaching consequences *

Caltech-USGS Seismic Processing Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...

, software for analyzing earthquake data *

Center for Urban Science and Progress The NYU Center for Urban Science and Progress (commonly referred to as CUSP) is a degree-granting technology and research institute in downtown Brooklyn, New York City. It is a graduate school of New York University focusing on urban informatics ...

, a graduate school of New York University focusing on urban informatics *

CubeSat for Solar Particles CubeSat for Solar Particles (CuSP) was a low-cost 6U CubeSat to orbit the Sun to study the dynamic particles and magnetic fields. The principal investigator for CuSP is Mihir Desai, at the Southwest Research Institute (SwRI) in San Antonio, T ...

, a satellite launched in 2022 *

Cusp (anatomy) A cusp is a pointed, projecting, or elevated feature. In animals, it is usually used to refer to raised points on the crowns of teeth. The concept is also used with regard to the leaflets of the four heart valves. The mitral valve, which has two ...

, a pointed structure on a tooth ** Nuclear cusp condition, in

electron density In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial va ...

Cusps of heart valves A heart valve is a one-way valve that allows blood to flow in one direction through the chambers of the heart. Four valves are usually present in a mammalian heart and together they determine the pathway of blood flow through the heart. A heart v ...

, leaflets of a heart valve

Other uses

Cusp (astrology) In astrology, a cusp (from the Latin for spear or point) is the imaginary line that separates a pair of consecutive signs in the zodiac or houses in the horoscope. Because the solar disc has a diameter of approximately half a degree, it is poss ...

* ''Cusp'' (film), a 2021 American documentary following three teenage girls at the end of summer * ''Cusp'' (novel), a 2005 science fiction story by Robert A. Metzger *

Cusp Conference Cusp Conference is an annual gathering of thinkers, innovators, creators, visionaries and explorers from the arts, sciences, technology, business and design. The program is eclectic by design, intended to provoke cross-pollination of ideas and gen ...

, an annual gathering of thinkers, innovators, etc. from various fields * Cusp generation, a name given to those born during the transitional years of two generations {{disambiguation