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132-506: 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 structural load-bearing arches became popular only after their adoption by the Ancient Romans in the 4th century BC . Arch-like structures can be horizontal, like an arch dam that withstands

264-565: A four-centred arch is made of two circle segments with distinct centers; usually the radius used closer to the springing point is smaller with a more pronounced curvature. Common in Islamic architecture ( Persian arch ), and, with upper portion flattened almost to straight lines ( Tudor arch ), in the English Perpendicular Gothic .A keel arch is a variant of four-centred arch with haunches almost straight, resembling

396-415: A hierarchical organization , but hierarchy makes it easier for a listener to understand and remember the music. In analogy to linguistic terminology, motifs and phrases can be combined to make complete musical ideas such as sentences and phrases . A larger form is known as the period . One such form that was widely used between 1600 and 1900 has two phrases, an antecedent and a consequent , with

528-417: A pointer that links them together in a particular order. Out of these any number of other data structures can be created such as stacks , queues , trees and hash tables . In solving a problem, a data structure is generally an integral part of the algorithm . In modern programming style, algorithms and data structures are encapsulated together in an abstract data type . Software architecture

660-580: A trefoil -like shouldered arch . The raised central part can vary all the way from a flat arch to ogee. The shouldered arches were used to decorate openings in Europe from medieval times to Late Gothic architecture , became common in Iranian architecture from the 14th century, and were later adopted in the Ottoman Turkey . In a stilted arch (also surmounted ), the springing line is located above

792-555: A balance-controlled watch before the Royal Society, may support Hooke's claim to priority for the idea. Nevertheless, it is Huygens who is credited with building the first watch to use a balance spring. Hooke's announcement of his law of elasticity using an anagram was a method scientists, such as Hooke, Huygens and Galileo , sometimes used to establish priority for a discovery without revealing details. Hooke used mechanical analogues to understand fundamental processes such as

924-456: A catenary is often misclassified as a parabola (per Galileo , "the [hanging] chain fits its parabola almost perfectly"). González et al. provide an example of Palau Güell , where researchers do not agree on classification of the arches or claim the prominence of parabolic arches, while the measurements show that just two of the 23 arches designed by Gaudi are actually parabolic. Three parabolic-looking curves in particular are of significance to

1056-513: A collapse (the oldest arch still standing is at Ramesseum ). Sacred buildings exhibited either lintel design or corbelled arches. Arches were mostly missing in Egypt temples even after the Roman conquest , even though Egyptians thought of the arch as a spiritual shape and used it in the rock-cut tombs and portable shrines. Auguste Mariette suggested that this choice was based on a relative fragility of

1188-506: A crystal have a structure that involves repetition of a basic unit called a unit cell . The atoms can be modeled as points on a lattice , and one can explore the effect of symmetry operations that include rotations about a point, reflections about a symmetry planes, and translations (movements of all the points by the same amount). Each crystal has a finite group, called the space group , of such operations that map it onto itself; there are 230 possible space groups. By Neumann's law ,

1320-499: A curator to furnish the society with experiments, and this was unanimously passed and Hooke was named on Boyle's recommendation. The Society did not have a reliable income to fully fund the post of Curator of Experiments but in 1664, John Cutler settled an annual gratuity of £50 on the Society to found a "Mechanick" lectureship at Gresham College on the understanding the Society would appoint Hooke to this task. On 27 June 1664, Hooke

1452-404: A decorative pattern, primarily at the top of window openings. The corbel (also corbelled ) arch, made of two corbels meeting in the middle of the span, is a true arch in a sense of being able to carry a load, but it is false in a structural sense, as its components are subject to bending stress. The typical profile is not curved, but has triangular shape. Invented prior to the semicircular arch,

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1584-421: A disgruntled, selfish, anti-social curmudgeon. For example, Arthur Berry said Hooke "claimed credit for most of the scientific discoveries of the time". Sullivan wrote he was "positively unscrupulous" and had an "uneasy apprehensive vanity" in dealings with Newton. Manuel described Hooke as "cantankerous, envious, vengeful". According to More, Hooke had both a "cynical temperament" and a "caustic tongue". Andrade

1716-490: A dog could be kept alive with its thorax opened, provided air was pumped in and out of its lungs. He noted the difference between venous and arterial blood, and thus demonstrated that the Pabulum vitae ("food of life") and flammae [flames] were the same thing. There were also experiments on gravity, the falling of objects, the weighing of bodies, the measurement of barometric pressure at different heights, and

1848-404: A half cadence in the middle and a full cadence at the end providing punctuation. On a larger scale are single-movement forms such as the sonata form and the contrapuntal form , and multi-movement forms such as the symphony . A social structure is a pattern of relationships. They are social organizations of individuals in various life situations. Structures are applicable to people in how

1980-618: A medium for transmitting attraction and repulsion between separated celestial bodies, Hooke argued for an attracting principle of gravitation in Micrographia (1665). In a communication to the Royal Society in 1666, he wrote: I will explain a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having

2112-457: A multilevel hierarchy of structures employing biominerals and proteins , at the bottom of which are collagen fibrils . In biology , one of the properties of life is its highly ordered structure, which can be observed at multiple levels such as in cells , tissues , organs , and organisms . In another context, structure can also observed in macromolecules , particularly proteins and nucleic acids . The function of these molecules

2244-517: A new hypothesis from Paris about planetary motions, which he described at length; efforts to carry out or improve national surveys; and the difference of latitude between London and Cambridge. Newton's reply offered "a fansy of my own" about a terrestrial experiment rather than a proposal about celestial motions that might detect the Earth's motion; the experiment would use a body suspended in air and then dropped. Hooke wanted to discern how Newton thought

2376-671: A parabolic vault which is considered one of the earliest evidences of arches in Iran. The use of true arches in Egypt also originated in the 4th millennium BC (underground barrel vaults at the Dendera cemetery). Standing arches were known since at least the Third Dynasty , but very few examples survived, since the arches were mostly used in non-durable secular buildings and made of mud brick voussoirs that were not wedge-shaped, but simply held in place by mortar , and thus susceptible to

2508-461: A redundant structure is needed so that if a component fails it has backups. A high redundancy is an essential part of the design of several systems in the Space Shuttle . As a branch of philosophy, logic is concerned with distinguishing good arguments from poor ones. A chief concern is with the structure of arguments. An argument consists of one or more premises from which a conclusion

2640-472: A rounded, not pointed, top. Common in Islamic architecture and Romanesque buildings influenced by it, it later became popular in the decorative motifs of the Late Gothic designs of Northern Europe. Each arc of an ogee arch consists of at least two circle segments (for a total of at least four), with the center of an upper circle being outside the extrados. After European appearance in the 13th century on

2772-492: A section view of a capsized ship. Popular in Islamic architecture, it can be also found in Europe, occasionally with a small ogee element at the top, so it is sometimes considered to be a variation of an ogee arch. Curtain arch (also known as inflexed arch , and, like the keel arch, usually decorative) uses two (or more) drooping curves that join at the apex. Utilized as a dressing for windows and doors primarily in Saxony in

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2904-457: A semicircle, is associated with Islamic architecture and was known in areas of Europe with Islamic influence ( Spain , Southern France , Italy ). Occasionally used in Gothics, it briefly enjoyed popularity as the entrance door treatment in the interwar England. A pointed arch consists of two (" two-centred arch ") or more circle segments culminating in a point at the top. It originated in

3036-435: A simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it. ... Hooke's 1674 Gresham lecture, An Attempt to Prove

3168-434: A society is as a system organized by a characteristic pattern of relationships. This is known as the social organization of the group. Sociologists have studied the changing structure of these groups. Structure and agency are two confronted theories about human behaviour. The debate surrounding the influence of structure and agency on human thought is one of the central issues in sociology. In this context, agency refers to

3300-624: A spinal deformity that was consistent with a diagnosis of Scheuermann's kyphosis , giving him in middle and later years a "thin and crooked body, over-large head and protruding eyes". Approaching these in a scientific spirit, he experimented with self-medication, diligently recording symptoms, substances and effects in his diary. He regularly used sal ammoniac , emetics, laxatives and opiates, which appear to have had an increasing effect on his physical and mental health over time. Hooke died in London on 3 March 1703, having been blind and bedridden during

3432-418: A vacuum might exist despite Aristotle 's maxim " Nature abhors a vacuum " had just begun to be considered . Hooke developed an air pump for Boyle's experiments rather than use Ralph Greatorex 's pump, which Hooke considered as "too gross to perform any great matter". Hooke's engine enabled the development of the eponymous law that was subsequently attributed to Boyle; Hooke had a particularly keen eye and

3564-471: A variety of diagrams called structural formulas . Lewis structures use a dot notation to represent the valence electrons for an atom; these are the electrons that determine the role of the atom in chemical reactions. Bonds between atoms can be represented by lines with one line for each pair of electrons that is shared. In a simplified version of such a diagram, called a skeletal formula , only carbon-carbon bonds and functional groups are shown. Atoms in

3696-494: A vault: "what would remain of the tombs and temples of Egyptians today, if they had preferred the vault?" Mycenaean architecture utilized only the corbel arches in their beehive tombs with triangular openings. Mycenaeans had also built probably the oldest still standing stone-arch bridge in the world, Arkadiko Bridge , in Greece. As evidenced by their imitations of the parabolic arches, Hittites most likely were exposed to

3828-408: Is inferred . The steps in this inference can be expressed in a formal way and their structure analyzed. Two basic types of inference are deduction and induction . In a valid deduction, the conclusion necessarily follows from the premises, regardless of whether they are true or not. An invalid deduction contains some error in the analysis. An inductive argument claims that if the premises are true,

3960-489: Is a load-bearing arc with elements held together by compression. In much of the world introduction of the true arch was a result of European influence. The term false arch has few meanings. It is usually used to designate an arch that has no structural purpose, like a proscenium arch in theaters used to frame the performance for the spectators, but is also applied to corbelled and triangular arches that are not based on compression. A typical true masonry arch consists of

4092-434: Is determined by their shape as well as their composition, and their structure has multiple levels. Protein structure has a four-level hierarchy. The primary structure is the sequence of amino acids that make it up. It has a peptide backbone made up of a repeated sequence of a nitrogen and two carbon atoms. The secondary structure consists of repeated patterns determined by hydrogen bonding . The two basic types are

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4224-455: Is much higher than another, the arch (frequently pointed ) is known as ramping arch  [ fr ] , raking arch , or rampant arch (from French : arc rampant ). Originally used to support inclined structures, like staircases , in the 13th-14th centuries their appeared as parts of flying buttresses used to counteract the thrust of Gothic ribbed vaults . A central part of an arch can be raised on short vertical supports, creating

4356-420: Is one of the tasks of structural engineering . The structural elements can be classified as one-dimensional ( ropes , struts , beams , arches ), two-dimensional ( membranes , plates, slab , shells , vaults ), or three-dimensional (solid masses). Three-dimensional elements were the main option available to early structures such as Chichen Itza . A one-dimensional element has one dimension much larger than

4488-402: Is subject to additional internal stress from thermal expansion and contraction, this kind of arch is statically indeterminate (the internal state is impossible to determine based on the external forces alone). The two-hinged arch is most often used to bridge long spans. This kind of arch has pinned connections at its base. Unlike that of the fixed arch, the pinned base can rotate, thus allowing

4620-413: Is that the reaction of the pinned bases is more predictable than the one for the fixed arch, allowing shallow, bearing-type foundations in spans of medial length. In the three-hinged arch "thermal expansion and contraction of the arch will cause vertical movements at the peak pin joint but will have no appreciable effect on the bases," which further simplifies foundational design. The arch became popular in

4752-625: Is the most common form of the pointed arch, with the centers of two circles forming the intrados coinciding with the springing points of the opposite segment. Together with the apex point, they form a equilateral triangle , thus the name. If the centers of circles are farther apart, the arch becomes a narrower and sharper lancet arch that appeared in France in the Early Gothic architecture ( Saint-Denis Abbey ) and became prominent in England in

4884-597: Is the one that frames the internal side of an opening in the external wall. Structurally, relieving arches (often blind or containing) can be used to take off load from some portions of the building (for example, to allow use of thinner exterior walls with larger window openings, or, as in the Roman Pantheon , to redirect the weight of the upper structures to particular strong points). Transverse arches , introduced in Carolingian architecture , are placed across

5016-516: Is the only one of the symmetric wedge shape), and that efficiently uses the compressive strength of the masonry in the same manner as a curved arch and thus requires a mass of masonry on both sides to absorb the considerable lateral thrust. Used in the Roman architecture to imitate the Greek lintels, Islamic architecture, European medieval and Renaissance architecture. The flat arch is still being used as

5148-489: Is the specific choices made between possible alternatives within a framework. For example, a framework might require a database and the architecture would specify the type and manufacturer of the database. The structure of software is the way in which it is partitioned into interrelated components. A key structural issue is minimizing dependencies between these components. This makes it possible to change one component without requiring changes in others. The purpose of structure

5280-420: Is to optimise for (brevity, readability, traceability, isolation and encapsulation, maintainability, extensibility, performance and efficiency), examples being: language choice , code , functions , libraries , builds , system evolution , or diagrams for flow logic and design . Structural elements reflect the requirements of the application: for example, if the system requires a high fault tolerance, then

5412-445: Is used when the arch needs to turn in the horizontal plane, for example, when a bridge crosses the river at an angle different than 90°. A splayed arch is used for the case of unequal spans on the sides of the arch (when, for example, an interior opening in the wall is larger than the exterior one), the intrados of a round splayed arch is not cylindrical, but has a conical shape. A wide arch with its rise less than 1 ⁄ 2 of

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5544-565: Is usually painted of Hooke as a morose ... recluse is completely false". He interacted with noted artisans such as clock-maker Thomas Tompion and instrument-maker Christopher Cocks (Cox). Hooke often met Christopher Wren, with whom he shared many interests, and had a lasting friendship with John Aubrey. His diaries also make frequent reference to meetings at coffeehouses and taverns, as well as to dinners with Robert Boyle. On many occasions, Hooke took tea with his lab assistant Harry Hunt. Although he largely lived alone – apart from

5676-587: The Great Red Spot of Jupiter for two hours as it moved across the planet's face. In March 1665, he published his findings and from them, the Italian astronomer Giovanni Cassini calculated the rotation period of Jupiter to be nine hours and fifty-five minutes. One of the most-challenging problems Hooke investigated was the measurement of the distance from Earth to a star other than the Sun. Hooke selected

5808-626: The Roman builders since the 4th century BC . It is considered to be the most common arch form, characteristic for Roman, Romanesque , and Renaissance architecture. A segmental arch , with a rounded shape that is less than a semicircle, is very old (the versions were cut in the rock in Ancient Egypt c. 2100 BC at Beni Hasan ). Since then it was occasionally used in Greek temples , utilized in Roman residential construction, Islamic architecture , and got popular as window pediments during

5940-618: The Roman times and mostly spread alongside the European influence, although it was known and occasionally used much earlier. Many ancient architectures avoided the use of arches, including the Viking and Hindu ones. True arches, as opposed to corbel arches , were known by a number of civilizations in the ancient Near East including the Levant , but their use was infrequent and mostly confined to underground structures, such as drains where

6072-413: The balance spring or hairspring, which for the first time enabled a portable timepiece – a watch – to keep time with reasonable accuracy. A bitter dispute between Hooke and Christiaan Huygens on the priority of this invention was to continue for centuries after the death of both but a note dated 23 June 1670 in the journals of the Royal Society, describing a demonstration of

6204-424: The dead load increases with a distance from the center. Unlike regular arches, the flat arch (also known as jack arch , lintel arch , straight arch , plate-bande ) is not curved. Instead, the arch is flat in profile and can be used under the same circumstances as lintel . However, lintels are subject to bending stress, while the flat arches are true arches, composed of irregular voussoir shapes (the keystone

6336-425: The lintel , especially in the masonry construction: with the same amount of material it can have larger span, carry more weight, and can be made from smaller and thus more manageable pieces. Their role in construction was diminished in the middle of the 19th century with introduction of the wrought iron (and later steel ): the high tensile strength of these new materials made long lintels possible. A true arch

6468-464: The nave to compartmentalize (together with longitudinal separating arches) the internal space into bays and support vaults . A diaphragm arch similarly goes in the transverse direction, but carries a section of wall on top. It is used to support or divide sections of the high roof. Strainer arches were built as an afterthought to prevent two adjacent supports from imploding due to miscalculation. Frequently they were made very decorative, with one of

6600-406: The organ and began his lifelong study of mechanics. He remained an accomplished draughtsman, as he was later to demonstrate in his drawings that illustrate the work of Robert Boyle and Hooke's own Micrographia . In 1653, Hooke secured a place at Christ Church , Oxford , receiving free tuition and accommodation as an organist and a chorister , and a basic income as a servitor , despite

6732-469: The temple of Apollo at Didyma and the stadium at Olympia . . The ancient Romans learned the semicircular arch from the Etruscans (both cultures apparently adopted the design in the 4th century BC), refined it and were the first builders in Europe to tap its full potential for above ground buildings: The Romans were the first builders in Europe, perhaps the first in the world, to fully appreciate

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6864-415: The α-helix and the β-pleated sheet . The tertiary structure is a back and forth bending of the polypeptide chain, and the quaternary structure is the way that tertiary units come together and interact. Structural biology is concerned with biomolecular structure of macromolecules. Chemical structure refers to both molecular geometry and electronic structure. The structure can be represented by

6996-613: The "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". At the same time, according to Edmond Halley 's contemporaneous report, Hooke agreed "the Demonstration of the Curves generated thereby" was wholly Newton's. According to a 2002 assessment of the early history of the inverse square law: "by the late 1660s, the assumption of an 'inverse proportion between gravity and

7128-670: The Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance". (Hooke's inference about the velocity is incorrect. ) In 1686, when the first book of Newton's Principia was presented to the Royal Society, Hooke said he had given Newton

7260-477: The Dutch scientist Antonie van Leeuwenhoek went on to develop increased magnification and so reveal protozoa , blood cells and spermatozoa . Micrographia also contains Hooke's, or perhaps Boyle's and Hooke's, ideas on combustion. Hooke's experiments led him to conclude combustion involves a component of air, a statement with which modern scientists would agree but that was not understood widely, if at all, in

7392-562: The Egyptian designs, but used the corbelled technique to build them. The Assyrians , also apparently under the Egyptian influence, adopted the true arch (with a slightly pointed profile) early in the 8th century. In ancient Persia , the Achaemenid Empire (550 BC–330 BC) built small barrel vaults (essentially a series of arches built together to form a hall) known as iwan , which became massive, monumental structures during

7524-475: The Islamic architecture, arrived in Europe in the second half of the 11th century ( Cluny Abbey ) and later became prominent in the Gothic architecture . The advantages of a pointed arch over a semicircular one are flexible ratio of span to rise and lower horizontal reaction at the base. This innovation allowed for taller and more closely spaced openings, which are typical of Gothic architecture. Equilateral arch

7656-405: The Late Gothic and early Renaissance buildings (late 15th to early 16th century), associated with Arnold von Westfalen  [ de ] . When the intrados has multiple concave segments, the arch is also called a draped arch or tented arch . A similar arch that uses a mixture of curved and straight segments or exhibits sharp turns between segments is a mixed-line arch . The popularity of

7788-702: The Motion of the Earth by Observations (published 1679), said gravitation applies to "all celestial bodies" and restated these three propositions. Hooke's statements up to 1674 make no mention, however, that an inverse square law applies or might apply to these attractions. His model of gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. Hooke did not provide accompanying evidence or mathematical demonstration; he stated in 1674: "Now what these several degrees [of gravitational attraction] are I have not yet experimentally verified", indicating he did not yet know what law

7920-477: The Renaissance. A basket-handle arch (also known as depressed arch , three-centred arch , basket arch ) consists of segments of three circles with origins at three different centers (sometimes uses five or seven segments, so can also be five-centred , etc.). Was used in late Gothic and Baroque architecture . A horseshoe arch (also known as keyhole arch ) has a rounded shape that includes more than

8052-427: The Royal Society's correspondence; Hooke therefore wanted to hear from members about their research or their views about the research of others. Hooke asked Newton's opinions about various matters. Among other items, Hooke mentioned "compounding the celestial motions of the planets of a direct motion by the tangent and an attractive motion towards the central body"; his "hypothesis of the lawes or causes of springinesse";

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8184-519: The Society could scarcely have survived, or, at least, would have developed in a quite different way. It is scarcely an exaggeration to say that he was, historically, the creator of the Royal Society. The Royal Society for the Improvement of Natural Knowledge by Experiment was founded in 1660 and given its Royal Charter in July 1662. On 5 November 1661, Robert Moray proposed the appointment of

8316-672: The advantages of the arch, the vault and the dome. Structure Buildings , aircraft , skeletons , anthills , beaver dams , bridges and salt domes are all examples of load -bearing structures. The results of construction are divided into buildings and non-building structures , and make up the infrastructure of a human society. Built structures are broadly divided by their varying design approaches and standards, into categories including building structures, architectural structures , civil engineering structures and mechanical structures. The effects of loads on physical structures are determined through structural analysis , which

8448-551: The age of 13, he took this to London to become an apprentice to the celebrated painter Peter Lely . Hooke also had "some instruction in drawing" from the limner Samuel Cowper but "the smell of the Oil Colours did not agree with his Constitution, increasing his Head-ache to which he was ever too much subject", and he became a pupil at Westminster School , living with its master Richard Busby . Hooke quickly mastered Latin, Greek and Euclid's Elements ; he also learnt to play

8580-517: The arch design: parabola itself, catenary , and weighted catenary . The arches naturally use the inverted (upside-down) versions of these curves. A parabola represents an ideal (all-compression) shape when the load is equally distributed along the span, while the weight of the arch itself is negligible. A catenary is the best solution for the case where an arch with uniform thickness carries just its own weight with no external load. The practical designs for bridges are somewhere in between, and thus use

8712-406: The arch is called " joggled ". A true arch, due to its rise, resolves the vertical loads into horizontal and vertical reactions at the ends, a so called arch action . The vertical load produces a positive bending moment in the arch, while the inward-directed horizontal reaction from the spandrel/abutment provides a counterbalancing negative moment. As a result, the bending moment in any segment of

8844-401: The arch is much smaller than in a beam with the equivalent load and span. The diagram on the right shows the difference between a loaded arch and a beam. Elements of the arch are mostly subject to compression (A), while in the beam a bending moment is present, with compression at the top and tension at the bottom (B). In the past, when arches were made of masonry pieces, the horizontal forces at

8976-502: The arches themselves got lighter, but the horizontal thrust can be further relieved by a tie connecting the ends of an arch. When evaluated from the perspective of an amount of material required to support a given load, the best solid structures are compression-only; with the flexible materials, the same is true for tension-only designs. There is a fundamental symmetry in nature between solid compression-only and flexible tension-only arrangements, noticed by Robert Hooke in 1676: "As hangs

9108-532: The arches using segments of a circle is due to simplicity of layout and construction, not their structural properties. Consequently, the architects historically used a variety of other curves in their designs: elliptical curves , hyperbolic cosine curves (including catenary ), and parabolic curves . There are two reasons behind the selection of these curves: The hyperbolic curve is not easy to trace, but there are known cases of its use. The non- circumferential curves look similar, and match at shallow profiles, so

9240-754: The best examples provided by the Wells Cathedral . Strainer arches can be " inverted " (upside-down) while remaining structural. When used across railway cuttings to prevent collapse of the walls, strainer arches may be referred to as flying arches . A counter-arch is built adjacent to another arch to oppose its horizontal action or help to stabilize it, for example, when constructing a flying buttress . The large variety of arch shapes (left) can mostly be classified into three broad categories: rounded , pointed , and parabolic . "Round" semicircular arches were commonly used for ancient arches that were constructed of heavy masonry, and were relied heavily on by

9372-441: The conclusion is likely. Robert Hooke Robert Hooke FRS ( / h ʊ k / ; 18 July 1635 – 3 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist and architect. He is credited as one of the first scientists to investigate living things at microscopic scale in 1665, using a compound microscope that he designed. Hooke

9504-708: The corbel arch was used already in the Egyptian and Mycenaean architecture in the 3rd and 2nd millennium BC . Like a corbel arch, the triangular arch is not a true arch in a structural sense. Its intrados is formed by two slabs leaning against each other. Brick builders would call triangular any arch with straight inclined sides. The design was common in Anglo-Saxon England until the late 11th century ( St Mary Goslany ). Mayan corbel arches are sometimes called triangular due to their shape. Few transformations can be applied to arch shapes. If one impost

9636-399: The curves that represent a compromise that combines both the catenary and the funicular curve for particular non-uniform distribution of load. The practical free-standing arches are stronger and thus heavier at the bottom, so a weighted catenary curve is utilized for them. The same curve also fits well an application where a bridge consists of an arch with a roadway of packed dirt above it, as

9768-440: The deaths of both Newton and Hooke, Alexis Clairaut , mathematical astronomer eminent in his own right in the field of gravitational studies, reviewed Hooke's published work on gravitation. According to Stephen Peter Rigaud , Clairaut wrote: "The example of Hooke and that of Kepler [serves] to show what a distance there is between a truth that is glimpsed and a truth that is demonstrated". I. Bernard Cohen said: "Hooke's claim to

9900-510: The diversion he gave me from my other studies to think on these things & for his dogmaticalness in writing as if he had found the motion in the Ellipsis, which inclined me to try it. Whilst Newton was primarily a pioneer in mathematical analysis and its applications, and optical experimentation, Hooke was a creative experimenter of such great range who left some of his ideas, such as those about gravitation, undeveloped. In 1759, decades after

10032-759: The earliest-recorded observation of a microorganism, the microfungus Mucor . Hooke coined the term " cell ", suggesting a resemblance between plant structures and honeycomb cells. The hand-crafted, leather-and-gold-tooled microscope he designed and used to make the observations for Micrographia , which Christopher Cock made for him in London, is on display at the National Museum of Health and Medicine in Maryland . Hooke's work developed from that of Henry Power , who published his microscopy work in Experimental Philosophy (1663); in turn,

10164-425: The ends of an arch caused the need for heavy abutments (cf. Roman triumphal arch ). The other way to counteract the forces, and thus allow thinner supports, was to use the counter-arches , as in an arcade arrangement, where the horizontal thrust of each arch is counterbalanced by its neighbors, and only the end arches need to buttressed . With new construction materials (steel, concrete, engineered wood ), not only

10296-432: The extinction of species, and argued hills and mountains had become elevated by geological processes. By identifying fossils of extinct species, Hooke presaged the theory of biological evolution . Much of what is known of Hooke's early life comes from an autobiography he commenced in 1696 but never completed; Richard Waller FRS mentions it in his introduction to The Posthumous Works of Robert Hooke, M.D. S.R.S. , which

10428-625: The facade of the St Mark's Basilica , the arch became a fixture of the English Decorated style , French Flamboyant , Venetian , and other Late Gothic styles. Ogee arch is also known as reversed curve arch , occasionally also called an inverted arch . The top of an ogee arch sometimes projects beyond the wall, forming the so-called nodding ogee popular in 14th century England ( pulpitum in Southwell Minster ). Each arc of

10560-521: The fact he did not officially matriculate until 1658. In 1662, Hooke was awarded a Master of Arts degree. While a student at Oxford, Hooke was also employed as an assistant to Dr Thomas Willis  – a physician, chemist and member of the Oxford Philosophical Club . The Philosophical Club had been founded by John Wilkins , Warden of Wadham College , who led this important group of scientists who went on to form

10692-482: The falling body could experimentally reveal the Earth's motion by its direction of deviation from the vertical but Hooke went on hypothetically to consider how its motion could continue if the solid Earth had not been in the way, on a spiral path to the centre. Hooke disagreed with Newton's idea of the body's continuing motion. A further short correspondence developed; towards the end of it, writing on 6 January 1680 to Newton, Hooke communicated his "supposition ... that

10824-465: The first practical Gregorian telescope that used a silvered glass mirror. In 1660, Hooke discovered the law of elasticity that bears his name and describes the linear variation of tension with extension in an elastic spring. Hooke first described this discovery in an anagram "ceiiinosssttuv", whose solution he published in 1678 as Ut tensio, sic vis ("As the extension, so the force"). His work on elasticity culminated in his development of

10956-619: The flexible line, so but inverted will stand the rigid arch", thus the study (and terminology) of arch shapes is inextricably linked to the study of hanging chains, the corresponding curves or polygons are called funicular . Just like the shape of a hanging chain will vary depending on the weights attached to it, the shape of an ideal (compression-only) arch will depend on the distribution of the load. There are multiple ways to classify an arch: A sequence of arches can be grouped together forming an arcade . Romans perfected this form, as shown, for example, by arched structures of Pont du Gard . In

11088-401: The following elements: A (left or right) half-segment of an arch is called an arc , the overall line of an arch is arcature (this term is also used for an arcade ). Archivolt is the exposed (front-facing) part of the arch, sometimes decorated (occasionally also used to designate the intrados). If the sides of voussoir blocks are not straight, but include angles and curves for interlocking,

11220-475: The formation of these craters and concluded their existence meant the Moon must have its own gravity, a radical departure from the contemporaneous Aristotelian celestial model . He also was an early observer of the rings of Saturn , and discovered one of the first-observed double-star systems Gamma Arietis in 1664. To achieve these discoveries, Hooke needed better instruments than those that were available at

11352-463: The foundation of his lifelong passion for science. The friends he made there, particularly Christopher Wren , were important to him throughout his career. Willis introduced Hooke to Robert Boyle , who the Club sought to attract to Oxford. In 1655, Boyle moved to Oxford and Hooke became nominally his assistant but in practice his co-experimenter. Boyle had been working on gas pressures; the possibility

11484-446: The gravitation might follow; and about his whole proposal, he said: "This I only hint at present ... having my self many other things in hand which I would first compleat, and therefore cannot so well attend it" (i.e. "prosecuting this Inquiry"). In November 1679, Hooke initiated a notable exchange of letters with Newton that was published in 1960. Hooke's ostensible purpose was to tell Newton he (Hooke) had been appointed to manage

11616-453: The history of life on Earth and, despite the objections of contemporary naturalists like John Ray  – who found the concept of extinction theologically unacceptable – that in some cases they might represent species that had become extinct through some geological disaster. In a series of lectures in 1668, Hooke proposed the then-heretical idea the Earth's surface had been formed by volcanoes and earthquakes, and that

11748-471: The horizontal hydrostatic pressure load. Arches are normally used as supports for many types of vaults , with the barrel vault in particular being a continuous arch. Extensive use of arches and vaults characterizes an arcuated construction , as opposed to the trabeated system, where, like in the architectures of ancient Greece, China, and Japan (as well as the modern steel-framed technique), posts and beams dominate. Arches had several advantages over

11880-471: The imposts (on "stilts"). Known to Islamic architects by the 8th century, the technique was utilized to vertically align the apexes of arches of different dimensions in Romanesque and Gothic architecture. Stilting was useful for semicircular arches, where the ratio of the rise fixed at 1 ⁄ 2 of the span, but was applied to the pointed arches, too. The skew arch (also known as an oblique arch )

12012-661: The individual human capacity to act independently and make free choices. Structure here refers to factors such as social class , religion , gender , ethnicity , customs, etc. that seem to limit or influence individual opportunities. In computer science , a data structure is a way of organizing information in a computer so that it can be used efficiently. Data structures are built out of two basic types: An array has an index that can be used for immediate access to any data item (some programming languages require array size to be initialized ). A linked list can be reorganized, grown or shrunk, but its elements must be accessed with

12144-617: The interior of hall churches , arcades of separating arches were used to separate the nave of a church from the side aisle, or two adjacent side aisles. Two-tiered arches , with two arches superimposed, were sometimes used in Islamic architecture , mostly for decorative purposes. An opening of the arch can be filled, creating a blind arch . Blind arches are frequently decorative, and were extensively used in Early Christian , Romanesque , and Islamic architecture. Alternatively,

12276-428: The invention was, by Hooke's death, in constant use among clock makers. Hooke announced he conceived a way to build a marine chronometer to determine longitude. and with the help of Boyle and others, he attempted to patent it. In the process, Hooke demonstrated a pocket-watch of his own devising that was fitted with a coil spring attached to the arbour of the balance. Hooke's refusal to accept an escape clause in

12408-472: The inverse-square law has masked Newton's far more fundamental debt to him, the analysis of curvilinear orbital motion. In asking for too much credit, Hooke effectively denied to himself the credit due him for a seminal idea". Hooke made important contributions to the science of timekeeping and was intimately involved in the advances of his time; these included refinement of the pendulum as a better regulator for clocks, increased precision of clock mechanisms and

12540-477: The last year of his life. A chest containing £8,000 in money and gold was found in his room at Gresham College . His library contained over 3,000 books in Latin, French, Italian and English. Although he had talked of leaving a generous bequest to the Royal Society, which would have given his name to a library, laboratory and lectures, no will was found and the money passed to a cousin named Elizabeth Stephens. Hooke

12672-615: The late 12th and early 13th centuries ( Salisbury Cathedral ). If the centers are closer to another, the result is a wider blunt arch . The intrados of the cusped arch (also known as multifoil arch , polyfoil arch , polylobed arch , and scalloped arch ) includes several independent circle segments in a scalloped arrangement. These primarily decorative arches are common in Islamic architecture and Northern European Late Gothic, can be found in Romanesque architecture . A similar trefoil arch includes only three segments and sometimes has

12804-527: The later Parthian Empire (247 BC–AD 224). This architectural tradition was continued by the Sasanian Empire (224–651), which built the Taq Kasra at Ctesiphon in the 6th century AD, the largest free-standing vault until modern times. An early European example of a voussoir arch appears in the 4th century BC Greek Rhodes Footbridge . Proto-true arches can also be found under the stairs of

12936-533: The latter were responsible for shell fossils being found far above sea level. In 1835, Charles Lyell , the Scottish geologist and associate of Charles Darwin , wrote of Hooke in Principles of Geology : "His treatise ... is the most philosophical production of that age, in regard to the causes of former changes in the organic and inorganic kingdoms of nature". Hooke's scientific model of human memory

13068-497: The love of his life, and he was devastated when she died in 1687. Inwood also mentions "The age difference between him and Grace was commonplace and would not have upset his contemporaries as it does us". The incestous relationship would nevertheless have been frowned upon and tried by an ecclesiastical court had it been discovered, it was not however a capital felony after 1660. Since childhood, Hooke suffered from migraine , tinnitus , dizziness and bouts of insomnia ; he also had

13200-513: The most ingenious book that ever I read in my life". One of the observations in Micrographia is of fossil wood , the microscopic structure of which Hooke compared to that of ordinary wood. This led him to conclude that fossilised objects like petrified wood and fossil shells such as ammonites were the remains of living things that had been soaked in mineral-laden petrifying water. He believed that such fossils provided reliable clues about

13332-556: The motion of a spherical pendulum and of a ball in a hollow cone, to demonstrate central force due to gravity, and a hanging chain net with point loads to provide the optimum shape for a dome with heavy cross on top. Despite continuing reports to the contrary, Hooke did not influence Thomas Newcomen 's invention of the steam engine ; this myth, which originated in an article in the third edition of " Encyclopædia Britannica ", has been found to be mistaken. While many of Hooke's contemporaries, such as Isaac Newton, believed in aether as

13464-440: The movement of pendulums up to 200 ft long (61 m). His biographer Margaret 'Espinasse described him as England's first meteorologist , in her description of his essay Method for making a history of the weather . (Hooke specifies that a thermometer, a hygrometer , a wind gauge and a record sheet be used for proper weather records. ) In May 1664, using a 12 ft (3.7 m) refracting telescope , Hooke observed

13596-561: The nucleus of the Royal Society . In 1659, Hooke described to the Club some elements of a method of heavier-than-air flight but concluded human muscles were insufficient to the task. Through the Club, Hooke met Seth Ward (the University's Savilian Professor of Astronomy ) and developed for Ward a mechanism that improved the regularity of pendulum clocks used for astronomical time-keeping. Hooke characterised his Oxford days as

13728-409: The opening can be filled with smaller arches, producing a containing arch , common in Gothic and Romanesque architecture. Multiple arches can be superimposed with an offset, creating an interlaced series of usually (with some exceptions) blind and decorative arches. Most likely of Islamic origin, the interlaced arcades were popular in Romanesque and Gothic architecture. Rear-arch (also rere-arch )

13860-865: The other two, so the other dimensions can be neglected in calculations; however, the ratio of the smaller dimensions and the composition can determine the flexural and compressive stiffness of the element. Two-dimensional elements with a thin third dimension have little of either but can resist biaxial traction. The structure elements are combined in structural systems . The majority of everyday load-bearing structures are section-active structures like frames, which are primarily composed of one-dimensional (bending) structures. Other types are Vector-active structures such as trusses , surface-active structures such as shells and folded plates, form-active structures such as cable or membrane structures, and hybrid structures. Load-bearing biological structures such as bones, teeth, shells, and tendons derive their strength from

13992-665: The problem of lateral thrust is greatly diminished. An example of the latter would be the Nippur arch, built before 3800 BC, and dated by H. V. Hilprecht  (1859–1925) to even before 4000 BC. Rare exceptions are an arched mudbrick home doorway dated to c.  2000 BC from Tell Taya in Iraq and two Bronze Age arched Canaanite city gates, one at Ashkelon (dated to c.  1850 BC ), and one at Tel Dan (dated to c.  1750 BC ), both in modern-day Israel . An Elamite tomb dated 1500 BC from Haft Teppe contains

14124-698: The proposed exclusive contract for the use of this idea resulted in its abandonment. Hooke developed the principle of the balance spring independently of Huygens and at least five years beforehand. Huygens published his own work in Journal de Scavans in February 1675 and built the first functioning watch to use a balance spring. In 1663 and 1664, Hooke made his microscopic, and some astronomic, observations, which he collated in Micrographia in 1665. His book, which describes observations with microscopes and telescopes, as well as original work in biology, contains

14256-576: The rotations of Mars and Jupiter . Hooke's 1665 book Micrographia , in which he coined the term cell , encouraged microscopic investigations. Investigating optics  – specifically light refraction  – Hooke inferred a wave theory of light . His is the first-recorded hypothesis of the cause of the expansion of matter by heat, of air's composition by small particles in constant motion that thus generate its pressure, and of heat as energy. In physics, Hooke inferred that gravity obeys an inverse square law and arguably

14388-498: The servants who ran his home – his niece Grace Hooke and his cousin Tom Giles lived with him for some years as children. Hooke never married. According to his diary, Hooke had a sexual relationship with his niece Grace, after she had turned 16. Grace was in his custody since the age of 10. He also had sexual relations with several maids and housekeepers. Hooke's biographer Stephen Inwood considers Grace to have been

14520-467: The seventeenth century. He also concluded respiration and combustion involve a specific and limited component of air. According to Partington, if "Hooke had continued his experiments on combustion, it is probable that he would have discovered oxygen". Samuel Pepys wrote of the book in his diary on 21 January 16 ⁠ 64 / 65 ⁠ : "Before I went to bed I sat up till two o’clock in my chamber reading of Mr. Hooke's Microscopicall Observations,

14652-443: The span (and thus the geometric circle of at least one segment is below the springing line) is called a surbased arch (sometimes also a depressed arch ). A drop arch is either a basket handle arch or a blunt arch. The practical arch bridges are built either as a fixed arch, a two-hinged arch, or a three-hinged arch. The fixed arch is most often used in reinforced concrete bridges and tunnels, which have short spans. Because it

14784-449: The square of distance' was rather common and had been advanced by a number of different people for different reasons". In the 1660s, Newton had shown for planetary motion under a circular assumption, force in the radial direction had an inverse-square relation with distance from the centre. Newton, who in May 1686 was presented with Hooke's claim to priority on the inverse square law, denied he

14916-455: The star Gamma Draconis and chose the method of parallax determination. In 1669, after several months of observing, Hooke believed the desired result had been achieved. It is now known his equipment was far too imprecise to obtain an accurate measurement. Hooke's Micrographia contains illustrations of the Pleiades star cluster and lunar craters . He conducted experiments to investigate

15048-433: The structure to move freely and compensate for the thermal expansion and contraction that changes in outdoor temperature cause. However, this can result in additional stresses, and therefore the two-hinged arch is also statically indeterminate, although not as much as the fixed arch. The three-hinged arch is not only hinged at its base, like the two-hinged arch, yet also at its apex. The additional apical connection allows

15180-826: The supposition, could only guess it was approximately valid "at great distances from the centre". Newton did accept and acknowledge, in all editions of the Principia , Hooke and others had separately appreciated the inverse square law in the solar system. Newton acknowledged Wren, Hooke and Halley in this connection in his "Scholium to Proposition 4" in Book   1. In a letter to Halley, Newton also acknowledged his correspondence with Hooke in 1679–1680 had reawakened his dormant interest in astronomical matters but that did not mean, according to Newton, Hooke had told Newton anything new or original. Newton wrote: Yet am I not beholden to him for any light into that business ... but only for

15312-557: The symmetry of a crystal determines what physical properties, including piezoelectricity and ferromagnetism , the crystal can have. A large part of numerical analysis involves identifying and interpreting the structure of musical works. Structure can be found at the level of part of a work, the entire work, or a group of works. Elements of music such as pitch , duration and timbre combine into small elements like motifs and phrases , and these in turn combine in larger structures. Not all music (for example, that of John Cage ) has

15444-417: The three-hinged arch to move in two opposite directions and compensate for any expansion and contraction. This kind of arch is thus not subject to additional stress from thermal change. Unlike the other two kinds of arch, the three-hinged arch is therefore statically determinate. It is most often used for spans of medial length, such as those of roofs of large buildings. Another advantage of the three-hinged arch

15576-459: The time. Accordingly, he invented three new mechanisms: the Hooke joint , a sophisticated universal joint that allowed his instruments to smoothly follow the apparent motion of the observed body; the first clockwork drive to automate the process; and a micrometer screw that allowed him to achieve a precision of ten seconds of arc . Hooke was dissatisfied with refracting telescopes so he built

15708-432: The type in which he was involved seem almost to be the rule rather than the exception. And Hooke's reaction to such controversy involving his own discoveries and inventions seems mild in comparison to the behaviour of some of his contemporaries". The publication of Hooke's diary in 1935 revealed previously unknown details about his social and familial relationships. His biographer Margaret 'Espinasse said: "the picture which

15840-415: The use of the balance spring to improve the timekeeping of watches. Galileo had observed the regularity of a pendulum and Huygens first incorporated it in a clock; in 1668, Hooke demonstrated his new device to keep a pendulum swinging regularly in unsteady conditions. His invention of a tooth-cutting machine enabled a substantial improvement in the accuracy and precision of timepieces. Waller reported

15972-404: Was an adept mathematician, neither of which applied to Boyle. Hooke taught Boyle Euclid's Elements and Descartes 's Principles of Philosophy ; it also caused them to recognise fire as a chemical reaction and not, as Aristotle taught, a fundamental element of nature. According to Henry Robinson, Librarian of The Royal Society in 1935: Without his weekly experiments and prolific work

16104-483: Was an impoverished scientific inquirer in young adulthood who went on to become one of the most important scientists of his time. After the Great Fire of London in 1666, Hooke (as a surveyor and architect) attained wealth and esteem by performing more than half of the property line surveys and assisting with the city's rapid reconstruction. Often vilified by writers in the centuries after his death, his reputation

16236-520: Was appointed its Joint Secretary. Although John Aubrey described Hooke as a person of "great virtue and goodness". much has been written about the unpleasant side of Hooke's personality. According to his first biographer Richard Waller, Hooke was "in person, but despicable", and "melancholy, mistrustful, and jealous". Waller's comments influenced other writers for more than 200 years such that many books and articles – especially biographies of Isaac Newton  – portray Hooke as

16368-471: Was buried at St Helen's Church, Bishopsgate , in the City of London but the precise location of his grave is unknown. Hooke's role at the Royal Society was to demonstrate experiments from his own methods or at the suggestion of members. Among his earliest demonstrations were discussions of the nature of air and the implosion of glass bubbles that had been sealed with enclosed hot air. He also demonstrated that

16500-436: Was confirmed to the office and on 11 January 1665, he was named Curator by Office for life with an annual salary of £80, which consisting of £30 from the Society and Cutler's £50 annuity. In June 1663, Hooke was elected a Fellow of the Royal Society (FRS). On 20 March 1665, he was also appointed Gresham Professor of Geometry . On 13 September 1667, Hooke became acting Secretary of the Society and on 19 December 1677, he

16632-545: Was frail and not expected to live. Although his father gave him some instruction in English, (Latin) Grammar and Divinity , Robert's education was largely neglected. Left to his own devices, he made little mechanical toys; seeing a brass clock dismantled, he built a wooden replica that "would go". Hooke's father died in October 1648, leaving £40 in his will to Robert (plus another £10 held over from his grandmother). At

16764-485: Was more sympathetic but still described Hooke as "difficult", "suspicious" and "irritable". In October 1675, the Council of the Royal Society considered a motion to expel Hooke because of an attack he made on Christiaan Huygens over scientific priority in watch design but it did not pass. According to Hooke's biographer Ellen Drake: if one studies the intellectual milieu of the time, the controversies and rivalries of

16896-646: Was one of the first of its kind. In a 1682 lecture to the Royal Society, Hooke proposed a mechanical analogue model of human memory that bore little resemblance to the mainly philosophical models of earlier writers. This model addressed the components of encoding, memory capacity, repetition, retrieval, and forgetting – some with surprisingly modern accuracy. According to psychology professor Douglas Hintzman, Hooke's model's most-interesting points are that it allows for attention and other top-down influences on encoding; it uses resonance to implement parallel, cue-dependent retrieval; it explains memory for recency; it offers

17028-645: Was printed in 1705. The work of Waller, along with John Ward 's Lives of the Gresham Professors , and John Aubrey 's Brief Lives form the major near-contemporaneous biographical accounts of his life. Hooke was born in 1635 in Freshwater, Isle of Wight , to Cecily Gyles and the Anglican priest John Hooke, who was the curate of All Saints' Church, Freshwater . Robert was the youngest, by seven years, of four siblings (two boys and two girls); he

17160-569: Was restored at the end of the twentieth century and he has been called "England's Leonardo [da Vinci] ". Hooke was a Fellow of the Royal Society and from 1662, he was its first Curator of Experiments. From 1665 to 1703, he was also Professor of Geometry at Gresham College . Hooke began his scientific career as an assistant to the physical scientist Robert Boyle . Hooke built the vacuum pumps that were used in Boyle's experiments on gas law and also conducted experiments. In 1664, Hooke identified

17292-515: Was the first to hypothesise such a relation in planetary motion, a principle Isaac Newton furthered and formalised in Newton's law of universal gravitation . Priority over this insight contributed to the rivalry between Hooke and Newton. In geology and palaeontology , Hooke originated the theory of a terraqueous globe, thus disputing the Biblical view of the Earth's age; he also hypothesised

17424-509: Was to be credited as author of the idea, giving reasons including the citation of prior work by others. Newton also said that, even if he had first heard of the inverse square proportion from Hooke (which Newton said he had not), he would still have some rights to it because of his mathematical developments and demonstrations. These, he said, enabled observations to be relied upon as evidence of its accuracy while according to Newton, Hooke, without mathematical demonstrations and evidence in favour of

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