Concorde
The Aérospatiale/BAC Concorde is a French-British turbojet-powered supersonic passenger airliner, operated from 1976 until 2003. It had a maximum speed over twice the speed of sound at Mach 2.04, with seating for 92 to 128 passengers. First flown in 1969, Concorde continued flying for the next 27 years, it is one of only two supersonic transports to have been operated commercially. Concorde was jointly developed and manufactured by Sud Aviation and the British Aircraft Corporation under an Anglo-French treaty. Twenty aircraft were built, including development aircraft. Air France and British Airways were the only airlines to fly Concorde; the aircraft was used by wealthy passengers who could afford to pay a high price in exchange for the aircraft's speed and luxury service. For example, in 1997, the round-trip ticket price from New York to London was $7,995, more than 30 times the cost of the cheapest option to fly this route; the original program cost estimate of £70 million met huge overruns and delays, with the program costing £1.3 billion.
It was this extreme cost that became the main factor in the production run being much smaller than anticipated. Another factor which affected the viability of all supersonic transport programmes was that supersonic flight could only be used on ocean-crossing routes, to prevent sonic boom disturbance over populated areas. With only seven airframes each being operated by the British and French, the per-unit cost was impossible to recoup, so the French and British governments absorbed the development costs. British Airways and Air France were able to operate Concorde at a profit, in spite of high maintenance costs, because the aircraft was able to sustain a high ticket price. Among other destinations, Concorde flew regular transatlantic flights from London's Heathrow Airport and Paris's Charles de Gaulle Airport to John F. Kennedy International Airport in New York, Washington Dulles International Airport in Virginia, Grantley Adams International Airport in Barbados. Concorde won the 2006 Great British Design Quest organised by the BBC and the Design Museum, beating other well-known designs such as the BMC Mini, the miniskirt, the Jaguar E-Type, the London Tube map and the Supermarine Spitfire.
The type was retired in 2003, three years after the crash of Air France Flight 4590, in which all passengers and crew were killed. The general downturn in the commercial aviation industry after the September 11 attacks in 2001 and the end of maintenance support for Concorde by Airbus contributed; the origins of the Concorde project date to the early 1950s, when Arnold Hall, director of the Royal Aircraft Establishment asked Morien Morgan to form a committee to study the supersonic transport concept. The group met for the first time in February 1954 and delivered their first report in April 1955. At the time it was known that the drag at supersonic speeds was related to the span of the wing; this led to the use of short-span thin trapezoidal wings such as those seen on the control surfaces of many missiles, or in aircraft like the Lockheed F-104 Starfighter or the Avro 730 that the team studied. The team outlined a baseline configuration that looked like an enlarged Avro 730; this same short span produced little lift at low speed, which resulted in long take-off runs and frighteningly high landing speeds.
In an SST design, this would have required enormous engine power to lift off from existing runways, to provide the fuel needed, "some horribly large aeroplanes" resulted. Based on this, the group considered the concept of an SST infeasible, instead suggested continued low-level studies into supersonic aerodynamics. Soon after, Johanna Weber and Dietrich Küchemann at the RAE published a series of reports on a new wing planform, known in the UK as the "slender delta" concept; the team, including Eric Maskell whose report "Flow Separation in Three Dimensions" contributed to an understanding of the physical nature of separated flow, worked with the fact that delta wings can produce strong vortices on their upper surfaces at high angles of attack. The vortex will lower the air pressure and cause lift to be increased; this effect had been noticed earlier, notably by Chuck Yeager in the Convair XF-92, but its qualities had not been appreciated. Weber suggested that this was no mere curiosity, the effect could be deliberately used to improve low speed performance.
Küchemann's and Weber's papers changed the entire nature of supersonic design overnight. Although the delta had been used on aircraft prior to this point, these designs used planforms that were not much different from a swept wing of the same span. Weber noted that the lift from the vortex was increased by the length of the wing it had to operate over, which suggested that the effect would be maximised by extending the wing along the fuselage as far as possible; such a layout would still have good supersonic performance inherent to the short span, while offering reasonable take-off and landing speeds using vortex generation. The only downside to such a design is that the aircraft would have to take off and land "nose high" to generate the required vortex lift, which led to questions about the low speed handling qualities of such a design, it would need to have long landing gear to produce the required angle of attack while still on the runway. Küchemann presented the idea at a meeting
Aircraft
An aircraft is a machine, able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. Common examples of aircraft include airplanes, airships and hot air balloons; the human activity that surrounds aircraft is called aviation. The science of aviation, including designing and building aircraft, is called aeronautics. Crewed aircraft are flown by an onboard pilot, but unmanned aerial vehicles may be remotely controlled or self-controlled by onboard computers. Aircraft may be classified by different criteria, such as lift type, aircraft propulsion and others. Flying model craft and stories of manned flight go back many centuries, however the first manned ascent – and safe descent – in modern times took place by larger hot-air balloons developed in the 18th century; each of the two World Wars led to great technical advances. The history of aircraft can be divided into five eras: Pioneers of flight, from the earliest experiments to 1914.
First World War, 1914 to 1918. Aviation between the World Wars, 1918 to 1939. Second World War, 1939 to 1945. Postwar era called the jet age, 1945 to the present day. Aerostats use buoyancy to float in the air in much the same way, they are characterized by one or more large gasbags or canopies, filled with a low-density gas such as helium, hydrogen, or hot air, less dense than the surrounding air. When the weight of this is added to the weight of the aircraft structure, it adds up to the same weight as the air that the craft displaces. Small hot-air balloons called sky lanterns were first invented in ancient China prior to the 3rd century BC and used in cultural celebrations, were only the second type of aircraft to fly, the first being kites which were first invented in ancient China over two thousand years ago. A balloon was any aerostat, while the term airship was used for large, powered aircraft designs – fixed-wing. In 1919 Frederick Handley Page was reported as referring to "ships of the air," with smaller passenger types as "Air yachts."
In the 1930s, large intercontinental flying boats were sometimes referred to as "ships of the air" or "flying-ships". – though none had yet been built. The advent of powered balloons, called dirigible balloons, of rigid hulls allowing a great increase in size, began to change the way these words were used. Huge powered aerostats, characterized by a rigid outer framework and separate aerodynamic skin surrounding the gas bags, were produced, the Zeppelins being the largest and most famous. There were still no fixed-wing aircraft or non-rigid balloons large enough to be called airships, so "airship" came to be synonymous with these aircraft. Several accidents, such as the Hindenburg disaster in 1937, led to the demise of these airships. Nowadays a "balloon" is an unpowered aerostat and an "airship" is a powered one. A powered, steerable aerostat is called a dirigible. Sometimes this term is applied only to non-rigid balloons, sometimes dirigible balloon is regarded as the definition of an airship.
Non-rigid dirigibles are characterized by a moderately aerodynamic gasbag with stabilizing fins at the back. These soon became known as blimps. During the Second World War, this shape was adopted for tethered balloons; the nickname blimp was adopted along with the shape. In modern times, any small dirigible or airship is called a blimp, though a blimp may be unpowered as well as powered. Heavier-than-air aircraft, such as airplanes, must find some way to push air or gas downwards, so that a reaction occurs to push the aircraft upwards; this dynamic movement through the air is the origin of the term aerodyne. There are two ways to produce dynamic upthrust: aerodynamic lift, powered lift in the form of engine thrust. Aerodynamic lift involving wings is the most common, with fixed-wing aircraft being kept in the air by the forward movement of wings, rotorcraft by spinning wing-shaped rotors sometimes called rotary wings. A wing is a flat, horizontal surface shaped in cross-section as an aerofoil. To fly, air must generate lift.
A flexible wing is a wing made of fabric or thin sheet material stretched over a rigid frame. A kite is tethered to the ground and relies on the speed of the wind over its wings, which may be flexible or rigid, fixed, or rotary. With powered lift, the aircraft directs its engine thrust vertically downward. V/STOL aircraft, such as the Harrier Jump Jet and F-35B take off and land vertically using powered lift and transfer to aerodynamic lift in steady flight. A pure rocket is not regarded as an aerodyne, because it does not depend on the air for its lift. Rocket-powered missiles that obtain aerodynamic lift at high speed due to airflow over their bodies are a marginal case; the forerunner of the fixed-wing aircraft is the kite. Whereas a fixed-wing aircraft relies on its forward speed to create airflow over the wings, a kite is tethered to the ground and relies on the wind blowing over its wings to provide lift. Kites were the first kind of aircraft to fly, were invented in China around 500 BC.
Much aerodynamic research was done with kites before test aircraft, wind tunnels, computer modelling programs became available. The first heavier-than-air craft capable of controlled free-flight were gliders. A glider designed by Geo
Patent drawing
A patent application or patent may contain drawings called patent drawings, illustrating the invention, some of its embodiments, or the prior art. The drawings may be required by the law to be in a particular form, the requirements may vary depending on the jurisdiction. Under the European Patent Convention, Article 78 EPC provides that a European patent application shall contain any drawings referred to in the description or the claims. Drawings are therefore optional. Rule 46 EPC specifies the form; the European search report is drawn up in respect of a European patent application on the basis of the claims, with due regard to the description and any drawings. In addition, the extent of the protection conferred by a European patent or a European patent application is determined by the claims, with the description and drawings being used to interpret the claims. Under the Patent Cooperation Treaty,Article 7 PCT notably provides that the drawings are required when they are necessary for the understanding of the invention.
Rule 11.13 PCT specifies special physical requirements for drawings in an international application. In the United States, the applicant for a patent is required by law to furnish a drawing of the invention whenever the nature of the case requires a drawing to understand the invention; this drawing must be filed with the application. This includes all inventions except compositions of matter or processes, but a drawing may be useful in the case of many processes; the drawing must show every feature of the invention specified in the claims, is required by the U. S. patent office rules to be in a particular form. The United States Patent and Trademark Office specifies the size of the sheet on which the drawing is made, the type of paper, the margins, other details relating to the making of the drawing; the reason for specifying the standards in detail is that the drawings are printed and published in a uniform style when the patent issues, the drawings must be such that they can be understood by persons using the patent descriptions.
No names or other identification are permitted within the “sight” of the drawing, applicants are expected to use the space above and between the hole locations to identify each sheet of drawings. This identification may consist of the attorney’s name and docket number or the inventor’s name and application number and may include the sheet number and the total number of sheets filed; the following rule, reproduced from title 37 of the Code of Federal Regulations, relates to the standards for drawings: From 1790 to 1880 in the US, patent models were required. A patent model was a scratch-built miniature model no larger than 12" by 12" by 12" 30 cm by 30 cm by 30 cm, that showed how an invention works; some inventors still willingly submitted models at the turn of the twentieth century. In some cases, an inventor may still want to present a "working model" as an evidence to prove actual reduction to practice in an interference proceeding. In some jurisdictions patent models stayed an aid to demonstrate the operation of the invention.
In applications involving genetics, samples of genetic material or DNA sequences may be required. The United States patent law was revised in 1793, it stated that the Commissioner of the USPTO could ask for additional information, drawings, or diagrams if the description is not clear. By the rate of patent grants had grown to about 20 per year and the time burden on the Secretary of State was considered to be too burdensome. Patent applications were no longer examined. Patents were granted by submitting a written description of an invention, a model of the invention, if appropriate, paying a fee of $30 and now $1000 in 2006 US dollars. In utility and design patent applications, drawings can be in black color. Black and white drawings are required. On rare occasions, color drawings may be necessary as the only practical medium by which to disclose the subject matter sought to be patented in a utility or design patent application or the subject matter of a statutory invention registration. Black and white photographs are not ordinarily permitted in utility and design patent applications, unless this is the only practicable medium for illustrating the claimed invention.
For example, photographs of electrophoresis gels, autoradiographs, cell cultures, histological tissue cross sections, plants, in vivo imaging, etc. Color photographs can be accepted in utility and design patent applications if the conditions for accepting color drawings and black and white photographs have been satisfied. Patent drawing features can contain the following features: Identification of drawings: includes the title of the invention, inventor’s name, application number.. etc. Graphic forms in drawings. Chemical or mathematical formulae and waveforms may be submitted as drawings and are subject to the same requirements as drawings; each chemical or mathematical formula must be labeled as a separate figure, using brackets when necessary, to show that information is properly integrated. Type of paper: flexible, white, smooth and durable. Size of paper: Must be the same size DIN size A4; some kind of Margin standard. Views; the drawing must contain as many views as necessary to show the invention.
The views may be plan, section, or perspective views. Arrangement of views: All views on the same sheet in the same direction. Front page view Scale: large enough to show the mechanism Shading: aids in understanding the invention used to indicate the surface or shape of spherical, cylindrical
Wind tunnel
Wind tunnels are large tubes with air moving inside. The tunnels are used to copy the actions of an object in flight. Researchers use wind tunnels to learn more about. NASA uses wind tunnels to test scale models of spacecraft; some wind tunnels are big enough to hold full-size versions of vehicles. The wind tunnel moves air around an object, making it seem like the object is flying. Most of the time, powerful fans move air through the tube; the object to be tested is fastened in the tunnel. The object can be a small model of a vehicle, it can be just a piece of a vehicle. It can be spacecraft, it can be a common object like a tennis ball. The air moving around the still object shows what would happen if the object were moving through the air. How the air moves can be studied in different ways. Smoke or dye can be seen as it moves. Threads can be attached to the object to show. Special instruments are used to measure the force of the air on the object; the earliest wind tunnels were invented towards the end of the 19th century, in the early days of aeronautic research, when many attempted to develop successful heavier-than-air flying machines.
The wind tunnel was envisioned as a means of reversing the usual paradigm: instead of the air standing still and an object moving at speed through it, the same effect would be obtained if the object stood still and the air moved at speed past it. In that way a stationary observer could study the flying object in action, could measure the aerodynamic forces being imposed on it; the development of wind tunnels accompanied the development of the airplane. Large wind tunnels were built during World War II. Wind tunnel testing was considered of strategic importance during the Cold War development of supersonic aircraft and missiles. On, wind tunnel study came into its own: the effects of wind on man made structures or objects needed to be studied when buildings became tall enough to present large surfaces to the wind, the resulting forces had to be resisted by the building's internal structure. Determining such forces was required before building codes could specify the required strength of such buildings and such tests continue to be used for large or unusual buildings.
Still wind-tunnel testing was applied to automobiles, not so much to determine aerodynamic forces per se but more to determine ways to reduce the power required to move the vehicle on roadways at a given speed. In these studies, the interaction between the road and the vehicle plays a significant role, this interaction must be taken into consideration when interpreting the test results. In an actual situation the roadway is moving relative to the vehicle but the air is stationary relative to the roadway, but in the wind tunnel the air is moving relative to the roadway, while the roadway is stationary relative to the test vehicle; some automotive-test wind tunnels have incorporated moving belts under the test vehicle in an effort to approximate the actual condition, similar devices are used in wind tunnel testing of aircraft take-off and landing configurations. Wind tunnel testing of sporting equipment has been prevalent over the years, including golf clubs, golf balls, Olympic bobsleds, Olympic cyclists, race car helmets.
Helmet aerodynamics is important in open cockpit race cars. Excessive lift forces on the helmet can cause considerable neck strain on the driver, flow separation on the back side of the helmet can cause turbulent buffeting and thus blurred vision for the driver at high speeds; the advances in computational fluid dynamics modelling on high speed digital computers has reduced the demand for wind tunnel testing. However, CFD results are still not reliable and wind tunnels are used to verify CFD predictions. Air velocity and pressures are measured in several ways in wind tunnels. Air velocity through the test section is determined by Bernoulli's principle. Measurement of the dynamic pressure, the static pressure, the temperature rise in the airflow; the direction of airflow around a model can be determined by tufts of yarn attached to the aerodynamic surfaces. The direction of airflow approaching a surface can be visualized by mounting threads in the airflow ahead of and aft of the test model. Smoke or bubbles of liquid can be introduced into the airflow upstream of the test model, their path around the model can be photographed.
Aerodynamic forces on the test model are measured with beam balances, connected to the test model with beams, strings, or cables. The pressure distributions across the test model have been measured by drilling many small holes along the airflow path, using multi-tube manometers to measure the pressure at each hole. Pressure distributions can more conveniently be measured by the use of pressure-sensitive paint, in which higher local pressure is indicated by lowered fluorescence of the paint at that point. Pressure distributions can be conveniently measured by the use of pressure-sensitive pressure belts, a recent development in which multiple ultra-miniaturized pressure sensor modules are integrated into a flexible strip; the strip is attached to the aerodynamic surface with tape, it sends signals depicting the pressure distribution along its surface. Pressure distributions on a test model can be determined by performing a wake survey, in which either a single pitot tube is used to obtain multiple readings downstream of the test model, or a multiple-tube manometer is mounted downstream and all its readings are taken.
The aerodynamic properties of an object can not all remain the same for a
Langley Research Center
Langley Research Center located in Hampton, United States, is the oldest of NASA's field centers. It directly borders the Back River on the Chesapeake Bay. LaRC has focused on aeronautical research, but has tested space hardware at the facility, such as the Apollo Lunar Module. In addition, a number of the earliest high-profile space missions were designed on-site. Established in 1917 by the National Advisory Committee for Aeronautics, the research center devotes two-thirds of its programs to aeronautics, the rest to space. LaRC researchers use more than 40 wind tunnels to study and improve aircraft and spacecraft safety and efficiency. Between 1958 and 1963, when NASA started Project Mercury, LaRC served as the main office of the Space Task Group. In June 2015, after serving as associate director deputy director, Dr. David E. Bowles was appointed director of NASA Langley. After US-German relations had deteriorated from neutral to hostile around 1916, the prospect of U. S. war entry became possible.
On February 15, 1917, the newly established Aviation Week warned that the U. S. military aviation capability was less than. President Woodrow Wilson sent Jerome Hunsaker to Europe to investigate, Hunsaker's report prompted Wilson to command the creation of the nation's first aeronautics laboratory, which became NASA Langley. In 1917, less than three years after it was created, the NACA established Langley Memorial Aeronautical Laboratory on Langley Field. Both Langley Field and the Langley Laboratory are named for aviation pioneer Samuel Pierpont Langley; the Aviation Section, U. S. Signal Corps had established a base there earlier that same year; the first research facilities were in place and aeronautical research was started by 1920. The laboratory included four researchers and 11 technicians. Langley Field and NACA began parallel growth as air power proved its utility during World War I; the center was established to explore the field of aerodynamic research involving airframe and propulsion engine design and performance.
In 1934 the world's largest wind tunnel was constructed at Langley Field with a 30 × 60 foot test section. It remained the world's largest wind tunnel until the 1940s, when a 40 × 80 foot tunnel was built at NASA Ames Research Center in California. Early in 1945, the center expanded to include rocket research, leading to the establishment of a flight station at Wallops Island, Virginia. A further expansion of the research program permitted Langley Research Center to orbit payloads, starting with NASA's Explorer 9 balloon satellite in mid-February 1961; as rocket research grew, aeronautics research continued to expand and played an important part when subsonic flight was advanced and supersonic and hypersonic flight were introduced. Langley Research Center can claim many historic firsts, some of which have proven to be revolutionary scientific breakthroughs; these accomplishments include the development of the concept of research aircraft leading to supersonic flight, the world's first transonic wind tunnels, the Lunar Landing Facility providing the simulation of lunar gravity, the Viking program for Mars exploration.
The center developed standards for the grooving of aircraft runways based on a previous British design used at Washington National Airport. Grooved runways reduce aquaplaning; this grooving is now the international standard for all runways around the world. Langley Research Center performs critical research on aeronautics, including wake vortex behavior, fixed-wing aircraft, rotary wing aircraft, aviation safety, human factors and aerospace engineering. LaRC supported the design and testing of the hypersonic X-43, which achieved a world speed record of Mach 9.6. LaRC assisted the NTSB in the investigation of the crash of American Airlines Flight 587. Work began in July 2011 to remove the 1940s era 16 feet transonic wind tunnel; the facility supported development and propulsion integration research for many military aircraft including all fighters since 1960 but had been inactive since 2004. Langley retained transonic wind tunnel testing capabilities facilities in the National Transonic Facility, a high pressure, cryogenically cooled 8.2 feet closed loop wind tunnel.
The EBF³ process produces structural metallic parts with immense strength, useful in performing repairs in remote locations. Additionally, the ability to build functionally graded, unitized parts directly from CAD data offers enhanced performance in numerous applications. LaRC has become home to this new type of machining process, used by their new room-sized electron-emitting device, which uses a High Frequency 42 kW, X-ray emitting electron gun, which melts either aluminum or titanium wire into the desired 3-dimensional metallic parts with a material strength comparable to that of wrought products; the machine's deposition rate is 150 in³/h, equivalent to its plastic-fabricating counterpart. Metallic parts are built directly from CAD without molds or tools, leaving the end product with no porosity. Other properties include: 6-axis positioning Heated or cooled platen 1×10−6 torr vacuum capability 72 × 24 × 24 inch build envelope Power efficiency in excess of 90% Near 100% feedstock efficiency Can deposit reflective materials not processable with lasers Potential portable EBF³ system (Unde
Eureka (word)
Eureka is an interjection used to celebrate a discovery or invention. It is a transliteration of an exclamation attributed to Ancient Greek mathematician and inventor Archimedes. "Eureka" comes from the Ancient Greek word εὕρηκα heúrēka, meaning "I found", the first person singular perfect indicative active of the verb εὑρίσκω heuriskō "I find". It is related to heuristic, which refers to experience-based techniques for problem solving and discovery; the accent of the English word is on the second syllable, following Latin rules of accent, which require that a penult must be accented if it contains a long vowel. In the Greek pronunciation, the first syllable has a high pitch accent, because the Ancient Greek rules of accent do not force accent to the penult unless the ultima has a long vowel; the long vowels in the first two syllables would sound like a double stress to English ears. The initial /h/ is dropped in some European languages, including Spanish and English, but preserved in others, such as Finnish and German.
The exclamation'Eureka!' is attributed to the ancient Greek scholar Archimedes. He proclaimed "Eureka! Eureka!" after he had stepped into a bath and noticed that the water level rose, whereupon he understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. He realized that the volume of irregular objects could be measured with precision, a intractable problem, he is said to have been so eager to share his discovery that he leapt out of his bathtub and ran naked through the streets of Syracuse. Archimedes' insight led to the solution of a problem posed by Hiero of Syracuse, on how to assess the purity of an irregular golden votive crown. Equipment for weighing objects with a fair amount of precision existed, now that Archimedes could measure volume, their ratio would give the object's density, an important indicator of purity; this story first appeared in written form in Vitruvius's books of architecture, two centuries after it took place.
Some scholars have doubted the accuracy of this tale, on the grounds that the votive crown was a fine item, thus an impure crown would displace water only minutely, compared to a pure one. Precise means needed to measure this minute difference was not available at the time. For the problem posed to Archimedes, there is a simple method which requires no precision equipment: balance the crown against pure gold on a scale in the air, submerge both the crown and the gold in water simultaneously. If the volumes are the same, the scale remains in balance, meaning that their densities are the same and therefore the crown must be pure gold, but if the volume of the crown is greater, increased buoyancy results in imbalance. Greater volume of the crown means its density is less than that of the gold, therefore the crown could not be pure gold. Galileo Galilei himself weighed in on the controversy, suggesting a design for a hydrostatic balance that could be used to compare the dry weight of an object with the weight of the same object submerged in water.
The expression is the state motto of California, referring to the momentous discovery of gold near Sutter's Mill in 1848. The California State Seal has included the word eureka since its original design by Robert S. Garnett in 1850. In 1957 the state legislature attempted to make "In God We Trust" the state motto as part of the same post WWII anti-Communist movement that added the term "under God" to the American Pledge of Allegiance in 1954, but this attempt did not succeed and "Eureka" was made the official motto in 1963; the city of Eureka, founded in 1850, uses the California State Seal as its official seal. Eureka is a considerable distance from Sutter's Mill, but was the jumping off point of a smaller gold rush in nearby Trinity County, California in 1850, it is the largest of at least eleven remaining US cities and towns named for the exclamation, "eureka!". As a result of the extensive use of the exclamation dating from 1849, there were nearly 40 locales so named by the 1880s in a nation that had none in the 1840s.
Many places, works of culture, other objects have since been named "Eureka". "Eureka" was associated with a gold rush in Ballarat, Australia. The Eureka Stockade was a revolt in 1854 by gold miners against unjust mining license fees and a brutal administration supervising the miners; the rebellion demonstrated the refusal of the workers to be dominated by unfair government and laws. The Eureka Stockade has been referred to as the "birth of democracy" in Australia. Another mathematician, Carl Friedrich Gauss, echoed Archimedes when in 1796 he wrote in his diary, "ΕΥΡΗΚΑ! num = Δ + Δ + Δ", referring to his discovery that any positive integer could be expressed as the sum of at most three triangular numbers. This result is now known as Gauss' Eureka theorem and is a special case of what became known as the Fermat polygonal number theorem. Heuristic Eureka effect
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