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0 | {\displaystyle x={\frac {{\sqrt {4ac+b^{2}}}-b}{2a}}.} The Bakhshali Manuscript written in India in the 7th century AD contained an algebraic formula for solving quadratic equations, as well as quadratic indeterminate equations (originally of type ax/c = y). Muhammad ibn Musa al-Khwarizmi (9th century), possibly inspir... | Quadratic equation | 0.881942 |
1 | In the days before calculators, people would use mathematical tables—lists of numbers showing the results of calculation with varying arguments—to simplify and speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks. Specialized tables were published for applicat... | Quadratic equation | 0.881942 |
2 | Statistics show that waste collection is one of the most dangerous jobs, at times more dangerous than police work, but consistently less dangerous than commercial fishing and ranch and farm work. On-the-job hazards include broken glass, medical waste such as syringes, caustic chemicals, objects falling out of overloade... | Garbage collector | 0.881522 |
3 | Stories about Biology Stories about Biologists Games and Simulations Body Depot Biology Bits PLOSable Image Gallery Puzzles – Word Search & Crossword Coloring Pages Mysterious World of Dr. Biology comic book adventure activity Audio Podcasts Co-host Contest Ugly Bug Contest Bird Finder Tool Virtual Pocket Seed Experime... | Ask a Biologist | 0.875125 |
4 | Students reconstructed a chain of events in the Dr. Biology laboratory and field site, writing their own narrative for the story. Early in 2007, Ask A Biologist became one of the early content channels on iTunes U with its audio podcast of the same name. Hosted by Dr. Biology, the program was soon listed as one of five... | Ask a Biologist | 0.875124 |
5 | The Virtual Bird Aviary, included the majority of bird species found in the Southwest United States including more than 400 vocal recordings and companion sonograms, bird images, text descriptions, and range maps. In 2005, the website was peer reviewed by the Multimedia Educational Resource for Learning and Online Teac... | Ask a Biologist | 0.875124 |
6 | Ask A Biologist is a pre-kindergarten through high school program dedicated to answering questions from students, their teachers, and parents. The primary focus of the program is to connect students and teachers with working scientists through a question and answer Web e-mail form. The companion website also includes a... | Ask a Biologist | 0.875124 |
7 | In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total pos... | Spring Constant | 0.873215 |
8 | Since DNA is an informative macromolecule in terms of transmission from one generation to another, DNA sequencing is used in evolutionary biology to study how different organisms are related and how they evolved. In February 2021, scientists reported, for the first time, the sequencing of DNA from animal remains, a mam... | DNA Sequencing | 0.87157 |
9 | Systems of linear inequalities can be simplified by Fourier–Motzkin elimination.The cylindrical algebraic decomposition is an algorithm that allows testing whether a system of polynomial equations and inequalities has solutions, and, if solutions exist, describing them. The complexity of this algorithm is doubly expone... | System of inequalities | 0.870745 |
10 | E&M is equivalent to an introductory college course in electricity and magnetism for physics or engineering majors. The course modules are: Electrostatics Conductors, capacitors, and dielectrics Electric circuits Magnetic fields Electromagnetism.Methods of calculus are used wherever appropriate in formulating physical ... | AP Physics C: Electricity and Magnetism | 0.868815 |
11 | The AP examination for AP Physics C: Electricity and Magnetism is separate from the AP examination for AP Physics C: Mechanics. Before 2006, test-takers paid only once and were given the choice of taking either one or two parts of the Physics C test. | AP Physics C: Electricity and Magnetism | 0.868815 |
12 | The grade distributions for the Physics C: Electricity and Magnetism scores since 2010 were: | AP Physics C: Electricity and Magnetism | 0.868815 |
13 | The exam is typically administered on a Monday afternoon in May. The exam is configured in two categories: a 35-question multiple choice section and a 3-question free response section. Test takers are allowed to use an approved calculator during the entire exam. The test is weighted such that each section is worth half... | AP Physics C: Electricity and Magnetism | 0.868815 |
14 | Advanced Placement (AP) Physics C: Electricity and Magnetism (also known as AP Physics C: E&M or AP E&M) is an introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a second-semester calculus-based university course in electricity and magnetism.... | AP Physics C: Electricity and Magnetism | 0.868815 |
15 | Given three fields arranged in a tower, say K a subfield of L which is in turn a subfield of M, there is a simple relation between the degrees of the three extensions L/K, M/L and M/K: = ⋅ . {\displaystyle =\cdot .} In other words, the degree going from the "bottom" to the "top" field is just the product of the degr... | Degree of an extension | 0.867439 |
16 | In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently. | Degree of an extension | 0.867439 |
17 | In the theory of quadratic forms, the parabola is the graph of the quadratic form x2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x2 + y2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x2 − y2. Generalizations to more... | Parabola | 0.865891 |
18 | If one replaces the real numbers by an arbitrary field, many geometric properties of the parabola y = x 2 {\displaystyle y=x^{2}} are still valid: A line intersects in at most two points. At any point ( x 0 , x 0 2 ) {\displaystyle (x_{0},x_{0}^{2})} the line y = 2 x 0 x − x 0 2 {\displaystyle y=2x_{0}x-x_{0}^{2}} is t... | Parabola | 0.865891 |
19 | Let three tangents to a parabola form a triangle. Then Lambert's theorem states that the focus of the parabola lies on the circumcircle of the triangle. : Corollary 20 Tsukerman's converse to Lambert's theorem states that, given three lines that bound a triangle, if two of the lines are tangent to a parabola whose focu... | Parabola | 0.865891 |
20 | Application: The 2-points–2-tangents property can be used for the construction of the tangent of a parabola at point P 2 {\displaystyle P_{2}} , if P 1 , P 2 {\displaystyle P_{1},P_{2}} and the tangent at P 1 {\displaystyle P_{1}} are given. Remark 1: The 2-points–2-tangents property of a parabola is an affine version ... | Parabola | 0.865891 |
21 | A short calculation shows: line Q 1 Q 2 {\displaystyle Q_{1}Q_{2}} has slope 2 x 0 {\displaystyle 2x_{0}} which is the slope of the tangent at point P 0 {\displaystyle P_{0}} . Application: The 3-points-1-tangent-property of a parabola can be used for the construction of the tangent at point P 0 {\displaystyle P_{0}} ,... | Parabola | 0.865891 |
22 | At higher speeds, such as in ballistics, the shape is highly distorted and does not resemble a parabola. Another hypothetical situation in which parabolas might arise, according to the theories of physics described in the 17th and 18th centuries by Sir Isaac Newton, is in two-body orbits, for example, the path of a sma... | Parabola | 0.865891 |
23 | In nature, approximations of parabolas and paraboloids are found in many diverse situations. The best-known instance of the parabola in the history of physics is the trajectory of a particle or body in motion under the influence of a uniform gravitational field without air resistance (for instance, a ball flying throug... | Parabola | 0.865891 |
24 | The same effects occur with sound and other waves. This reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design of ballistic missiles. It is frequently used in p... | Parabola | 0.865891 |
25 | Any parabola can be described in a suitable coordinate system by an equation y = a x 2 {\displaystyle y=ax^{2}} . Proof: straightforward calculation for the unit parabola y = x 2 {\displaystyle y=x^{2}} . Application: The 4-points property of a parabola can be used for the construction of point P 4 {\displaystyle P_{4}... | Parabola | 0.865891 |
26 | This can be done with calculus, or by using a line that is parallel to the axis of symmetry of the parabola and passes through the midpoint of the chord. The required point is where this line intersects the parabola. Then, using the formula given in Distance from a point to a line, calculate the perpendicular distance ... | Parabola | 0.865891 |
27 | A theorem equivalent to this one, but different in details, was derived by Archimedes in the 3rd century BCE. He used the areas of triangles, rather than that of the parallelogram. See The Quadrature of the Parabola. | Parabola | 0.865891 |
28 | The above proofs of the reflective and tangent bisection properties use a line of calculus. Here a geometric proof is presented. In this diagram, F is the focus of the parabola, and T and U lie on its directrix. P is an arbitrary point on the parabola. | Parabola | 0.865891 |
29 | Tensor algebra, symmetric algebra and exterior algebra of a finite-dimensional vector space are graded quadratic (in fact, Koszul) algebras. Universal enveloping algebra of a finite-dimensional Lie algebra is a filtered quadratic algebra. | Quadratic algebra | 0.864868 |
30 | In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2. It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups. The most important class of graded quadratic algebras is Koszul algebras. | Quadratic algebra | 0.864868 |
31 | A graded quadratic algebra A is determined by a vector space of generators V = A1 and a subspace of homogeneous quadratic relations S ⊂ V ⊗ V (Polishchuk & Positselski 2005, p. 6). Thus A = T ( V ) / ⟨ S ⟩ {\displaystyle A=T(V)/\langle S\rangle } and inherits its grading from the tensor algebra T(V). If the subspace of... | Quadratic algebra | 0.864868 |
32 | Note that there are 3 translation "windows", or reading frames, depending on where you start reading the code. Finally, use the table at Genetic code to translate the above into a structural formula as used in chemistry. This will give you the primary structure of the protein. | Protein translation | 0.864804 |
33 | It developed over time to chromosomal analysis, then genetic marker analysis, and eventual genomic analysis. Identifying traits and their underlying genetics allowed for transferring useful genes and the traits they controlled from either wild or mutant plants to crop plants. Understanding and manipulating of plant gen... | Plant genetics | 0.863828 |
34 | Arabidopsis thaliana, also known as thale cress, has been the model organism for the study of plant genetics. As Drosophila, a species of fruit fly, was to the understanding of early genetics, so has been A. thaliana to the understanding of plant genetics. It was the first plant to ever have its genome sequenced in the... | Plant genetics | 0.863828 |
35 | Speciation can be easier in many plants due to unique genetic abilities, such as being well adapted to polyploidy. Plants are unique in that they are able to produce energy-dense carbohydrates via photosynthesis, a process which is achieved by use of chloroplasts. Chloroplasts, like the superficially similar mitochondr... | Plant genetics | 0.863828 |
36 | Much of Mendel's work with plants still forms the basis for modern plant genetics. Plants, like all known organisms, use DNA to pass on their traits. Animal genetics often focuses on parentage and lineage, but this can sometimes be difficult in plant genetics due to the fact that plants can, unlike most animals, be sel... | Plant genetics | 0.863828 |
37 | Plant genetics is the study of genes, genetic variation, and heredity specifically in plants. It is generally considered a field of biology and botany, but intersects frequently with many other life sciences and is strongly linked with the study of information systems. Plant genetics is similar in many ways to animal g... | Plant genetics | 0.863828 |
38 | The strict requirements for producing hybrid seed led to the development of careful population and inbred line maintenance, keeping plants isolated and unable to out-cross, which produced plants that better allowed researchers to tease out different genetic concepts. The structure of these populations allowed scientist... | Plant genetics | 0.863828 |
39 | Castle discovered that while individual traits may segregate and change over time with selection, that when selection is stopped and environmental effects are taken into account, the genetic ratio stops changing and reach a sort of stasis, the foundation of Population Genetics. This was independently discovered by G. H... | Plant genetics | 0.863828 |
40 | His discoveries, deduction of segregation ratios, and subsequent laws have not only been used in research to gain a better understanding of plant genetics, but also play a large role in plant breeding. Mendel's works along with the works of Charles Darwin and Alfred Wallace on selection provided the basis for much of g... | Plant genetics | 0.863828 |
41 | Mendel died in 1884. The significance of Mendel's work was not recognized until the turn of the 20th century. Its rediscovery prompted the foundation of modern genetics. | Plant genetics | 0.863828 |
42 | Mendel's work tracked many phenotypic traits of pea plants, such as their height, flower color, and seed characteristics. Mendel showed that the inheritance of these traits follows two particular laws, which were later named after him. His seminal work on genetics, “Versuche über Pflanzen-Hybriden” (Experiments on Plan... | Plant genetics | 0.863828 |
43 | The earliest evidence of plant domestication found has been dated to 11,000 years before present in ancestral wheat. While initially selection may have happened unintentionally, it is very likely that by 5,000 years ago farmers had a basic understanding of heredity and inheritance, the foundation of genetics. This sele... | Plant genetics | 0.863828 |
44 | Genetic modification has been the cause for much research into modern plant genetics, and has also led to the sequencing of many plant genomes. Today there are two predominant procedures of transforming genes in organisms: the "Gene gun" method and the Agrobacterium method. | Plant genetics | 0.863828 |
45 | In plant breeding, people create hybrids between plant species for economic and aesthetic reasons. For example, the yield of Corn has increased nearly five-fold in the past century due in part to the discovery and proliferation of hybrid corn varieties. Plant genetics can be used to predict which combination of plants ... | Plant genetics | 0.863828 |
46 | The square root of 2, often known as root 2, radical 2, or Pythagoras' constant, and written as √2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property. Geometr... | Mathematical constants | 0.863742 |
47 | In the computer science subfield of algorithmic information theory, Chaitin's constant is the real number representing the probability that a randomly chosen Turing machine will halt, formed from a construction due to Argentine-American mathematician and computer scientist Gregory Chaitin. Chaitin's constant, though no... | Mathematical constants | 0.863742 |
48 | Secosteroids (Latin seco, "to cut") are a subclass of steroidal compounds resulting, biosynthetically or conceptually, from scission (cleavage) of parent steroid rings (generally one of the four). Major secosteroid subclasses are defined by the steroid carbon atoms where this scission has taken place. For instance, the... | Steroid | 0.863628 |
49 | The objective wave function evolves deterministically but, according to the Copenhagen interpretation, it deals with probabilities of observing, the outcome being explained by a wave function collapse when an observation is made. However, the loss of determinism for the sake of instrumentalism did not meet with univers... | Probability | 0.863489 |
50 | Physicists face the same situation in the kinetic theory of gases, where the system, while deterministic in principle, is so complex (with the number of molecules typically the order of magnitude of the Avogadro constant 6.02×1023) that only a statistical description of its properties is feasible. Probability theory is... | Probability | 0.863489 |
51 | However, it is possible to define a conditional probability for some zero-probability events using a σ-algebra of such events (such as those arising from a continuous random variable).For example, in a bag of 2 red balls and 2 blue balls (4 balls in total), the probability of taking a red ball is 1 / 2 ; {\displaystyle... | Probability | 0.863489 |
52 | In Cox's theorem, probability is taken as a primitive (i.e., not further analyzed), and the emphasis is on constructing a consistent assignment of probability values to propositions. In both cases, the laws of probability are the same, except for technical details. There are other methods for quantifying uncertainty, s... | Probability | 0.863489 |
53 | In probability theory and applications, Bayes' rule relates the odds of event A 1 {\displaystyle A_{1}} to event A 2 , {\displaystyle A_{2},} before (prior to) and after (posterior to) conditioning on another event B . {\displaystyle B.} The odds on A 1 {\displaystyle A_{1}} to event A 2 {\displaystyle A_{2}} is simply... | Probability | 0.863489 |
54 | The product of the prior and the likelihood, when normalized, results in a posterior probability distribution that incorporates all the information known to date. By Aumann's agreement theorem, Bayesian agents whose prior beliefs are similar will end up with similar posterior beliefs. However, sufficiently different pr... | Probability | 0.863489 |
55 | Augustus De Morgan and George Boole improved the exposition of the theory. In 1906, Andrey Markov introduced the notion of Markov chains, which played an important role in stochastic processes theory and its applications. The modern theory of probability based on measure theory was developed by Andrey Kolmogorov in 193... | Probability | 0.863489 |
56 | The theory of behavioral finance emerged to describe the effect of such groupthink on pricing, on policy, and on peace and conflict.In addition to financial assessment, probability can be used to analyze trends in biology (e.g., disease spread) as well as ecology (e.g., biological Punnett squares). As with finance, ris... | Probability | 0.863489 |
57 | An example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole. An assessment by a commodity trader that a war is more likely can send that commodity's prices up or down, a... | Probability | 0.863489 |
58 | Probability theory is applied in everyday life in risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis, and financial regulation. | Probability | 0.863489 |
59 | Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been give... | Probability | 0.863489 |
60 | In quantum mechanics, the measurement problem is the problem of how, or whether, wave function collapse occurs. The inability to observe such a collapse directly has given rise to different interpretations of quantum mechanics and poses a key set of questions that each interpretation must answer. The wave function in q... | Problem of measurement | 0.86331 |
61 | The heuristic method In optimization problems, heuristic algorithms can be used to find a solution close to the optimal solution in cases where finding the optimal solution is impractical. These algorithms work by getting closer and closer to the optimal solution as they progress. In principle, if run for an infinite a... | Computer algorithms | 0.863147 |
62 | For some problems they can find the optimal solution while for others they stop at local optima, that is, at solutions that cannot be improved by the algorithm but are not optimum. The most popular use of greedy algorithms is for finding the minimal spanning tree where finding the optimal solution is possible with this... | Computer algorithms | 0.863147 |
63 | For optimization problems there is a more specific classification of algorithms; an algorithm for such problems may fall into one or more of the general categories described above as well as into one of the following: Linear programming When searching for optimal solutions to a linear function bound to linear equality ... | Computer algorithms | 0.863147 |
64 | In rapid succession the following appeared: Alonzo Church, Stephen Kleene and J.B. Rosser's λ-calculus a finely honed definition of "general recursion" from the work of Gödel acting on suggestions of Jacques Herbrand (cf. Gödel's Princeton lectures of 1934) and subsequent simplifications by Kleene. Church's proof that ... | Computer algorithms | 0.863147 |
65 | Louis Georges Gouy in 1910 and David Leonard Chapman in 1913 both observed that capacitance was not a constant and that it depended on the applied potential and the ionic concentration. The "Gouy–Chapman model" made significant improvements by introducing a diffuse model of the DL. In this model, the charge distributio... | Electric surface potential | 0.86177 |
66 | Most research in the area of memory models revolves around: Designing a memory model that allows a maximal degree of freedom for compiler optimizations while still giving sufficient guarantees about race-free and (perhaps more importantly) race-containing programs. Proving program optimizations that are correct with re... | Memory model (programming) | 0.861157 |
67 | The memory model stipulates that changes to the values of shared variables only need to be made visible to other threads when such a synchronization barrier is reached. Moreover, the entire notion of a race condition is defined over the order of operations with respect to these memory barriers.These semantics then give... | Memory model (programming) | 0.861157 |
68 | Or for some compilers assume no multi-threaded execution (so better optimized code can be produced), which can lead to optimizations that are incompatible with multi-threading - these can often lead to subtle bugs, that don't show up in early testing. Modern programming languages like Java therefore implement a memory ... | Memory model (programming) | 0.861157 |
69 | A memory model allows a compiler to perform many important optimizations. Compiler optimizations like loop fusion move statements in the program, which can influence the order of read and write operations of potentially shared variables. Changes in the ordering of reads and writes can cause race conditions. Without a m... | Memory model (programming) | 0.861157 |
70 | Sometimes, a set is endowed with more than one feature simultaneously, which allows mathematicians to study the interaction between the different structures more richly. For example, an ordering imposes a rigid form, shape, or topology on the set, and if a set has both a topology feature and a group feature, such that ... | Mathematical structure | 0.860057 |
71 | In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. A partial list of possible structures are measure... | Mathematical structure | 0.860057 |
72 | By moving the two points closer together so that Δy and Δx decrease, the secant line more closely approximates a tangent line to the curve, and as such the slope of the secant approaches that of the tangent. Using differential calculus, we can determine the limit, or the value that Δy/Δx approaches as Δy and Δx get clo... | Slope of a line | 0.860053 |
73 | For a line, the secant between any two points is the line itself, but this is not the case for any other type of curve. For example, the slope of the secant intersecting y = x2 at (0,0) and (3,9) is 3. (The slope of the tangent at x = 3⁄2 is also 3 − a consequence of the mean value theorem.) | Slope of a line | 0.860053 |
74 | The concept of a slope is central to differential calculus. For non-linear functions, the rate of change varies along the curve. The derivative of the function at a point is the slope of the line tangent to the curve at the point, and is thus equal to the rate of change of the function at that point. If we let Δx and Δ... | Slope of a line | 0.860053 |
75 | In statistics, the gradient of the least-squares regression best-fitting line for a given sample of data may be written as: m = r s y s x {\displaystyle m={\frac {rs_{y}}{s_{x}}}} ,This quantity m is called as the regression slope for the line y = m x + c {\displaystyle y=mx+c} . The quantity r {\displaystyle r} is Pea... | Slope of a line | 0.860053 |
76 | When the curve is given by a series of points in a diagram or in a list of the coordinates of points, the slope may be calculated not at a point but between any two given points. When the curve is given as a continuous function, perhaps as an algebraic expression, then the differential calculus provides rules giving a ... | Slope of a line | 0.860053 |
77 | The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope m of a line is related to its angle of inclination θ by the tangent function m = tan ( θ ) {\displaystyle m=\tan(\theta )} Thus, a 45° rising line has a slope of +1 and a 45° falling line h... | Slope of a line | 0.860053 |
78 | Additionally, tables of equations, information, and constants are provided for all portions of the exam as of 2015. This and AP Physics C: Electricity and Magnetism are the shortest AP exams, with total testing time of 90 minutes.The topics covered by the exam are as follows: As a result of the 2019-20 coronavirus pand... | AP Physics C: Mechanics | 0.859946 |
79 | Advanced Placement (AP) Physics C: Mechanics (also known as AP Mechanics) is an introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a one-semester calculus-based university course in mechanics. The content of Physics C: Mechanics overlaps with... | AP Physics C: Mechanics | 0.859946 |
80 | The AP examination for AP Physics C: Mechanics is separate from the AP examination for AP Physics C: Electricity and Magnetism. Before 2006, test-takers paid only once and were given the choice of taking either one or two parts of the Physics C test. | AP Physics C: Mechanics | 0.859946 |
81 | Intended to be equivalent to an introductory college course in mechanics for physics or engineering majors, the course modules are: Kinematics Newton's laws of motion Work, energy and power Systems of particles and linear momentum Circular motion and rotation Oscillations and gravitation.Methods of calculus are used wh... | AP Physics C: Mechanics | 0.859946 |
82 | In a similar fashion, constants appear in the solutions to differential equations where not enough initial values or boundary conditions are given. For example, the ordinary differential equation y' = y(x) has solution Cex where C is an arbitrary constant. When dealing with partial differential equations, the constants... | Mathematical constant | 0.858972 |
83 | Abbreviations used: R – Rational number, I – Irrational number (may be algebraic or transcendental), A – Algebraic number (irrational), T – Transcendental number Gen – General, NuT – Number theory, ChT – Chaos theory, Com – Combinatorics, Inf – Information theory, Ana – Mathematical analysis | Mathematical constant | 0.858972 |
84 | When unspecified, constants indicate classes of similar objects, commonly functions, all equal up to a constant—technically speaking, this may be viewed as 'similarity up to a constant'. Such constants appear frequently when dealing with integrals and differential equations. Though unspecified, they have a specific val... | Mathematical constant | 0.858972 |
85 | Kepler proved that it is the limit of the ratio of consecutive Fibonacci numbers. The golden ratio has the slowest convergence of any irrational number. It is, for that reason, one of the worst cases of Lagrange's approximation theorem and it is an extremal case of the Hurwitz inequality for Diophantine approximations. | Mathematical constant | 0.858972 |
86 | The number φ, also called the golden ratio, turns up frequently in geometry, particularly in figures with pentagonal symmetry. Indeed, the length of a regular pentagon's diagonal is φ times its side. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles. Also, it appears in the ... | Mathematical constant | 0.858972 |
87 | The term "imaginary" was coined because there is no (real) number having a negative square. There are in fact two complex square roots of −1, namely i and −i, just as there are two complex square roots of every other real number (except zero, which has one double square root). In contexts where the symbol i is ambiguou... | Mathematical constant | 0.858972 |
88 | Euler's number e, also known as the exponential growth constant, appears in many areas of mathematics, and one possible definition of it is the value of the following expression: e = lim n → ∞ ( 1 + 1 n ) n {\displaystyle e=\lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}} The constant e is intrinsically related t... | Mathematical constant | 0.858972 |
89 | A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e an... | Mathematical constant | 0.858972 |
90 | The constant π (pi) has a natural definition in Euclidean geometry as the ratio between the circumference and diameter of a circle. It may be found in many other places in mathematics: for example, the Gaussian integral, the complex roots of unity, and Cauchy distributions in probability. However, its ubiquity is not l... | Mathematical constant | 0.858972 |
91 | The Euler–Mascheroni constant is defined as the following limit: γ = lim n → ∞ ( ( ∑ k = 1 n 1 k ) − ln n ) {\displaystyle {\begin{aligned}\gamma &=\lim _{n\to \infty }\left(\left(\sum _{k=1}^{n}{\frac {1}{k}}\right)-\ln n\right)\\\end{aligned}}} The Euler–Mascheroni constant appears in Mertens' third theorem and has... | Mathematical constant | 0.858972 |
92 | In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variab... | Response variable | 0.858803 |
93 | We distinguish between two kinds of features: Static features are in most cases some counts and statistics (e.g., clauses-to-variables ratio in SAT). These features ranges from very cheap features (e.g. number of variables) to very complex features (e.g., statistics about variable-clause graphs). Probing features (some... | Algorithm selection | 0.858412 |
94 | In machine learning, algorithm selection is better known as meta-learning. The portfolio of algorithms consists of machine learning algorithms (e.g., Random Forest, SVM, DNN), the instances are data sets and the cost metric is for example the error rate. So, the goal is to predict which machine learning algorithm will ... | Algorithm selection | 0.858412 |
95 | Algorithm selection is not limited to single domains but can be applied to any kind of algorithm if the above requirements are satisfied. Application domains include: hard combinatorial problems: SAT, Mixed Integer Programming, CSP, AI Planning, TSP, MAXSAT, QBF and Answer Set Programming combinatorial auctions in mach... | Algorithm selection | 0.858412 |
96 | The algorithm selection problem is mainly solved with machine learning techniques. By representing the problem instances by numerical features f {\displaystyle f} , algorithm selection can be seen as a multi-class classification problem by learning a mapping f i ↦ A {\displaystyle f_{i}\mapsto {\mathcal {A}}} for a giv... | Algorithm selection | 0.858412 |
97 | Algorithms were also used in Babylonian astronomy. Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events.Algorithms for arithmetic are also found in ancient Egyptian mathematics, dating back to the Rhind Mathematical Papyrus c. 1550 BC. | Algorithm | 0.85781 |
98 | Muhammad ibn Mūsā al-Khwārizmī, a Persian mathematician, wrote the Al-jabr in the 9th century. The terms "algorism" and "algorithm" are derived from the name al-Khwārizmī, while the term "algebra" is derived from the book Al-jabr. In Europe, the word "algorithm" was originally used to refer to the sets of rules and tec... | Algorithm | 0.85781 |
99 | ; Spillane, C. (1999) Biotechnology assisted participatory plant breeding: Complement or contradiction? CGIAR Program on Participatory Research and Gender Analysis, Working Document No.4, CIAT: Cali. | Plant breeding | 0.857805 |
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