Wh first discovered the basic shape of an airfoil?
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Wright Brothers. They actually invent aeronautical engineering. Their basic principles are still used today. Their models airfoils indicated thin wings worked. Large wings and slow air thicker gives more lift. It was about the only refinement of their work. Their propeller was designed from the principles of airfoil as well and the curves are the ones still used today.\nThey rewrote the erroneous lifting tables of Lillinathall, Bell, others. Amazing really.
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The symbol  was first introduced by William Jones [7,8] in 1706 to denote the ratio between the perimeter and the diameter on any given circle. In other words, dividing the perimeter of any circle by its diameter always gives the same answer, and this number is defined to be . A 14-digit approximation of  is given by \n\nOver human history there were many attempts to calculate this number precisely. One of the oldest approximations appears in the Rhind Papyrus (circa 1650 B.C.) where a geometrical construction is given where  is used as an approximation to  although this was not explicitly mentioned.\n\nIt wasn't until the Greeks that there were systematical attemps to calculate . Archimedes [1], in the third century B.C. used regular polygons inscribed and circumscribed to a circle to approximate : the more sides a polygon has, the closer to the circle it becomes and therefore the ratio between the polygon's area between the square of the radius yields approximations to . Using this method he showed that  .\n\nAround the world there were also attemps to calculate . Brahmagupta [1] gave the value of  using a method similar to Archimedes'. Chinese mathematician Tsu Chung-Chih (ca. 500 A.D.) gave the approximation .\n\nLater, during the renaissance, Leonardo de Pisa (Fibonacci) [1] used 96-sideed regular polygons to find the approximation
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Can't answer this one directly as memory fails me but try a book by A C Kermode called Principles of Aeronautics.  This is an oldish book but still in print and used in the Royal Air Force for all its engineers and technicians.
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A. Square from Flatland was the first person to see an angle.
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The first 4 is the maximum mean line camber in % of chord.\nThe second 4 is the position of the max camber in tenths of c.\nThe 12 is the maximum thickness of the airfoil in % c.\n\nThe airfoil you mention was derived by the folks at NACA in the late 1920s and was used on such planes as the Luscombe and  Aeronca.  Definitely a vintage model........
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Invented by Fabrizio Mordente (1532 - c. 1608) to measure the smallest fraction of a ..................\n\n(1564-1642) T Geometric and military compass of Galileo Galilei ...............................
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It seems research on this has continued. Still sounds very preliminary though - experiments on small models or paper planes ;)  But maybe you'd like to check the links.
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Fundamentals of Sailplane Design\n("Grundlagen für den Entwurf von Segelflugzeugen")\nby Fred Thomas\nForeword by L. M. M. Boermans (President, OSTIV)\n\nISBN 0-9669553-0-7\nLibrary of Congress Catalog Card Number: 99-61150\n9" x 10.5", 286 pages, hardcover\nIndex and Bibliography\n\n\n$50 US + S&H\nNow available!\nOrdering information below. \n\nThe definitive text on sailplane design by Fred Thomas, Professor of Aerospace Engineering at the Technical University of Braunschweig (Germany). Covers the basics of sailplane design, including aerodynamics and flight mechanics, operational and regulatory requirements, aerodynamic design optimization, wind tunnel and flight test procedures, and historical outlook. Appendix with extensive collection of detailed design data and 3-view drawings for over 150 sailplanes, including both vintage gliders and modern sailplanes. \n\nContents\n\nBasic Aerodynamics and Flight Mechanics: Fluid dynamics and the sailplane - Airfoil and wing theory - Performance and handling qualities - Aeroelasticity \nDesign Requirements: Certification requirements - JAR-22 - Cross country theory - Thermal models and climb performance \nSailplane Design Optimization: Basic considerations - Wing design - Variable geometry - Flying wings - The World Class - Fuselage and wing-fuselage transition - Empennage and controls \nDetermination of Performance and Handling Characteristics: Theoretical methods - Experimental methods \nTrends in Sailplane Development: Sailplane class definitions - Early glider designs - Sailplane development to date - Outlook \nAppendices: Tabulated design data and three-view drawings - "Zacher" flight test protocol - German-English glossary of technical terms \n\nAn errata sheet is available here. \n\nHow to order\nPlease order "Fundamentals of Sailplane Design" from one of the following suppliers. Most accept online orders. You can also order the title through your local bookstore (it will, however, take longer). \n\n\nNorth and South America:\nKnauff and Grove Soaring Supplies (Julian, PA) Toll free: (888) 724-3677; (814) 355-2483, fax (814) 355-2633. Ships internationally. Accepts Credit Cards. \n\nDAR Corporation (Lawrence, Kansas) (785) 832-0434 Ships internationally. Accepts Credit Cards. \nAircraft Technical Book Co. (Tabernash, CO) (970) 887-2207, (800) 780-4115 (toll free) Ships internationally. Accepts Credit Cards. \nKiona Publishing Inc. (Richland, WA) Ph/Fax (509) 627-0456, (866) 627-0456 (toll free) Ships internationally. Accepts Credit Cards. \nSailplane Homebuilders Association (Tehachapi, CA) (join SHA and receive book at discount) \nBob Wander's Soaring Books and Supplies (Minneapolis, MN) Toll free: (800) 660-0238 Accepts Credit Cards
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Johann Castillon used the name cardioid for the first time, in a paper in the Philosophical Transactions of the Royal Society (1741).\n\nHowever, he was not the first person who used it.  For example, it was studied by Roemer (1674) in an investigation for the best form of gear teeth. \n\nCardioid is a special case of limacon of Pascal: a family of curves studied and named after Etienne Pascal (1588-1640), father of Blaise Pascal (1623-1662). \n\nI don't know whether they originally used polar co-ordinates which followed after the Cartesian system developed by Descartes in 1637. But given that the general formula for the limacon is a ± bcos(theta) or a ± bsin(theta), it's certainly possible.
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Descartes made one of the greatest advances in geometry by connecting algebra and geometry. A myth is that he was watching a fly on the ceiling when he conceived of locating points on a plane with a pair of numbers. Maybe this has something to do with the fact that he stayed in bed everyday until 11:00 A.M. Fermat also discovered coordinate geometry, but it's Descartes' version that we use today.\n\nCo-ordinate Geometry\nCo-ordinate geometry was introduced by Fermat and Descartes, ignoring rather than solving the foundational problems which had prevented the Greeks from taking this step (viz: the lack of any well understood number system which could account for incommensurable ratios). \nThis development is important to science because it makes geometry quantitative and permits the use of algebraic methods. Geometry must be quantitative for it to be useful in science and engineering, and algebraic methods permit more rapid development of mathematics than the less systematic (if more rigourous) methods required by the Greek axiomatic approach to geometry. \n \nIn co-ordinate geometry the points of a plane are labelled by 2 co-ordinates, its distances from the 2 axes, and familiar figures become the loci of points satisfying an algebraic equation. Thus, geometry is incorporated into algebra and the way is opened for the introduction of spaces of arbitrarily large dimension, important in mechanics. Curvature, in its simplest form, is a number attached to a surface at a point. The flatter the surface, the smaller the number (positive for a sphere, negative for a saddle-shaped surface). \nFrench mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, Fermat discovered the fundamental principle of analytic geometry. His methods for finding tangents to curves and their maximum and minimum points led him to be regarded as the inventor of the differential calculus. Through his correspondence with Blaise Pascal he was a co-founder of the theory of probability.\n\n\nhttp://people.bath.ac.uk/jm255/Geometry.htm this website will help u aswell!\n\nAnalytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. Usually the Cartesian coordinate system is applied to manipulate equations for planes, lines, curves, and circles, often in two and sometimes in three dimensions of measurement. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining geometrical shapes in a numerical way, and extracting numerical information from that representation. The numerical output, however, might also be a vector or a shape. Some consider that the introduction of analytic geometry was the beginning of modern mathematics.\n\nRené Descartes is popularly regarded as having introduced the foundation for the methods of analytic geometry in 1637 in the appendix titled Geometry of the titled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences, commonly referred to as Discourse on Method. This work, written in his native language (French), and its philosophical principles, provided the foundation for calculus in Europe.\n\nThe relationship between algebra and geometry is nontrivial. There exist proofs of this relationship based on the theory of geometry and notions of geometric length.\n\n\n\nwrite this down and im finding more info ......
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They perform that feat by two methods. The classical method that was been taught since the mid 1700's is called the Bernoulli effect discovered by Daniel Bernoulli, a Swiss mathematician. This effect is that a fluid flowing with a greater velocity has a lower pressure than a fluid flowing with a lesser velocity. This pricipal has been put into effect with the construction of the aircraft wing. The upper surface of the wing is curved and has a longer surface over which air must flow than the lower surface. Therefore the air must flow faster over the upper surface than the lower surface. This lowers the air pressure over the upper surface of the wing and causes a lift by the pressure of the air on the lower surface.\n\nThis however is not the only force acting to keep the aircraft afloat though it has been taught as the force for many years. \n\nThe second force that is used, is cause by the angle of attact of the wing on the air. As the aircraft is in level flight the wing is tilted slightly upward. This causes the air to push against the bottom of the wing at a slight angle. \n\nTake your left hand and hold it at a slight angle to the horizontal in front of your eyes with the fingers pointing toward the right. Then with the fingers of the other hand pointing opposite to the fingers of the hand held at an angle, push horizontally against the palm of the hand.\n\nWhen you do this you will notice that the left hand tends to rise as you push against it. That is the second force that helps keeps the plane afloat.
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We invented the concept of pi before the Greeks. Using higher math, we were able to create a perfect circle in three dimensions. Scultping the columns only required a complex circular leveling device using water which we invented in the 8th dynasty.
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homologous structures are also used as "evidence" for evolution: Darwin suggested that bird wings and human arms had a common ancestor because they looked similar.  I think they looked similar because our Creator created them that way!
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Euclid.\nGreek geometer who wrote the Elements , the world's most definitive text on geometry. The book synthesized earlier knowledge about geometry, and was used for centuries in western Europe as a geometry textbook. The text began with definitions, postulates ("Euclid's postulates "), and common opinions, then proceeded to obtain results by rigorous geometric proof. Euclid also proved what is generally known as Euclid's second theorem:  the number of primes  is infinite.  The beautiful proof Euclid gave of this theorem is still a gem and is generally acknowledged to be one of the "classic" proofs of all times in terms of its conciseness and clarity. In the Elements , Euclid used the method of exhaustion and reductio ad absurdum. He also discussed the so-called Euclidean algorithm  for finding the greatest common divisor  of two numbers, and is credited with the well-known proof of the Pythagorean theorem. \nNeither the year nor place of his birth have been established, nor the circumstances of his death, although he is known to have lived and worked in Alexandria for much of his life. In addition, no bust which can be verified to be his likeness is known (Tietze 1965, p. 8).
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There are various accounts of who first introduced polar coordinates as part of a formal coordinate system. The full history of the subject is described in Harvard professor Julian Lowell Coolidge's "Origin of Polar Coordinates."  \n\nGrégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts at about the same time. Saint-Vincent wrote about them privately in 1625 and published in 1647, while Cavalieri published in 1635 with a corrected version appearing in 1653. Cavalieri first utilized polar coordinates to solve a problem relating to the area within an Archimedean spiral. Blaise Pascal subsequently used polar coordinates to calculate the length of parabolic arcs.\n\nIn "Method of Fluxions" (written 1671, published 1736), Sir Isaac Newton was the first to look upon polar coordinates as a method of locating any point in the plane.  Newton examined the transformations between polar coordinates and nine other coordinate systems. In "Acta eruditorum" (1691), Jacob Bernoulli used a system with a point on a line, called the pole and polar axis respectively. Coordinates were specified by the distance from the pole and the angle from the polar axis. Bernoulli's work extended to finding the radius of curvature of curves expressed in these coordinates.\n\nThe actual term polar coordinates has been attributed to Gregorio Fontana and was used by 18th century Italian writers. The term appeared in English in George Peacock's 1816 translation of "Lacroix's Differential and Integral Calculus."\n\nAlexis Clairaut and Leonhard Euler are credited with extending the concept of polar coordinates to three dimensions.
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Since ancient history regarding the concept.\n\nHistory of the notation:\n\nThe symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler. In either case, 'π' is the first letter of περιφέρεια (periphereia, the Greek word for periphery) or περίμετρον (perimetron), meaning 'measure around' in Greek.
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In 1450, the Italian art architect Leon Battista Alberti invented the first mechanical anemometer. This instrument consisted of a disk placed perpendicular to the wind. It would rotate by the force of the wind, and by the angle of inclination of the disk the wind force momentary showed itself. The same type of anemometer was later re-invented by Englishman Robert Hooke who is often mistakenly considered the inventor of the first anemometer. The Mayans were also building wind towers (anemometers) at the same time as Hooke. Another reference credits Wolfius as re-inventing the anemometer in 1709.