The Fibonacci sequence is named after Italian mathematician Leonardo of Pisa, known as Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, the sequence described in Liber Abaci began with F1 =1. Fibonacci numbers are related to Lucas numbers L n in that they form a complementary pair of Lucas sequences U n = F n and V n = L n. They are intimately connected with the ratio, for example. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is a journal dedicated to their study. The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody, in the Sanskrit tradition of prosody, there was interest in enumerating all patterns of long syllables that are 2 units of duration, and short syllables that are 1 unit of duration. Counting the different patterns of L and S of a given duration results in the Fibonacci numbers, susantha Goonatilake writes that the development of the Fibonacci sequence is attributed in part to Pingala, being associated with Virahanka, Gopāla, and Hemachandra.
He dates Pingala before 450 BC, the clearest exposition of the sequence arises in the work of Virahanka, whose own work is lost, but is available in a quotation by Gopala, Variations of two earlier meters. For example, for four, variations of meters of two three being mixed, five happens, in this way, the process should be followed in all mātrā-vṛttas. The sequence is discussed by Gopala and by the Jain scholar Hemachandra, outside India, the Fibonacci sequence first appears in the book Liber Abaci by Fibonacci. The puzzle that Fibonacci posed was, how many pairs will there be in one year, at the end of the first month, they mate, but there is still only 1 pair. At the end of the month the female produces a new pair. At the end of the month, the original female produces a second pair. At the end of the month, the original female has produced yet another new pair. At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs plus the number of pairs alive last month and this is the nth Fibonacci number.
The name Fibonacci sequence was first used by the 19th-century number theorist Édouard Lucas, the most common such problem is that of counting the number of compositions of 1s and 2s that sum to a given total n, there are Fn+1 ways to do this. For example, if n =5, Fn+1 = F6 =8 counts the eight compositions, 1+1+1+1+1 = 1+1+1+2 = 1+1+2+1 = 1+2+1+1 = 2+1+1+1 = 2+2+1 = 2+1+2 = 1+2+2, all of which sum to 5. The Fibonacci numbers can be found in different ways among the set of strings, or equivalently
In mathematics, an exponential function is a function of the form in which the input variable x occurs as an exponent. A function of the form f = b x + c, as functions of a real variable, exponential functions are uniquely characterized by the fact that the growth rate of such a function is directly proportional to the value of the function. The constant of proportionality of this relationship is the logarithm of the base b. The argument of the function can be any real or complex number or even an entirely different kind of mathematical object. Its ubiquitous occurrence in pure and applied mathematics has led mathematician W. Rudin to opine that the function is the most important function in mathematics. In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same change in the dependent variable. The graph of y = e x is upward-sloping, and increases faster as x increases, the graph always lies above the x -axis but can get arbitrarily close to it for negative x, the x -axis is a horizontal asymptote.
The slope of the tangent to the graph at each point is equal to its y -coordinate at that point, as implied by its derivative function. Its inverse function is the logarithm, denoted log, ln, or log e, because of this. The exponential function exp, C → C can be characterized in a variety of equivalent ways, the constant e is defined as e = exp = ∑ k =0 ∞. The exponential function arises whenever a quantity grows or decays at a proportional to its current value. One such situation is continuously compounded interest, and in fact it was this observation that led Jacob Bernoulli in 1683 to the number lim n → ∞ n now known as e, later, in 1697, Johann Bernoulli studied the calculus of the exponential function. If instead interest is compounded daily, this becomes 365, letting the number of time intervals per year grow without bound leads to the limit definition of the exponential function, exp = lim n → ∞ n first given by Euler. This is one of a number of characterizations of the exponential function, from any of these definitions it can be shown that the exponential function obeys the basic exponentiation identity, exp = exp ⋅ exp which is why it can be written as ex.
The derivative of the function is the exponential function itself. More generally, a function with a rate of change proportional to the function itself is expressible in terms of the exponential function and this function property leads to exponential growth and exponential decay. The exponential function extends to a function on the complex plane. Eulers formula relates its values at purely imaginary arguments to trigonometric functions, the exponential function has analogues for which the argument is a matrix, or even an element of a Banach algebra or a Lie algebra
In mathematics, a self-similar object is exactly or approximately similar to a part of itself. Many objects in the world, such as coastlines, are statistically self-similar. Self-similarity is a property of fractals. Scale invariance is a form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant, it can be continually magnified 3x without changing shape, the non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a line may resemble the whole. It happens if the quantity f exhibits dynamic scaling, the idea is just an extension of the idea of similarity of two triangles. Note that two triangles are similar if the values of their sides are different however the corresponding dimensionless quantities, such as their angles. In mathematics, self-affinity is a feature of a fractal whose pieces are scaled by different amounts in the x- and this means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an anisotropic affine transformation.
We call L = a self-similar structure, the homeomorphisms may be iterated, resulting in an iterated function system. The composition of functions creates the algebraic structure of a monoid, when the set S has only two elements, the monoid is known as the dyadic monoid. The dyadic monoid can be visualized as a binary tree, more generally, if the set S has p elements. The automorphisms of the monoid is the modular group, the automorphisms can be pictured as hyperbolic rotations of the binary tree. A more general notion than self-similarity is Self-affinity, the Mandelbrot set is self-similar around Misiurewicz points. Self-similarity has important consequences for the design of networks, as typical network traffic has self-similar properties. For example, in engineering, packet switched data traffic patterns seem to be statistically self-similar. This property means that simple models using a Poisson distribution are inaccurate, andrew Lo describes stock market log return self-similarity in econometrics.
Finite subdivision rules are a technique for building self-similar sets, including the Cantor set
Iceland is a Nordic island country in the North Atlantic Ocean. It has a population of 332,529 and an area of 103,000 km2, the capital and largest city is Reykjavík. Reykjavík and the areas in the southwest of the country are home to over two-thirds of the population. Iceland is volcanically and geologically active, the interior consists of a plateau characterised by sand and lava fields and glaciers, while many glacial rivers flow to the sea through the lowlands. Iceland is warmed by the Gulf Stream and has a climate, despite a high latitude just outside the Arctic Circle. Its high latitude and marine influence still keeps summers chilly, with most of the archipelago having a tundra climate. According to the ancient manuscript Landnámabók, the settlement of Iceland began in the year 874 AD when the Norwegian chieftain Ingólfr Arnarson became the first permanent settler on the island. In the following centuries, and to a lesser extent other Scandinavians, emigrated to Iceland, the island was governed as an independent commonwealth under the Althing, one of the worlds oldest functioning legislative assemblies.
Following a period of strife, Iceland acceded to Norwegian rule in the 13th century. The establishment of the Kalmar Union in 1397 united the kingdoms of Norway, Iceland thus followed Norways integration to that Union and came under Danish rule after Swedens secession from that union in 1523. In the wake of the French revolution and the Napoleonic wars, Icelands struggle for independence took form and culminated in independence in 1918, until the 20th century, Iceland relied largely on subsistence fishing and agriculture, and was among the poorest in Europe. Industrialisation of the fisheries and Marshall Plan aid following World War II brought prosperity, in 1994, it became a part of the European Economic Area, which further diversified the economy into sectors such as finance and manufacturing. Iceland has an economy with relatively low taxes compared to other OECD countries. It maintains a Nordic social welfare system that provides health care. Iceland ranks high in economic and social stability and equality, in 2013, it was ranked as the 13th most-developed country in the world by the United Nations Human Development Index.
Iceland runs almost completely on renewable energy, some bankers were jailed, and the economy has made a significant recovery, in large part due to a surge in tourism. Icelandic culture is founded upon the nations Scandinavian heritage, most Icelanders are descendants of Germanic and Gaelic settlers. Icelandic, a North Germanic language, is descended from Old Norse and is related to Faroese
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Two major definitions of spiral in a respected American dictionary are, a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point. b. A three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis, in another example, the center lines of the arms of a spiral galaxy trace logarithmic spirals. In the side picture, the curve at the bottom is an Archimedean spiral. The curve shown in red is a conic helix, a two-dimensional spiral may be described most easily using polar coordinates, where the radius r is a monotonic continuous function of angle θ. The circle would be regarded as a degenerate case, for example, a conic helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of θ. The helix and vortex can be viewed as a kind of three-dimensional spiral, for a helix with thickness, see spring. A rhumb line is the curve on a sphere traced by a ship with constant bearing, the study of spirals in nature has a long history.
D’Arcy Wentworth Thompsons On Growth and Form gives extensive treatment to these spirals and he describes how shells are formed by rotating a closed curve around a fixed axis, the shape of the curve remains fixed but its size grows in a geometric progression. In some shell such as Nautilus and ammonites the generating curve revolves in a perpendicular to the axis. In others it follows a path forming a helico-spiral pattern. Thompson studied spirals occurring in horns, claws, a model for the pattern of florets in the head of a sunflower was proposed by H Vogel. This has the form θ = n ×137.5 ∘, r = c n n is the index number of the floret and c is a constant scaling factor. The angle 137. 5° is the angle which is related to the golden ratio. Spirals in plants and animals are described as whorls. This is the given to spiral shaped fingerprints. A spiral like form has been found in Mezine, the spiral and triple spiral motif is a Neolithic symbol in Europe. The Celtic symbol the triple spiral is in fact a pre-Celtic symbol and it is carved into the rock of a stone lozenge near the main entrance of the prehistoric Newgrange monument in County Meath, Ireland
Extratropical cyclones are capable of producing anything from cloudiness and mild showers to heavy gales, thunderstorms and tornadoes. These types of cyclones are defined as large scale low pressure systems that occur in the middle latitudes of the Earth. In contrast with tropical cyclones, extratropical cyclones produce rapid changes in temperature and dew point along broad lines, called weather fronts, the term cyclone applies to numerous types of low pressure areas, one of which is the extratropical cyclone. The descriptor extratropical signifies that this type of cyclone generally occurs outside the tropics and they are termed mid-latitude cyclones if they form within those latitudes, or post-tropical cyclones if a tropical cyclone has intruded into the mid latitudes. Weather forecasters and the public often describe them simply as depressions or lows. Terms like frontal cyclone, frontal depression, frontal low, extratropical low, non-tropical low, Extratropical cyclones are classified mainly as baroclinic, because they form along zones of temperature and dewpoint gradient known as frontal zones.
They can become barotropic late in their cycle, when the distribution of heat around the cyclone becomes fairly uniform with its radius. Extratropical cyclones form anywhere within the regions of the Earth. A study of extratropical cyclones in the Southern Hemisphere shows that between the 30th and 70th parallels, there are an average of 37 cyclones in existence during any 6-hour period, a separate study in the Northern Hemisphere suggests that approximately 234 significant extratropical cyclones form each winter. Extratropical cyclones form along linear bands of temperature/dewpoint gradient with significant vertical wind shear, cyclogenesis, or low pressure formation, occurs along frontal zones near a favorable quadrant of a maximum in the upper level jetstream known as a jet streak. The favorable quadrants are usually at the rear and left front quadrants. The divergence causes air to rush out from the top of the air column and this in turn forces convergence in the low-level wind field and increased upward motion within the column.
The increased upward motion causes atmospheric pressure at ground level to lower and this is because the upward air motion counteracts gravity, lessening the weight of the atmosphere in that location. The lowered pressure strengthens the cyclone, as the cyclone strengthens, the cold front sweeps towards the equator and moves around the back of the cyclone. Meanwhile, its associated warm front progresses more slowly, as the air ahead of the system is denser. Later, the cyclones occlude as the portion of the cold front overtakes a section of the warm front, forcing a tongue, or trowal. Eventually, the cyclone will become cold and begin to weaken. Atmospheric pressure can fall very rapidly when there are upper level forces on the system
The Whirlpool Galaxy, known as Messier 51a, M51a, or NGC5194, is an interacting grand-design spiral galaxy with a Seyfert 2 active galactic nucleus in the constellation Canes Venatici. It was the first galaxy to be classified as a spiral galaxy, recently it was estimated to be 23 ±4 million light-years from the Milky Way, but different methods yield distances between 15 and 35 million light-years. Messier 51 is one of the best known galaxies in the sky, the galaxy and its companion, NGC5195, are easily observed by amateur astronomers, and the two galaxies may even be seen with binoculars. The Whirlpool Galaxy is a target for professional astronomers. Its companion galaxy, NGC5195, was discovered in 1781 by Pierre Méchain, the advent of radio astronomy and subsequent radio images of M51 unequivocally demonstrated that the Whirlpool and its companion galaxy are indeed interacting. Sometimes the designation M51 is used to refer to the pair of galaxies, in case the individual galaxies may be referred to as M51A.
Located within the constellation Canes Venatici, M51 is found by following the easternmost star of the Big Dipper, Eta Ursae Majoris, M51 is visible through binoculars under dark sky conditions and can be resolved in detail with modern amateur telescopes. When seen through a 100 mm telescope the basic outlines of M51, under dark skies, and with a moderate eyepiece through a 150 mm telescope, M51s intrinsic spiral structure can be detected. With larger instruments under dark sky conditions, the spiral bands are apparent with HII regions visible. As is usual for galaxies, the extent of its structure can only be gathered from inspecting photographs. In January 2005 the Hubble Heritage Project constructed a 11477 × 7965-pixel composite image of M51 using Hubbles ACS instrument, the image highlights the galaxys spiral arms, and shows detail into some of the structures inside the arms. With the recent SN 2005cs derived estimate of 23 Mly distance, overall the galaxy is about 35% the size of the Milky Way.
Its mass is estimated to be 160 billion solar masses, a black hole, surrounded by a ring of dust, is thought to exist at the heart of the spiral. The dust ring stands almost perpendicular to the relatively flat spiral nebula, a secondary ring crosses the primary ring on a different axis, a phenomenon that is contrary to expectations. A pair of ionization cones extend from the axis of the main dust ring, stars are usually formed in the center of the galaxy. The center part of M51 appears to be undergoing a period of enhanced star formation and it is estimated that the current high rate of star formation can last no more than another 100 million years or so. Induced spiral structure in the galaxy is not the only effect of the interaction. Significant compression of gas occurs that leads to the development of starbirth regions
The nautilus is a pelagic marine mollusc of the cephalopod family Nautilidae, the sole extant family of the superfamily Nautilaceae and of its smaller but near equal suborder, Nautilina. It comprises six living species in two genera, the type of which is the genus Nautilus, though it more specifically refers to species Nautilus pompilius, the name chambered nautilus is used for any species of the Nautilidae. All are protected under CITES Appendix II, having survived relatively unchanged for millions of years, nautiluses represent the only living members of the subclass nautiloidea, and are often considered living fossils. Each nautilus tentacle is composed of a long, flexible cirrus and is retractable into a corresponding hardened sheath, nautiluses typically have more tentacles than other cephalopods — up to ninety. Nautilus tentacles differ from those of other cephalopods, lacking pads, the tentacles stick to prey by virtue of their ridged surface. Attempts to take an object already seized by a nautilus may tear away the creatures tentacles, the main tentacles emerge from sheaths which cohere into a single firm fleshy mass.
Two pairs of tentacles are separate from the other 90-ish, the pre-ocular and post-ocular, situated before and these are more evidently grooved, with more pronounced ridges. They are extensively ciliated and serve an olfactory purpose, the radula is wide and distinctively has nine teeth. The mouth consists of a beak made up of two interlocking jaws capable of ripping the animals food— mostly crustaceans— from the rocks to which they are attached. The crop is the largest portion of the tract, and is highly extensible. From the crop, food passes to the small muscular stomach for crushing, like all cephalopods, the blood of the nautilus contains hemocyanin, which is blue in its oxygenated state. There are two pairs of gills which are the remnants of the ancestral metamerism to be visible in extant cephalopods. The one exception to this is the vena cava, a large vein running along the underside of the crop into which nearly all other vessels containing deoxygenated blood empty. All blood passes through one of the four sets of filtering organs upon leaving the vena cava, blood waste is emptied through a series of corresponding pores into the pallial cavity.
From this ring extend all of the forward to the mouth and funnel, laterally to the eyes and rhinophores. Nautiluses tend to have rather short memory spans, and the ring is not protected by any form of brain case. Nautiluses are the sole living cephalopods whose bony body structure is externalized as a shell, the animal can withdraw completely into its shell and close the opening with a leathery hood formed from two specially folded tentacles. The shell is coiled, aragonitic and pressure resistant, the nautilus shell is composed of two layers, a matte white outer layer, and a striking white iridescent inner layer
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling and this means that either object can be rescaled and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a uniform scaling of the other. A modern and novel perspective of similarity is to consider geometrical objects similar if one appears congruent to the other zoomed in or out at some level. For example, all circles are similar to other, all squares are similar to each other. On the other hand, ellipses are not all similar to other, rectangles are not all similar to each other. If two angles of a triangle have measures equal to the measures of two angles of triangle, the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure and it can be shown that two triangles having congruent angles are similar, that is, the corresponding sides can be proved to be proportional.
This is known as the AAA similarity theorem, due to this theorem, several authors simplify the definition of similar triangles to only require that the corresponding three angles are congruent. There are several statements each of which is necessary and sufficient for two triangles to be similar,1, the triangles have two congruent angles, which in Euclidean geometry implies that all their angles are congruent. That is, If ∠BAC is equal in measure to ∠B′A′C′, and ∠ABC is equal in measure to ∠A′B′C′, this implies that ∠ACB is equal in measure to ∠A′C′B′, all the corresponding sides have lengths in the same ratio, AB/A′B′ = BC/B′C′ = AC/A′C′. This is equivalent to saying that one triangle is an enlargement of the other, two sides have lengths in the same ratio, and the angles included between these sides have the same measure. For instance, AB/A′B′ = BC/B′C′ and ∠ABC is equal in measure to ∠A′B′C′ and this is known as the SAS Similarity Criterion. When two triangles △ABC and △A′B′C′ are similar, one writes △ABC ∼ △A′B′C′, there are several elementary results concerning similar triangles in Euclidean geometry, Any two equilateral triangles are similar.
Two triangles, both similar to a triangle, are similar to each other. Corresponding altitudes of similar triangles have the ratio as the corresponding sides. Two right triangles are similar if the hypotenuse and one side have lengths in the same ratio. Given a triangle △ABC and a line segment DE one can, with ruler and compass, the statement that the point F satisfying this condition exists is Walliss Postulate and is logically equivalent to Euclids Parallel Postulate
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation i2 = −1. In this expression, a is the part and b is the imaginary part of the complex number. If z = a + b i, ℜ z = a, ℑ z = b, Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point in the complex plane, a complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the numbers are a field extension of the ordinary real numbers. As well as their use within mathematics, complex numbers have applications in many fields, including physics, biology, electrical engineering. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers and he called them fictitious during his attempts to find solutions to cubic equations in the 16th century.
Complex numbers allow solutions to equations that have no solutions in real numbers. For example, the equation 2 = −9 has no real solution, Complex numbers provide a solution to this problem. The idea is to extend the real numbers with the unit i where i2 = −1. According to the theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. A complex number is a number of the form a + bi, for example, −3.5 + 2i is a complex number. The real number a is called the part of the complex number a + bi. By this convention the imaginary part does not include the unit, hence b. The real part of a number z is denoted by Re or ℜ. For example, Re = −3.5 Im =2, hence, in terms of its real and imaginary parts, a complex number z is equal to Re + Im ⋅ i. This expression is known as the Cartesian form of z. A real number a can be regarded as a number a + 0i whose imaginary part is 0
Evangelista Torricelli was born on 15 October 1608 in Rome, he invented the barometer in Florence, Italy. The firstborn child of Gaspare Ruberti and Giacoma Torricelli and his family was from Faenza in the Province of Ravenna, part of the Papal States. His father was a worker and the family was very poor. Seeing his talents, his parents sent him to be educated in Faenza, under the care of his uncle, Jacobo, a Camaldolese monk, who first ensured that his nephew was given a sound basic education. He entered young Torricelli into a Jesuit College in 1624, possibly the one in Faenza itself, to mathematics and philosophy until 1626, by which time his father. The uncle sent Torricelli to Rome to study science under the Benedictine monk Benedetto Castelli, Castelli was a student of Galileo Galilei. Benedetto Castelli made experiments on running water, and he was entrusted by Pope Urban VIII with hydraulic undertakings, there is no actual evidence that Torricelli was enrolled at the university. It is almost certain that Torricelli was taught by Castelli, in exchange he worked for him as his secretary from 1626 to 1632 as a private arrangement.
Because of this, Torricelli was exposed to experiments funded by Pope Urban VIII, while living in Rome, Torricelli became the student of the brilliant mathematician, Bonaventura Cavalieri, with whom he became great friends. It was in Rome that Torricelli became friends with two students of Castelli, Raffaello Magiotti and Antonio Nardi. Galileo referred to Torricelli and Nardi affectionately as his triumvirate in Rome, although Galileo promptly invited Torricelli to visit, he did not accept until just three months before Galileos death. The reason for this was that Torricellis mother, Caterina Angetti died, after Galileos death on 8 January 1642, Grand Duke Ferdinando II de Medici asked him to succeed Galileo as the grand-ducal mathematician and chair of mathematics at the University of Pisa. Right before the appointment, Torricelli was considering returning to Rome because of there being nothing left for him in Florence, in this role he solved some of the great mathematical problems of the day, such as finding a cycloids area and center of gravity.
As a result of study, he wrote the book the Opera Geometrica in which he described his observations. The book was published in 1644 and he was interested in Optics, and invented a method whereby microscopic lenses might be made of glass which could be easily melted in a lamp. As a result, he designed and built a number of telescopes and simple microscopes, several large lenses, on 11 June 1644, he famously wrote in a letter to Michelangelo Ricci, Noi viviamo sommersi nel fondo dun pelago daria. Torricelli died in Florence on 25 October 1647,10 days after his 39th birthday and he left all his belongings to his adopted son Alessandro. This early work owes much to the study of the classics, in Faenza, a statue of Torricelli was created in 1868 as a thank you for all that Torricelli had done in advancing science during his short lifetime
Hawks are a group of medium-sized diurnal birds of prey of the family Accipitridae which are widely distributed and varying greatly in size. The subfamily Accipitrinae includes goshawks, the sharp-shinned hawk and these are mainly woodland birds with long tails and high visual acuity, hunting by sudden dashes from a concealed perch. In the Americas, members of the Buteo group are called hawks, generally buteos have broad wings and sturdy builds. They are relatively larger winged, shorter-tailed and soar more extensively in areas than accipiters. The terms accipitrine hawk and buteonine hawk may be used to distinguish the two types, in regions where hawk applies to both, the term true hawk is sometimes used for the accipitrine hawks, in regions where buzzard is preferred for the buteonine hawks. All these groups are members of the Accipitridae family, which includes the hawks and buzzards as well as kites, some authors use hawk generally for any small to medium Accipitrid that is not an eagle.
The common names of birds include the term hawk, reflecting traditional usage rather than taxonomy. Falconry was called hawking, and any bird used for falconry could be referred to as a hawk, aristotle listed eleven types of ἱέρακες, aisalōn, hypotriorchēs, leios, phassophonos, pternis and triorchēs. Pliny numbered sixteen kinds of hawks, but named only aigithos, kenchrēïs, the accipitrine hawks generally take birds as their primary prey. They have been called hen-hawks, or wood-hawks because of their woodland habitat, the subfamily Accipitrinae contains Accipiter, it contains genera Micronisus and Megatriorchis. Melierax may be included in the subfamily, or given a subfamily of its own, erythrotriorchis is traditionally included in Accipitrinae, but is possibly a convergent genus from an unrelated group. The Buteo group includes genera Buteo, Geranoetus, members of this group have been called hawk-buzzards. Proposed new genera Morphnarchus and Pseudastur are formed from members of Buteo, the Buteogallus group are called hawks, with the exception of the solitary eagles.
Buteo is the genus of the subfamily Buteoninae. Traditionally this subfamily includes eagles and sea-eagles and Mindell proposed placing those into separate subfamilies, leaving just the buteonine hawks/buzzards in Buteoninae. In February 2005, the Canadian ornithologist Louis Lefebvre announced a method of measuring avian IQ in terms of their innovation in feeding habits, Hawks were named among the most intelligent birds based on his scale. Hawks have four types of receptors in the eye. These give birds the ability to not only the visible range but the ultraviolet part of the spectrum