An ogive ( ) is the roundly tapered end of a two- or

three-dimensional object Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its in ...

. Ogive curves and surfaces are used in

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

architecture Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and construction, constructi ...

woodworking Woodworking is the skill of making items from wood, and includes cabinetry, furniture making, wood carving, joinery, carpentry, and woodturning. History Along with stone, clay and animal parts, wood was one of the first materials worked b ...

, and

ballistics Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially weapon munitions such as bullets, unguided bombs, rockets and the like; the science or art of designing and acceler ...

Etymology

The French Orientalist Georges Séraphin Colin gives as the term's origin the

Arabic Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns lang ...

''al-ġubb'' () '

cistern A cistern (; , ; ) is a waterproof receptacle for holding liquids, usually water. Cisterns are often built to catch and store rainwater. To prevent leakage, the interior of the cistern is often lined with hydraulic plaster. Cisterns are disti ...

', pronounced ''al-ġibb'' () in vernacular Iberian Arabic, through the Spanish ''aljibe'' or archaically ''algibe.'' The earliest use of the word ''ogive'' is found in the 13th-century sketchbook of

Villard de Honnecourt Villard de Honnecourt (''Wilars dehonecort'', ''Vilars de Honecourt'') was a 13th-century artist from Picardy in northern France. He is known to history only through a surviving portfolio or "sketchbook" containing about 250 drawings and designs ...

, from Picardy in northern France. The ''

Oxford English Dictionary The ''Oxford English Dictionary'' (''OED'') is the principal historical dictionary of the English language, published by Oxford University Press (OUP), a University of Oxford publishing house. The dictionary, which published its first editio ...

'' considers the French term's origin obscure; it might come from the

Late Latin Late Latin is the scholarly name for the form of Literary Latin of late antiquity.Roberts (1996), p. 537. English dictionary definitions of Late Latin date this period from the 3rd to 6th centuries CE, and continuing into the 7th century in ...

, the feminine perfect passive participle of , meaning the one who has met or encountered the other. However, Merriam-Webster's dictionary says it is from the "Middle English stone comprising an arch, from Middle French diagonal arch". According to Wiktionary, the French term comes "from Vulgar Latin augīvus, from Latin augēre, as the ogive goes on increasing, and the arch it forms increases the strength of the vault. In Old French we find the phrase arc ogif, itself from Latin arcus augivus. The word was also written as augive in the 17th century."

Types and use in applied physical science and engineering

aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...

, an ogive is a pointed, curved surface mainly used to form the approximately streamlined nose of a

bullet A bullet is a kinetic projectile, a component of firearm ammunition that is shot from a gun barrel. They are made of a variety of materials, such as copper, lead, steel, polymer, rubber and even wax; and are made in various shapes and constru ...

or other projectile, reducing air resistance or the drag of air. The French word ''ogive'' can be translated as "nose cone" or "warhead". The traditional or

secant ogive Given the problem of the aerodynamic design of the nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket or aircraft, missile, shell or bullet), an important problem is the determination ...

is a

surface of revolution A surface of revolution is a Surface (mathematics), surface in Euclidean space created by rotating a curve (the ''generatrix'') one full revolution (unit), revolution around an ''axis of rotation'' (normally not Intersection (geometry), intersec ...

of the same curve that forms a

Gothic arch A pointed arch, ogival arch, or Gothic arch is an arch with a pointed crown meet at an angle at the top of the arch. Also known as a two-centred arch, its form is derived from the intersection of two circles. This architectural element was part ...

; that is, a

circular arc A circular arc is the arc of a circle between a pair of distinct points. If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than radians (180 ...

, of greater

radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...

than the diameter of the

cylindrical A cylinder () has traditionally been a Solid geometry, three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a Prism (geometry), prism with a circle as its base. A cylinder may ...

section ("shank"), is drawn from the edge of the shank until it intercepts the axis. If this arc is drawn so that it meets the shank at zero angle (that is, the distance of the centre of the arc from the axis, plus the radius of the shank, equals the radius of the arc), then it is called a

tangent 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 o ...

or spitzer ogive. This is a very common ogive for high velocity (

supersonic Supersonic speed is the speed of an object that exceeds the speed of sound (Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...

)

rifle A rifle is a long gun, long-barreled firearm designed for accurate shooting and higher stopping power, with a gun barrel, barrel that has a helical or spiralling pattern of grooves (rifling) cut into the bore wall. In keeping with their focus o ...

bullets. The sharpness of this ogive is expressed by the ratio of its radius to the diameter of the cylinder; a value of one half being a

hemispherical A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

dome, and larger values being progressively more pointed. Values of 4 to 10 are commonly used in rifle bullets, with 6 being the most common. Another common ogive for bullets is the elliptical ogive. This is a curve very similar to the spitzer ogive, except that the circular arc is replaced by an ellipse defined in such a way that it meets the axis at exactly 90°. This gives a somewhat rounded nose regardless of the sharpness ratio. An elliptical ogive is normally described in terms of the ratio of the length of the ogive to the diameter of the shank. A ratio of one half would be, once again, a hemisphere. Values close to 1 are common in practice. Elliptical ogives are mainly used in

pistol A pistol is a type of handgun, characterised by a gun barrel, barrel with an integral chamber (firearms), chamber. The word "pistol" derives from the Middle French ''pistolet'' (), meaning a small gun or knife, and first appeared in the Englis ...

bullets. More complex ogives can be derived from minimum

turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between ...

calculations rather than geometric forms, such as the

von Kármán ogive The term () is used in German surnames either as a nobiliary particle indicating a noble patrilineality, or as a simple preposition used by commoners that means or . Nobility directories like the often abbreviate the noble term to ''v.'' I ...

used for supersonic missiles, aircraft and ordnance.

Architecture

One of the defining characteristics of

Gothic architecture Gothic architecture is an architectural style that was prevalent in Europe from the late 12th to the 16th century, during the High Middle Ages, High and Late Middle Ages, surviving into the 17th and 18th centuries in some areas. It evolved f ...

is the

pointed arch A pointed arch, ogival arch, or Gothic arch is an arch with a pointed crown meet at an angle at the top of the arch. Also known as a two-centred arch, its form is derived from the intersection of two circles. This architectural element was partic ...

History

Pointed arches may have originated as in the Sitamarhi caves in the 3rd century BCE. The free-standing temple of Trivikrama at Ter in Maharashtra (India) (dated to the Satavahana period of the 2nd century BCE to the 3rd century CE) also contains an ogive arch but it is constructed using

corbel In architecture, a corbel is a structural piece of stone, wood or metal keyed into and projecting from a wall to carry a wikt:superincumbent, bearing weight, a type of bracket (architecture), bracket. A corbel is a solid piece of material in t ...

principles. Excavations conducted by

Archaeological Survey of India The Archaeological Survey of India (ASI) is an Indian government agency that is responsible for archaeological research and the conservation and preservation of cultural historical monuments in the country. It was founded in 1861 by Alexander ...

(ASI) at Kausambi revealed a palace with foundations from the 8th century BCE until the 2nd century CE, built in six phases. The last phase, dated to 1st–2nd century CE, includes an extensive structure which features four centered pointed arches which were used to span narrow passageways and segmental arches for wider areas. Pointed arches with load-bearing functions were also employed in

Gandhara Gandhara () was an ancient Indo-Aryan people, Indo-Aryan civilization in present-day northwest Pakistan and northeast Afghanistan. The core of the region of Gandhara was the Peshawar valley, Peshawar (Pushkalawati) and Swat valleys extending ...

. A two pointed-arch vault-system was built inside the

Bhitargaon Bhitargaon is a town, near city of Kanpur in Kanpur Nagar district, Uttar Pradesh, India, known for its ancient Hindu temple, the largest Indian brick temple to survive from the time of the Gupta Empire. Despite being heavily restored, a numb ...

temple (as noted by

Alexander Cunningham Major General Sir Alexander Cunningham (23 January 1814 – 28 November 1893) was a British Army engineer with the Bengal Sappers who later took an interest in the history and archaeology of India. In 1861, he was appointed to the newly crea ...

) which is dated to the early

Gupta period The Gupta Empire was an Indian empire during the classical period of the Indian subcontinent which existed from the mid 3rd century to mid 6th century CE. At its zenith, the dynasty ruled over an empire that spanned much of the northern Indian ...

of the 4th–5th centuries CE. Pointed arches also appeared in Mahabodhi temple with relieving arches and vaults between the 6th and 7th centuries CE. The 5th- or 6th-century CE Romano-Byzantine Karamagara Bridge in Cappadocia (in present-day Turkish Central Anatolia) features an early pointed arch as part of an apparent Romano-Greco-Syrian architectural tradition. Several scholars see the pointed arch as first established as an architectonic principle in the

Middle East The Middle East (term originally coined in English language) is a geopolitical region encompassing the Arabian Peninsula, the Levant, Turkey, Egypt, Iran, and Iraq. The term came into widespread usage by the United Kingdom and western Eur ...

Islamic architecture Islamic architecture comprises the architectural styles of buildings associated with Islam. It encompasses both Secularity, secular and religious styles from the early history of Islam to the present day. The Muslim world, Islamic world encompasse ...

during the

Abbasid Caliphate The Abbasid Caliphate or Abbasid Empire (; ) was the third caliphate to succeed the Islamic prophet Muhammad. It was founded by a dynasty descended from Muhammad's uncle, Abbas ibn Abd al-Muttalib (566–653 CE), from whom the dynasty takes ...

in the middle of the 8th century CE. Pointed arches appeared in Christian Europe by the 11th century CE.

Debate

Some scholars have refused to accept an Indian origin of the pointed arch, including Hill (1993); some scholars have argued that pointed arches were used in the

Near East The Near East () is a transcontinental region around the Eastern Mediterranean encompassing the historical Fertile Crescent, the Levant, Anatolia, Egypt, Mesopotamia, and coastal areas of the Arabian Peninsula. The term was invented in the 20th ...

in pre-Islamic architecture, but others have stated that these arches were, in fact, parabolic and not pointed arches.

Usage

Gothic architecture features ogives as the intersecting transverse ribs of

arch An arch is a curved vertical structure spanning an open space underneath it. Arches may support the load above them, or they may perform a purely decorative role. As a decorative element, the arch dates back to the 4th millennium BC, but stru ...

es which establish the surface of a Gothic

vault Vault may refer to: * Jumping, the act of propelling oneself upwards Architecture * Vault (architecture), an arched form above an enclosed space * Bank vault, a reinforced room or compartment where valuables are stored * Burial vault (enclosur ...

. An ogive or ogival arch is a pointed, "Gothic" arch, drawn with compasses as outlined above, or with arcs of an ellipse as described. A very narrow, steeply pointed ogive arch is sometimes called a "lancet arch". The most common form is an equilateral arch, where the radius is the same as the width. In the later

Flamboyant Gothic Flamboyant () is a lavishly-decorated style of Gothic architecture that appeared in France and Spain in the 15th century, and lasted until the mid-sixteenth century and the beginning of the Renaissance.Encyclopedia Britannica, "Flamboyant style ...

style, an "

ogee arch An ogee ( ) is an object, element, or curve—often seen in architecture and building trades—that has a serpentine- or extended S-shape (sigmoid). Ogees consist of a "double curve", the combination of two semicircular curves or arcs that, as ...

", an arch with a pointed head, like S-shaped curves, became prevalent.

Glaciology

glaciology Glaciology (; ) is the scientific study of glaciers, or, more generally, ice and natural phenomena that involve ice. Glaciology is an interdisciplinary Earth science that integrates geophysics, geology, physical geography, geomorphology, clim ...

, the term ogives refers to alternating bands of light and dark coloured ice that occur as a result of glaciers moving through an

icefall An icefall is a portion of certain glaciers characterized by relatively rapid flow and chaotic crevassed surface, caused in part by gravity. The term ''icefall'' is formed by analogy with the word ''waterfall'', which is a similar phenomenon of ...