D. C. Heath and Company
D. C. Heath and Company was an American publishing company located at 125 Spring Street in Lexington, specializing in textbooks; the company was founded in Boston by Edwin Ginn and Daniel Collamore Heath in 1885. D. C. Heath and Company was owned by Raytheon from 1966 to 1995; when Raytheon exited the textbook market, it sold the company to Houghton Mifflin. D. C. Heath started a small division of software editors to supplement the textbooks in the early 80's; the editors strove to make the software packages independent of the books. There were test banks that allowed teachers to pick and choose questions for their quizzes and tests. Development was further supported to enable teachers to create their own questions including a formula editor, tagging items by objectives, including custom graphics in the question as well as in the answer key; this was for the Apple 2 later Windows and Macintoshes. Many titles were commissioned for the areas of science, reading, social studies, modern languages; these were interactive original programs.
D. C. Heath gave this group Collamore Educational Publishing; the editors were involved in all facets of the publishing process including contracts, design, publishing and sales. Schools were just transitioning from the one computer classroom to the computer lab. In 1988 most of the software was being supported by William K. Bradford Publishing Company composed by D. C. Heath / Collamore personnel. Publications- Heath Elementary Science, by Herman and Nina Schneider, 6 volumes Heath middle level literature ISBN 0-669-42948-1 Heath Physics ISBN 0-669-25793-1 Fundamentals of Personal Rapid Transit Discovering French Bleu: Complete Lesson Plans The Enduring Vision: A History of the American People Third Edition Ruy Blas by Victor Hugo The Renaissance Medieval or Modern? The Enduring South: Subcultural Persistence in Mass Society, by John Shelton Reed; the Story of Georgia and Wood, 1904 MC68000: Assembly Language and Systems Programming ISBN 0-669-16085-7 Victor Hugo's Les Misérables: French Edition Elizabeth Rice Allgeier, Albert Richard Allgeier, Sexual Interactions, 1991 A Short German Grammar for High Schools and Colleges.
By E. S. Sheldon, tutor in German in Harvard University, copyright 1879 The Causes of the American Revolution Builders of the Old World, Written by Gertrude Hartman and Illustrated by Marjorie Quennell Composition and Rhetoric by William Williams copyright 1890 published 1893 The Nazi Revolution: Germany's Guilt or Germany's Fate? Children and Their Helpers New American Readers For Catholic Schools by School Sisters of Notre Dame. Donald Duck Sees South America H. Marion Palmer, Walt Disney Old Time Stories of the Old North State by L. A. McCorkle Old Testament Narratives selected and edited by Roy L. French and Mary Dawson Hamlet The Arden Shakespeare, edited by E. K. Chambers, B. A Discussions of Literature series, general editor Joseph H. Summers Eugenie Grandet: French Edition, by Honore de Balzac and Edited with Introduction Notes and Vocabulary by A. G. H. Spiers, PH. D. "The Bug In The Hut" and "Nat The Rat", unknown authors, Modern European History - Revised Edition - by Hutton Webster Ph. D.
Hints Toward A Select and Descriptive Bibliography of Education - by G Stanley Hall and John M Mansfield Heath's Modern Language Series. Gerstacker's Germelshausen. 1894. Klaeber, Friedrich. Beowulf and The Fight at Finnsburg. Boston: D. C. Heath & Company. Elementary Linear Algebra: Second Edition by Roland E. Larson and Bruce H. Edwards ISBN 0-669-24592-5 2. Software initial addition by Hal Wexler, software editor, 1984-1988 transitioned to William K. Bradford Publishing Company
Prentice Hall
Prentice Hall is a major educational publisher owned by Pearson plc. Prentice Hall publishes print and digital content for the higher-education market. Prentice Hall distributes its technical titles through the Safari Books Online e-reference service. On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names—Prentice and Hall—to name their new company. Prentice Hall was acquired by Gulf+Western in 1984, became part of that company's publishing division Simon & Schuster. Publication of trade books ended in 1991. Simon & Schuster's educational division, including Prentice Hall, was sold to Pearson by G+W successor Viacom in 1998. There were two or more authors, their books turned up missing. One book'The Roof Builder's Handbook' is still being sold in 2018 for as much as $230 per new copy, but the author William C. McElroy was told by Pearson that all new books were either destroyed or went missing in 1995.
Some 2,385 copies are missing. Prentice Hall is the publisher of Magruder's American Government as well as Biology by Ken Miller and Joe Levine, their artificial intelligence series includes Artificial Intelligence: A Modern Approach by Stuart J. Russell and Peter Norvig and ANSI Common Lisp by Paul Graham, they published the well-known computer programming book The C Programming Language by Brian Kernighan and Dennis Ritchie and Operating Systems: Design and Implementation by Andrew S. Tanenbaum. Other titles include Dennis Nolan's Big Pig, Monster Bubbles: A Counting Book, Wizard McBean and his Flying Machine, Witch Bazooza, Llama Beans, The Joy of Chickens. A Prentice Hall subsidiary, Reston Publishing, was in the foreground of technical-book publishing when microcomputers were first becoming available, it was still unclear who would be buying and using "personal computers," and the scarcity of useful software and instruction created a publishing market niche whose target audience yet had to be defined.
In the spirit of the pioneers who made PCs possible, Reston Publishing's editors addressed non-technical users with the reassuring, mildly experimental, Computer Anatomy for Beginners by Marlin Ouverson of People's Computer Company. They followed with a collection of books, by and for programmers, building a stalwart list of titles relied on by many in the first generation of microcomputers users. Prentice Hall International Series in Computer Science Prentice Hall website Prentice Hall School website Prentice Hall Higher Education website Prentice Hall Professional Technical Reference website
Composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than itself; every positive integer is composite, prime, or the unit 1, so the composite numbers are the numbers that are not prime and not a unit. For example, the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7; the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself. The composite numbers up to 150 are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150.
Every composite number can be written as the product of two or more primes. For example, the composite number 299 can be written as 13 × 23, the composite number 360 can be written as 23 × 32 × 5; this fact is called the fundamental theorem of arithmetic. There are several known primality tests that can determine whether a number is prime or composite, without revealing the factorization of a composite input. One way to classify composite numbers is by counting the number of prime factors. A composite number with two prime factors is a 2-almost prime. A composite number with three distinct prime factors is a sphenic number. In some applications, it is necessary to differentiate between composite numbers with an odd number of distinct prime factors and those with an number of distinct prime factors. For the latter μ = 2 x = 1, while for the former μ = 2 x + 1 = − 1. However, for prime numbers, the function returns −1 and μ = 1. For a number n with one or more repeated prime factors, μ = 0. If all the prime factors of a number are repeated it is called a powerful number.
If none of its prime factors are repeated, it is called squarefree. For example, 72 = 23 × 32, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7, none of the prime factors are repeated, so 42 is squarefree. Another way to classify composite numbers is by counting the number of divisors. All composite numbers have at least three divisors. In the case of squares of primes, those divisors are. A number n that has more divisors than any x < n is a composite number. Composite numbers have been called "rectangular numbers", but that name can refer to the pronic numbers, numbers that are the product of two consecutive integers, yet another way to classify composite numbers is to determine whether all prime factors are either all below or all above some fixed number. Such numbers are called rough numbers, respectively. Canonical representation of a positive integer Integer factorization Sieve of Eratosthenes Table of prime factors Fraleigh, John B. A First Course In Abstract Algebra, Reading: Addison-Wesley, ISBN 0-201-01984-1 Herstein, I. N.
Topics In Algebra, Waltham: Blaisdell Publishing Company, ISBN 978-1114541016 Long, Calvin T. Elementary Introduction to Number Theory, Lexington: D. C. Heath and Company, LCCN 77-171950 McCoy, Neal H. Introduction To Modern Algebra, Revised Edition, Boston: Allyn and Bacon, LCCN 68-15225 Pettofrezzo, Anthony J.. Elements of Number Theory, Englewood Cliffs: Prentice Hall, LCCN 77-81766 Lists of composites with prime factorization Divisor Plot
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing, automated reasoning, other tasks; as an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states producing "output" and terminating at a final ending state; the transition from one state to the next is not deterministic. The concept of algorithm has existed for centuries. Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers, the Euclidean algorithm for finding the greatest common divisor of two numbers; the word algorithm itself is derived from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized Algoritmi.
A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem posed by David Hilbert in 1928. Formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, Alan Turing's Turing machines of 1936–37 and 1939. The word'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to algorismus. Al-Khwārizmī was a Persian mathematician, astronomer and scholar in the House of Wisdom in Baghdad, whose name means'the native of Khwarazm', a region, part of Greater Iran and is now in Uzbekistan. About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, translated into Latin during the 12th century under the title Algoritmi de numero Indorum; this title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.
Al-Khwarizmi was the most read mathematician in Europe in the late Middle Ages through another of his books, the Algebra. In late medieval Latin, English'algorism', the corruption of his name meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός'number', the Latin word was altered to algorithmus, the corresponding English term'algorithm' is first attested in the 17th century. In English, it was first used in about 1230 and by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu, it begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates as: Algorism is the art by which at present we use those Indian figures, which number two times five; the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals.
An informal definition could be "a set of rules that defines a sequence of operations". Which would include all computer programs, including programs that do not perform numeric calculations. A program is only an algorithm if it stops eventually. A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers. Boolos, Jeffrey & 1974, 1999 offer an informal meaning of the word in the following quotation: No human being can write fast enough, or long enough, or small enough† to list all members of an enumerably infinite set by writing out their names, one after another, in some notation, but humans can do something useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human, capable of carrying out only elementary operations on symbols.
An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large, thus an algorithm can be an algebraic equation such as y = m + n – two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of: Precise instructions for a fast, efficient, "good" process that specifies the "moves" of "the computer" to find and process arbitrary input integers/symbols m and n, symbols + and =... and "effectively" produce, in a "reasonable" time, output-integer y at a specified place and in a specified format
Oxford University Press
Oxford University Press is the largest university press in the world, the second oldest after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the vice-chancellor known as the delegates of the press, they are headed by the secretary to the delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University has used a similar system to oversee OUP since the 17th century; the Press is located on opposite Somerville College, in the suburb Jericho. The Oxford University Press Museum is located on Oxford. Visits are led by a member of the archive staff. Displays include a 19th-century printing press, the OUP buildings, the printing and history of the Oxford Almanack, Alice in Wonderland and the Oxford English Dictionary; the university became involved in the print trade around 1480, grew into a major printer of Bibles, prayer books, scholarly works. OUP took on the project that became the Oxford English Dictionary in the late 19th century, expanded to meet the ever-rising costs of the work.
As a result, the last hundred years has seen Oxford publish children's books, school text books, journals, the World's Classics series, a range of English language teaching texts. Moves into international markets led to OUP opening its own offices outside the United Kingdom, beginning with New York City in 1896. With the advent of computer technology and harsh trading conditions, the Press's printing house at Oxford was closed in 1989, its former paper mill at Wolvercote was demolished in 2004. By contracting out its printing and binding operations, the modern OUP publishes some 6,000 new titles around the world each year; the first printer associated with Oxford University was Theoderic Rood. A business associate of William Caxton, Rood seems to have brought his own wooden printing press to Oxford from Cologne as a speculative venture, to have worked in the city between around 1480 and 1483; the first book printed in Oxford, in 1478, an edition of Rufinus's Expositio in symbolum apostolorum, was printed by another, printer.
Famously, this was mis-dated in Roman numerals as "1468", thus pre-dating Caxton. Rood's printing included John Ankywyll's Compendium totius grammaticae, which set new standards for teaching of Latin grammar. After Rood, printing connected with the university remained sporadic for over half a century. Records or surviving work are few, Oxford did not put its printing on a firm footing until the 1580s. In response to constraints on printing outside London imposed by the Crown and the Stationers' Company, Oxford petitioned Elizabeth I of England for the formal right to operate a press at the university; the chancellor, Robert Dudley, 1st Earl of Leicester, pleaded Oxford's case. Some royal assent was obtained, since the printer Joseph Barnes began work, a decree of Star Chamber noted the legal existence of a press at "the universitie of Oxforde" in 1586. Oxford's chancellor, Archbishop William Laud, consolidated the legal status of the university's printing in the 1630s. Laud envisaged a unified press of world repute.
Oxford would establish it on university property, govern its operations, employ its staff, determine its printed work, benefit from its proceeds. To that end, he petitioned Charles I for rights that would enable Oxford to compete with the Stationers' Company and the King's Printer, obtained a succession of royal grants to aid it; these were brought together in Oxford's "Great Charter" in 1636, which gave the university the right to print "all manner of books". Laud obtained the "privilege" from the Crown of printing the King James or Authorized Version of Scripture at Oxford; this "privilege" created substantial returns in the next 250 years, although it was held in abeyance. The Stationers' Company was alarmed by the threat to its trade and lost little time in establishing a "Covenant of Forbearance" with Oxford. Under this, the Stationers paid an annual rent for the university not to exercise its full printing rights – money Oxford used to purchase new printing equipment for smaller purposes.
Laud made progress with internal organization of the Press. Besides establishing the system of Delegates, he created the wide-ranging supervisory post of "Architypographus": an academic who would have responsibility for every function of the business, from print shop management to proofreading; the post was more an ideal than a workable reality, but it survived in the loosely structured Press until the 18th century. In practice, Oxford's Warehouse-Keeper dealt with sales and the hiring and firing of print shop staff. Laud's plans, hit terrible obstacles, both personal and political. Falling foul of political intrigue, he was executed in 1645, by which time the English Civil War had broken out. Oxford became a Royalist stronghold during the conflict, many printers in the city concentrated on producing political pamphlets or sermons; some outstanding mathematical and Orientalist works emerged at this time—notably, texts edited by Edward Pococke, the Regius Professor of Hebrew—but no university press on Laud's model was possible before the Restoration of the Monarchy in 1660.
It was established by the vice-chancellor, John Fell, Dean of Christ Church, Bishop of Oxford, Secretary to the Delegates. Fell regarded Laud as a martyr, was determined to honour his vision of the Press. Using the provisions of the Great Charter, Fell persuaded Oxford to refuse any further payments from the Stationers and drew
Arithmetic
Arithmetic is a branch of mathematics that consists of the study of numbers the properties of the traditional operations on them—addition, subtraction and division. Arithmetic is an elementary part of number theory, number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra and analysis; the terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory. The prehistory of arithmetic is limited to a small number of artifacts which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed; the earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system influence the complexity of the methods.
The hieroglyphic system for Egyptian numerals, like the Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board or the Roman abacus to obtain the results. Early number systems that included positional notation were not decimal, including the sexagesimal system for Babylonian numerals and the vigesimal system that defined Maya numerals; because of this place-value concept, the ability to reuse the same digits for different values contributed to simpler and more efficient methods of calculation. The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, although it originated much than the Babylonian and Egyptian examples. Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.
For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, their relationships to each other, in his Introduction to Arithmetic. Greek numerals were used by Archimedes and others in a positional notation not different from ours; the ancient Greeks lacked a symbol for zero until the Hellenistic period, they used three separate sets of symbols as digits: one set for the units place, one for the tens place, one for the hundreds. For the thousands place they would reuse the symbols for the units place, so on, their addition algorithm was identical to ours, their multiplication algorithm was only slightly different. Their long division algorithm was the same, the digit-by-digit square root algorithm, popularly used as as the 20th century, was known to Archimedes, who may have invented it, he preferred it to Hero's method of successive approximation because, once computed, a digit doesn't change, the square roots of perfect squares, such as 7485696, terminate as 2736.
For numbers with a fractional part, such as 546.934, they used negative powers of 60 instead of negative powers of 10 for the fractional part 0.934. The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra; the ancient Chinese used a positional notation similar to that of the Greeks. Since they lacked a symbol for zero, they had one set of symbols for the unit's place, a second set for the ten's place. For the hundred's place they reused the symbols for the unit's place, so on, their symbols were based on the ancient counting rods. It is a complicated question to determine when the Chinese started calculating with positional representation, but it was before 400 BC; the ancient Chinese were the first to meaningfully discover and apply negative numbers as explained in the Nine Chapters on the Mathematical Art, written by Liu Hui. The gradual development of the Hindu–Arabic numeral system independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing 0.
This allowed the system to represent both large and small integers. This approach replaced all other systems. In the early 6th century AD, the Indian mathematician Aryabhata incorporated an existing version of this system in his work, experimented with different notations. In the 7th century, Brahmagupta established the use of 0 as a separate number and determined the results for multiplication, division and subtraction of zero and all other numbers, except for the result of division by 0, his contemporary, the Syriac bishop Severus Sebokht said, "Indians possess a method of calculation that no word can praise enough. Their rational system of mathematics, or of their method of calculation. I mean the system using nine symbols." The Arabs learned this new method and called it hesab. Although the Codex Vigilanus described an early form of Arabic numerals by 976 AD, Leonardo of Pisa was responsible for spreading their use throughout Europe after the publication of his book Liber Abaci in 1202, he wrote, "The method of the Indians surpasses any known method to compute.
It's a marvelous method. They do their computations using nine figures and symbol zero". In the Middle Ages, arithmetic was one of the seven
Gear
A gear or cogwheel is a rotating machine part having cut teeth, or in the case of a cogwheel, inserted teeth, which mesh with another toothed part to transmit torque. Geared devices can change the speed and direction of a power source. Gears always produce a change in torque, creating a mechanical advantage, through their gear ratio, thus may be considered a simple machine; the teeth on the two meshing gears all have the same shape. Two or more meshing gears, working in a sequence, are called a transmission. A gear can mesh with a linear toothed part, called a rack, producing translation instead of rotation; the gears in a transmission are analogous to the wheels in belt pulley system. An advantage of gears is; when two gears mesh, if one gear is bigger than the other, a mechanical advantage is produced, with the rotational speeds, the torques, of the two gears differing in proportion to their diameters. In transmissions with multiple gear ratios—such as bicycles and cars—the term "gear" as in "first gear" refers to a gear ratio rather than an actual physical gear.
The term describes similar devices when the gear ratio is continuous rather than discrete, or when the device does not contain gears, as in a continuously variable transmission. Early examples of gears date from the 4th century BC in China, which have been preserved at the Luoyang Museum of Henan Province, China; the earliest preserved gears in Europe were found in the Antikythera mechanism, an example of a early and intricate geared device, designed to calculate astronomical positions. Its time of construction is now estimated between 150 and 100 BC. Gears appear in works connected to Hero of Alexandria, in Roman Egypt circa AD 50, but can be traced back to the mechanics of the Alexandrian school in 3rd-century BC Ptolemaic Egypt, were developed by the Greek polymath Archimedes; the segmental gear, which receives/communicates reciprocating motion from/to a cogwheel, consisting of a sector of a circular gear/ring having cogs on the periphery, was invented by Arab engineer Al-Jazari in 1206.
The worm gear was invented in the Indian subcontinent, for use in roller cotton gins, some time during the 13th–14th centuries. Differential gears may have been used in some of the Chinese south-pointing chariots, but the first verifiable use of differential gears was by the British clock maker Joseph Williamson in 1720. Examples of early gear applications include: The Antikythera mechanism Ma Jun used gears as part of a south-pointing chariot; the first geared mechanical clocks were built in China in 725. Al-Jazari invented the segmental gear as part of a water-lifting device; the worm gear was invented as part of a roller cotton gin in the Indian subcontinent. The 1386 Salisbury cathedral clock may be the world's oldest still working geared mechanical clock; the definite ratio that teeth give gears provides an advantage over other drives in precision machines such as watches that depend upon an exact velocity ratio. In cases where driver and follower are proximal, gears have an advantage over other drives in the reduced number of parts required.
The downside is that gears are more expensive to manufacture and their lubrication requirements may impose a higher operating cost per hour. An external gear is one with the teeth formed on the outer surface of a cone. Conversely, an internal gear is one with the teeth formed on the inner surface of a cylinder or cone. For bevel gears, an internal gear is one with the pitch angle exceeding 90 degrees. Internal gears do not cause output shaft direction reversal. Spur gears or straight-cut gears are the simplest type of gear, they consist of a disk with teeth projecting radially. Though the teeth are not straight-sided, the edge of each tooth is straight and aligned parallel to the axis of rotation; these gears mesh together only if fitted to parallel shafts. No axial thrust is created by the tooth loads. Spur gears tend to be noisy at high speeds. Helical or "dry fixed" gears offer a refinement over spur gears; the leading edges of the teeth are set at an angle. Since the gear is curved, this angling makes.
Helical gears can be meshed in crossed orientations. The former refers to. In the latter, the shafts are non-parallel, in this configuration the gears are sometimes known as "skew gears"; the angled teeth engage more than do spur gear teeth, causing them to run more smoothly and quietly. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel. In spur gears, teeth meet at a line contact across their entire width, causing stress and noise. Spur gears make a characteristic whine at high speeds. For this reason spur gears are used in low-speed applications and in situations where noise control is not a problem, helical gears are used in high-speed applications, large power transmission, or where noise abatement is important; the speed is considered high. A disadvantage of helical gears is a resultant thrust along the axis of the gear, which must