History of Math

This essay has a total of 4848 words and 20 pages.

History of Math

Mathematics, study of relationships among quantities, magnitudes, and properties and of
logical operations by which unknown quantities, magnitudes, and properties may be deduced.
In the past, mathematics was regarded as the science of quantity, whether of magnitudes,
as in geometry, or of numbers, as in arithmetic, or of the generalization of these two
fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to
be regarded increasingly as the science of relations, or as the science that draws
necessary conclusions. This latter view encompasses mathematical or symbolic logic, the
science of using symbols to provide an exact theory of logical deduction and inference
based on definitions, axioms, postulates, and rules for combining and transforming
primitive elements into more complex relations and theorems.

This brief survey of the history of mathematics traces the evolution of mathematical ideas
and concepts, beginning in prehistory. Indeed, mathematics is nearly as old as humanity
itself; evidence of a sense of geometry and interest in geometric pattern has been found
in the designs of prehistoric pottery and textiles and in cave paintings. Primitive
counting systems were almost certainly based on using the fingers of one or both hands, as
evidenced by the predominance of the numbers 5 and 10 as the bases for most number systems
today.

Ancient Mathematics
The earliest records of advanced, organized mathematics date back to the ancient
Mesopotamian country of Babylonia and to Egypt of the 3rd millennium BC. There mathematics
was dominated by arithmetic, with an emphasis on measurement and calculation in geometry
and with no trace of later mathematical concepts such as axioms or proofs.

The earliest Egyptian texts, composed about 1800 BC, reveal a decimal numeration system
with separate symbols for the successive powers of 10 (1, 10, 100, and so forth), just as
in the system used by the Romans. Numbers were represented by writing down the symbol for
1, 10, 100, and so on as many times as the unit was in a given number. For example, the
symbol for 1 was written five times to represent the number 5, the symbol for 10 was
written six times to represent the number 60, and the symbol for 100 was written three
times to represent the number 300. Together, these symbols represented the number 365.
Addition was done by totaling separately the units-10s, 100s, and so forth-in the numbers
to be added. Multiplication was based on successive doublings, and division was based on
the inverse of this process.

The Egyptians used sums of unit fractions (a), supplemented by the fraction B, to express
all other fractions. For example, the fraction E was the sum of the fractions 3 and *.
Using this system, the Egyptians were able to solve all problems of arithmetic that
involved fractions, as well as some elementary problems in algebra. In geometry, the
Egyptians calculated the correct areas of triangles, rectangles, and trapezoids and the
volumes of figures such as bricks, cylinders, and pyramids. To find the area of a circle,
the Egyptians used the square on U of the diameter of the circle, a value of about
3.16-close to the value of the ratio known as pi, which is about 3.14.

The Babylonian system of numeration was quite different from the Egyptian system. In the
Babylonian system-which, when using clay tablets, consisted of various wedge-shaped
marks-a single wedge indicated 1 and an arrowlike wedge stood for 10 (see table). Numbers
up through 59 were formed from these symbols through an additive process, as in Egyptian
mathematics. The number 60, however, was represented by the same symbol as 1, and from
this point on a positional symbol was used. That is, the value of one of the first 59
numerals depended henceforth on its position in the total numeral. For example, a numeral
consisting of a symbol for 2 followed by one for 27 and ending in one for 10 stood for 2 ×
602 27 × 60 10. This principle was extended to the representation of fractions as
well, so that the above sequence of numbers could equally well represent 2 × 60 27 10
× (†), or 2 27 × (†) 10 × (†-2). With this sexagesimal system (base
60), as it is called, the Babylonians had as convenient a numerical system as the 10-based
system.

The Babylonians in time developed a sophisticated mathematics by which they could find the
positive roots of any quadratic equation (Equation). They could even find the roots of
certain cubic equations. The Babylonians had a variety of tables, including tables for
multiplication and division, tables of squares, and tables of compound interest. They
could solve complicated problems using the Pythagorean theorem; one of their tables
contains integer solutions to the Pythagorean equation, a2 b2 = c2, arranged so that
c2/a2 decreases steadily from 2 to about J. The Babylonians were able to sum arithmetic
and some geometric progressions, as well as sequences of squares. They also arrived at a
good approximation for ¸. In geometry, they calculated the areas of rectangles, triangles,
and trapezoids, as well as the volumes of simple shapes such as bricks and cylinders.
However, the Babylonians did not arrive at the correct formula for the volume of a
pyramid.

Greek Mathematics
The Greeks adopted elements of mathematics from both the Babylonians and the Egyptians.
The new element in Greek mathematics, however, was the invention of an abstract
mathematics founded on a logical structure of definitions, axioms, and proofs. According
to later Greek accounts, this development began in the 6th century BC with Thales of
Miletus and Pythagoras of Samos, the latter a religious leader who taught the importance
of studying numbers in order to understand the world. Some of his disciples made important
discoveries about the theory of numbers and geometry, all of which were attributed to
Pythagoras.

In the 5th century BC, some of the great geometers were the atomist philosopher Democritus
of Abdera, who discovered the correct formula for the volume of a pyramid, and Hippocrates
of Chios, who discovered that the areas of crescent-shaped figures bounded by arcs of
circles are equal to areas of certain triangles. This discovery is related to the famous
problem of squaring the circle-that is, constructing a square equal in area to a given
circle. Two other famous mathematical problems that originated during the century were
those of trisecting an angle and doubling a cube-that is, constructing a cube the volume
of which is double that of a given cube. All of these problems were solved, and in a
variety of ways, all involving the use of instruments more complicated than a straightedge
and a geometrical compass. Not until the 19th century, however, was it shown that the
three problems mentioned above could never have been solved using those instruments alone.

In the latter part of the 5th century BC, an unknown mathematician discovered that no unit
of length would measure both the side and diagonal of a square. That is, the two lengths
are incommensurable. This means that no counting numbers n and m exist whose ratio
expresses the relationship of the side to the diagonal. Since the Greeks considered only
the counting numbers (1, 2, 3, and so on) as numbers, they had no numerical way to express
this ratio of diagonal to side. (This ratio, ¸, would today be called irrational.) As a
consequence the Pythagorean theory of ratio, based on numbers, had to be abandoned and a
new, nonnumerical theory introduced. This was done by the 4th-century BC mathematician
Eudoxus of Cnidus, whose solution may be found in the Elements of Euclid. Eudoxus also
discovered a method for rigorously proving statements about areas and volumes by
successive approximations.

Euclid was a mathematician and teacher who worked at the famed Museum of Alexandria and
who also wrote on optics, astronomy, and music. The 13 books that make up his Elements
contain much of the basic mathematical knowledge discovered up to the end of the 4th
century BC on the geometry of polygons and the circle, the theory of numbers, the theory
of incommensurables, solid geometry, and the elementary theory of areas and volumes.

The century that followed Euclid was marked by mathematical brilliance, as displayed in
the works of Archimedes of Syracuse and a younger contemporary, Apollonius of Perga.
Archimedes used a method of discovery, based on theoretically weighing infinitely thin
slices of figures, to find the areas and volumes of figures arising from the conic
sections. These conic sections had been discovered by a pupil of Eudoxus named Menaechmus,
and they were the subject of a treatise by Euclid, but Archimedes' writings on them are
the earliest to survive. Archimedes also investigated centers of gravity and the stability
of various solids floating in water. Much of his work is part of the tradition that led,
in the 17th century, to the discovery of the calculus. Archimedes was killed by a Roman
soldier during the sack of Syracuse. His younger contemporary, Apollonius, produced an
eight-book treatise on the conic sections that established the names of the sections:
ellipse, parabola, and hyperbola. It also provided the basic treatment of their geometry
until the time of the French philosopher and scientist René Descartes in the 17th century.

After Euclid, Archimedes, and Apollonius, Greece produced no geometers of comparable
stature. The writings of Hero of Alexandria in the 1st century AD show how elements of
both the Babylonian and Egyptian mensurational, arithmetic traditions survived alongside
the logical edifices of the great geometers. Very much in the same tradition, but
concerned with much more difficult problems, are the books of Diophantus of Alexandria in
the 3rd century AD. They deal with finding rational solutions to kinds of problems that
lead immediately to equations in several unknowns. Such equations are now called
Diophantine equations (see Diophantine Analysis).

Applied Mathematics in Greece
Paralleling the studies described in pure mathematics were studies made in optics,
mechanics, and astronomy. Many of the greatest mathematical writers, such as Euclid and
Archimedes, also wrote on astronomical topics. Shortly after the time of Apollonius, Greek
astronomers adopted the Babylonian system for recording fractions and, at about the same
time, composed tables of chords in a circle. For a circle of some fixed radius, such
tables give the length of the chords subtending a sequence of arcs increasing by some
fixed amount. They are equivalent to a modern sine table, and their composition marks the
beginnings of trigonometry. In the earliest such tables-those of Hipparchus in about 150
BC-the arcs increased by steps of 71°, from 0° to 180°. By the time of the astronomer
Ptolemy in the 2nd century AD, however, Greek mastery of numerical procedures had
progressed to the point where Ptolemy was able to include in his Almagest a table of
chords in a circle for steps of 3°, which, although expressed sexagesimally, is accurate

In the meantime, methods were developed for solving problems involving plane triangles,
and a theorem-named after the astronomer Menelaus of Alexandria-was established for
finding the lengths of certain arcs on a sphere when other arcs are known. These advances
gave Greek astronomers what they needed to solve the problems of spherical astronomy and
to develop an astronomical system that held sway until the time of the German astronomer
Johannes Kepler.

Medieval and Renaissance Mathematics
Following the time of Ptolemy, a tradition of study of the mathematical masterpieces of
the preceding centuries was established in various centers of Greek learning. The
preservation of such works as have survived to modern times began with this tradition. It
was continued in the Islamic world, where original developments based on these
masterpieces first appeared.

Islamic and Indian Mathematics
After a century of expansion in which the religion of Islam spread from its beginnings in
the Arabian Peninsula to dominate an area extending from Spain to the borders of China,
Muslims began to acquire the results of the “foreign sciences.” At centers such as the
House of Wisdom in Baghdad, supported by the ruling caliphs and wealthy individuals,
translators produced Arabic versions of Greek and Indian mathematical works.

By the year 900 AD the acquisition was complete, and Muslim scholars began to build on
what they had acquired. Thus mathematicians extended the Hindu decimal positional system
of arithmetic from whole numbers to include decimal fractions, and the 12th-century
Persian mathematician Omar Khayyam generalized Hindu methods for extracting square and
cube roots to include fourth, fifth, and higher roots. In algebra, al-Karaji completed the
algebra of polynomials of Muhammad al-Khwarizmi. Al-Karaji included polynomials with an
infinite number of terms. (Al-Khwarizmi's name, incidentally, is the source of the word
algorithm, and the title of one of his books is the source of the word algebra.) Geometers
such as Ibrahim ibn Sinan continued Archimedes' investigations of areas and volumes, and
Kamal al-Din and others applied the theory of conic sections to solve optical problems.
Using the Hindu sine function and Menelaus's theorem, mathematicians from Habas al-Hasib
to Nasir ad-Din at-Tusi created the mathematical disciplines of plane and spherical
trigonometry. These did not become mathematical disciplines in the West, however, until
the publication of De Triangulis Omnimodibus by the German astronomer Regiomontanus.

Finally, a number of Muslim mathematicians made important discoveries in the theory of
numbers, while others explained a variety of numerical methods for solving equations. The
Latin West acquired much of this learning during the 12th century, the great century of
translation. Together with translations of the Greek classics, these Muslim works were
responsible for the growth of mathematics in the West during the late Middle Ages. Italian
mathematicians such as Leonardo Fibonacci and Luca Pacioli, one of the many 15th-century
writers on algebra and arithmetic for merchants, depended heavily on Arabic sources for
their knowledge.

Western Renaissance Mathematics
Although the late medieval period saw some fruitful mathematical considerations of
problems of infinity by writers such as Nicole Oresme, it was not until the early 16th
century that a truly important mathematical discovery was made in the West. The discovery,
an algebraic formula for the solution of both the cubic and quartic equations, was
published in 1545 by the Italian mathematician Gerolamo Cardano in his Ars Magna. The
discovery drew the attention of mathematicians to complex numbers and stimulated a search
for solutions to equations of degree higher than 4. It was this search, in turn, that led
to the first work on group theory (Group) at the end of the 18th century, and to the
theory of equations developed by the French mathematician Évariste Galois in the early
19th century.

The 16th century also saw the beginnings of modern algebraic symbolism (Mathematical
Symbols), as well as the remarkable work on the solution of equations by the French
mathematician François Viète. His writings influenced many mathematicians of the following
century, including Pierre de Fermat in France and Isaac Newton in England.

Mathematics Since the 16th Century
Europeans dominated in the development of mathematics after the Renaissance.
17th Century
During the 17th century, the greatest advances were made in mathematics since the time of
Archimedes and Apollonius. The century opened with the discovery of logarithms by the

• Education and Egalitarianism in America
Education and Egalitarianism in America The American educator Horace Mann once said: "As an apple is not in any proper sense an apple until it is ripe, so a human being is not in any proper sense a human being until he is educated." Education is the process through which people endeavor to pass along to their children their hard-won wisdom and their aspirations for a better world. This process begins shortly after birth, as parents seek to train the infant to behave as their culture demands. The
• The Rise of the Y2K Bug
The Rise of the Y2K Bug "The Y2K problem is the electronic equivalent of the El Niño and there will be nasty surprises around the globe."--John Hamre, Dep. Secretary of Defense When I was in the first grade, my elementary school invested in several computers and started Introduction to Computers classes. I remember playing math games and drawing with art programs, in awe of, and slightly intimidated by the beastly piece of technology in front of me. I had little idea of how it worked, and even l
• Is literacy a good thing
is literacy a good thing Essay IV Is Literacy a Good Thing? How many times do you remember saying to yourself, “I don’t want to go to school today.”, or seen commercials where children do whatever it takes to stay home? Well lets just say your not alone, however if you had the government on you, making sure you went, do you still think you would’ve said that, or even worried about anything else like a job or a family? Well when you have a communist government on you it’s no longer a choice but,
• Religions
Religions The formation of our modern American School System has been heavily influenced by the religious views of our predecessors, the colonial settlers of New England. The general interest of settlers in their children’s ability to read, their establishment of elementary and secondary grammar schools, and the founding of colleges and universities were all religiously motivated advances in early American education. While the twentieth century has brought about a separation between church and s
• Religions Influence on the American School System
Religions Influence on the American School System The formation of our modern American School System has been heavily influenced by the religious views of our predecessors, the colonial settlers of New England. The general interest of settlers in their children’s ability to read, their establishment of elementary and secondary grammar schools, and the founding of colleges and universities were all religiously motivated advances in early American education. While the twentieth century has brought
• Eskimos
eskimos peoples of Alaska and their Eskimo Culture Alaska is still the last frontier in the minds of many Americans. Interest in the "Great Land" has increased sharply since Alaska The Native became a full fledged state in January o f 1959. In spite of this great interest, many Americans know very little of the Eskimos, Indians and Aleuts (Al-ee-oots) who live in the remote regions. At the time Alaska was discovered in 1741 by Vitus Bering, Alaska Natives populated all parts of Alaska including
• Catherine the Great
Catherine the Great Throughout history, Russia has been viewed as a regressive cluster of barely civilized people on the verge of barbarism. In the eighteenth century, ideas of science and secularism grasped hold of Europe, and Russian Czars, realizing how behind Muscovite culture was, sought out this knowledge, attempting to imbed it into Russian society. Catherine II was one of these Czars. She listened to both the ideas of the philosophes and the problems of her people and strove to enlighten
• Education in the 1800s
Education in the 1800s Education had an emphasis on many different aspects during the time prior to the Civil War. There was a certain irony that set the mode of this time making things that were said irrelevant to the actions that were taken. The paradoxes of education in Pre civil war America, are evidenced in subject matter, gender, class and race, as well as purpose. American education developed from European intellectual traditions and institutions transplanted to the new world and modified
• Progressive education
Progressive education To meet the needs of an increasing industrialized Canadian society in the late 1930’s, the elementary curriculum was revised. This essay will explore the changes BC curriculum endured as a result of the progressive movement within the Greater Victoria area by way of the Greater Victoria Survey of Schools of 1937-38 and the Curriculum Guide: The New Programme of Studies 1936-7. The new system is commonly known as progressive education or the “new education”. Jean Barman desc
• History of Math
History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the scienc
• History of Math
History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the scienc
• Chaucers Life and works
Chaucers Life and works In Todays writing, writers conform to the readers wants and needs, contrary to the writers of the 13th and 14th centuries. In these times writers wrote from the heart not from the pocket book. They wrote on their beliefs and morals and dreams. But never did they judge. Their styles taken from their trials and tribulations. As so in Geoffery Chaucers works he used his life experiences to influence his every word. Geoggrey Chaucer is the first literly personality in English
• Downs syndrome1
downs syndrome1 Down syndrome, the most common genetic birth defect associated with mental retardation, occurs equally across all races and levels of society. The effects of the disorder on physical and mental development are severe and are expressed throughout the life span. The individual\'s family is also affected emotionally, economically, and socially (Bellenir 1996). Characteristics associated with Down syndrome include: epicanthal folds, unilateral squints, a flat saddle nose, flat jaw bo
• Education Aided or Replaced by Computers
Education Aided or Replaced by Computers Education: Aided or Replaced by Computers People said that the horseless carriage would never amount to a thing. New ideas always undergo severe scrutiny, but sometimes they survive the cynical blows and begin a new road of innovations. David Gelernter, of Yale University, writes in his essay "Unplugged" that people should weigh the value of technology because it is not always as advantageous as it seems. He claims, for example, that the misuse of compute
• Eskimos1
eskimos1 peoples of Alaska and their Eskimo Culture Alaska is still the last frontier in the minds of many Americans. Interest in the "Great Land" has increased sharply since Alaska The Native became a full fledged state in January o f 1959. In spite of this great interest, many Americans know very little of the Eskimos, Indians and Aleuts (Al-ee-oots) who live in the remote regions. At the time Alaska was discovered in 1741 by Vitus Bering, Alaska Natives populated all parts of Alaska including
• Haha1
haha1 Teaching Kids The issue of morals and values being taught to our children is one of the most pressing problems in our society today. The responsibility of raising children with a strong moral base has been lost in the chaos of the modern world. With an increase in single parenting and more homes where both parents are employed full-time, the role of parents in their children\'s lives has drastically changed. Many parents are no longer involved in raising their children, which leaves the re
• Welfare Reformation
Welfare Reformation TITLE} “This week we offered a plan to end welfare as we know it—a plan that will encourage personality and help strengthen our families through tougher child support, more education and training, and an absolute requirement to go to work after a period of time.” -Bill Clinton, radio address, 6/18/94 The welfare system is in deep distress. From the time of Franklin Delano Roosevelt to the current reigning of Bill Clinton, many a bills have been brought for to reform it. Origi
• Technology for specialty education
technology for specialty education Technology and Special Education We live in an era where computers are used in most people’s everyday life. Technology has achieved remarkable progress and with this knowledge it’s time that important issues are addressed. Homelessness, abortion, taxes, and welfare reform are a few examples of the humanitarian issues I’m talking about. But, the most important issue is education. Because everything we do begins with learning. We learn from our parents and siblin
• Transparencey
transparencey INTRODUCTION The ancient Greeks knew that reasoning is a structured process governed, at least partially, by a system of explainable rules. Aristotele codified syllogisms; Euclide formulated geometric theorems; Vitruvius defined the criterion and referential key so that every architectural element could be proportioned according to an ideal model, symbolizing the aspirations and aptitudes of that particular civil society. In these forms of reasoning it is possible to distinguish c
• Symbolism of Albrecht Durer8217s 8220Master Engrav
Symbolism of Albrecht Durer8217s 8220Master Engravings8221 Albrecht Durer completed the Master Engravings in the years 1513 and 1514. With these three engravings (Knight, Death, and Devil, St. Jerome in His Study, and Melencolia I) he reached the high point of his artistic expression and concentration. each print represents a different philosophical perspective on the worlds respectively of action, spirit, and intellect. Although Durer himself evidently did not think of the three as a set,
• Learning Disabilities an Overview
Learning Disabilities an Overview Learning Disabilities: An Overview This semester we have spent the majority of our time learning about and discussing how we can best assist exceptional students. Many of these students are individuals with learning dissabilities. Although it would be difficult for every teacher to understand the distinctions, symptoms, weaknesses and strengths of every disability, it can be very helpful to have a general knowledge of the disabilities that may hinder a students
• What it should be
What it should be Education and Egalitarianism in America The American educator Horace Mann once said: "As an apple is not in any proper sense an apple until it is ripe, so a human being is not in any proper sense a human being until he is educated." Education is the process through which people endeavor to pass along to their children their hard-won wisdom and their aspirations for a better world. This process begins shortly after birth, as parents seek to train the infant to behave as their c
• Industrial revolution in england
Industrial revolution in england Labour, leisure and economic thought before the nineteenth century. Author/s: John Hatcher Issue: August, 1998 I When manual labour was overwhelmingly the most important factor in the generation of wealth, the labourers, artisans, servants and peasants who performed it were recognized as \'the most valuable treasure of a country\'.(1) The efficient running of the economy, social stability and the maintenance of civilized life were all dependent upon the masses p
• Medieval Universities
Medieval Universities Medieval Universities Would Today\'s Student Like to Study in Those Times? The appearance of universities was part of the same high-medieval education boom. Originally universities were institutions where students could attain specialized instruction in advanced studies. These types of studies were not available in the average cathedral schools. Advanced schools existed in the ancient world, but did not promote a fixed curricula or award degrees. The term university origin
• Wagner and hitler
wagner and hitler Being a carpenter Upon the interviews of two trade carpenters, a detailed description of the occupation of a carpenter came clearly into view. From some of the most general there was received a more descriptive perspective. What would someone interested in this job need to do to get started? What personal qualities/traits should a person have to be successful at this job? How did you get started in this field? How much of a challenge is your type of work? What types of writing
• Carl Gauss
Carl Gauss Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world. Carl Gauss was born Johann Carl Friedric
• Egyptian Math
Egyptian Math Kevin Mann 4-20-00 Dr Johnston Ancient Egyptian Mathematics The use of organized mathematics in Egypt has been dated back to the third millennium BC. Egyptian mathematics was dominated by arithmetic, with an emphasis on measurement and calculation in geometry. With their vast knowledge of geometry, they were able to correctly calculate the areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. They were also able to build
• History of Math
History of Math History Of Math History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be re
• Marijuana10
Marijuana10 Term Papers Can\'t find it here? Try MegaEssays.com Public Discourse By: konceited In Amusing Ourselves to Death, Neil Postman alerts us to the dangers brought about by the way television conditions us to tolerate the brevity of visual entertainment. His message is that with each new technological medium introduced, there is a significant trade-off. His primary example was the medium of television. TV is structured to provide information to the viewer on a platform which is both qui
• Marijuana10
Marijuana10 Term Papers Can\'t find it here? Try MegaEssays.com Public Discourse By: konceited In Amusing Ourselves to Death, Neil Postman alerts us to the dangers brought about by the way television conditions us to tolerate the brevity of visual entertainment. His message is that with each new technological medium introduced, there is a significant trade-off. His primary example was the medium of television. TV is structured to provide information to the viewer on a platform which is both qui
• Math4
math4 History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the
• Missionaries and Education in Bengal
Missionaries and Education in Bengal Nineteenth Century Missionaries and Education in Bengal: An Analysis of Historical Literature This paper is about how missionaries implemented education and how their reforms reflected the cultural, political, religious, social, and economical situation of Bengal throughout the years of 1793-1837. Michael A. Laird is clear to state that missionaries did not actually arrive in Bengal until around 1800. However, it is important to analyze the educational clima
• Public Discourse
Public Discourse In Amusing Ourselves to Death, Neil Postman alerts us to the dangers brought about by the way television conditions us to tolerate the brevity of visual entertainment. His message is that with each new technological medium introduced, there is a significant trade-off. His primary example was the medium of television. TV is structured to provide information to the viewer on a platform which is both quick and entertaining. This discourages any viewer subjectivity, allowing televi
• Education and Religion
edu Education and Religion “Our father’s God to, thee, author of Liberty, to thee we sing. Long may our land be bright with freedoms holy light; protect us by thy might, Great God our King.” Since the late 1950’s, when separation between Church and state was forced into practice, public schools have shown a dramatic decrease in the amount of ethics and morality taught in the classroom. All the while, school violence is on the rise. All we need to do is look at the horror with transpired at Colu
• Educationreligion
educationreligion Education and Religion “Our father’s God to, thee, author of Liberty, to thee we sing. Long may our land be bright with freedoms holy light; protect us by thy might, Great God our King.” Since the late 1950’s, when separation between Church and state was forced into practice, public schools have shown a dramatic decrease in the amount of ethics and morality taught in the classroom. All the while, school violence is on the rise. All we need to do is look at the horror with tran
• Dawn of the Digital Age
Dawn of the Digital Age The Dawn of the Digital Age The history of computers starts out about two thousand years ago, at the birth of the abacus. The abacus is a wooden rack holding two horizontal wires with beads strung on them. When these beads are moved around, according to "programming" rules memorized by the user, all regular arithmetic problems can be done. Blaise Pascal is usually credited for building the first digital computer in 1642. It added numbers entered with dials and was made t
• Blaise Pascal
Blaise Pascal Blaise Pascal Blaise Pascal was born on June 19, 1623 in Clermont-Ferrand, France and died August 19, 1662 of stomach cancer. Pascal was not only a great mathematician, he was also a man of great knowledge. Philosopher, mathematician, inventor, and scientific genius are just a few of the things he became in his life. Pascal helped create many things for this world as a whole, like when he invented the barometer, the hydraulic press, and of course (my personal favorite) the syringe.
• Japanese School Systems vs. American
Japanese School Systems vs. American Japanese School Systems vs. American For years, people have always felt that the Japanese school system was superior or more effective than that of the United States. Although some feel this way, others feel that the Japanese system is too strict and not flexible enough for those who may need extra help along the way. Through researching two different case studies, and also reading other materials, I have found many similarities along with many differences be
• Education in the past
education in the past Education wasn\'t an option for Romans and Greeks; it was both a tool and a necessity. Without education, neither of these cultures would have been what they were or remembered as they are today. Without education, neither of these cultures would have experienced the fame and success that they experienced during their individual time periods. About 200 BC, a Roman system of education developed which was different from the Greek tradition, but Romans borrowed some of the anc
• Carl Gauss
Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world.Carl Gauss was born Johann Carl Friedrich Gauss, on t
• Symbolism Of Albrecht Durer?s ?Master Engravings?
Symbolism Of Albrecht Durer?s ?Master Engravings? Albrecht Durer completed the "Master Engravings" in the years 1513 and 1514. With these three engravings (Knight, Death, and Devil, St. Jerome in His Study, and Melencolia I) he reached the high point of his artistic expression and concentration. each print represents a different philosophical perspective on the "worlds" respectively of action, spirit, and intellect. Although Durer himself evidently did not think of the three as a set, He sometim
• Islam and Science
Islam and Science Islam and Science The 6th century Islamic empire inherited the scientific tradition of late antiquity. They preserved it, elaborated it, and finally, passed it to Europe (Science: The Islamic Legacy 3). At this early date, the Islamic dynasty of the Umayyads showed a great interest in science. The Dark Ages for Europeans were centuries of philosophical and scientific discovery and development for Muslim scholars. The Arabs at the time assimilated the ancient wisdom of Persia an
• Computers in education
computers in education It is now about fifteen years since microcomputers and therefore educational computing began to appear in schools. Since that time there has been much excitement with regard to the role that these machines would have on education in our schools. During that fifteen years, we have seen many examples of uses of computers in school. Teachers experimented with this technology in their teaching. These teachers spent many hours of their own time coming to grips with this technol
• History Of Math
History Of Math History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasing
• History of Computing
History of Computing 1 General principles 1 2 Etymology (Where the word is from) 2 3 The exponential progress of computer development 2 4 Classification of computers 2 4.1 Classification by intended use 2 4.2 Classification by implementation technology 3 4.3 Classification by design features 3 4.3.1 Digital versus analog 3 4.3.2 Binary versus decimal 4 4.3.3 Programmability 4 4.3.4 Storage 4 4.4 Classification by capability 4 4.4.1 General-purpose computers 4 4.4.2 Special-purpose computers 6 4.
• The Beneficial Relationship of Music and Mathemati
The Beneficial Relationship of Music and Mathematics for Young Children Many educators would agree that music has the ability to unlock doors for young children to learn the various aspects of mathematics. The relationship of the two subjects can be traced back to the early stages of ancient history where they were taught together, unlike a majority of America\'s public schools. Fortunately, there are public schools beginning to recognize this close relationship once again and have developed les
• Egyptian math
egyptian math Taras Malsky MT.1102 AB Dr.S.Washburn Egyptian Math The use of organized mathematics in Egypt has been dated back to the third millennium BC. Egyptian mathematics was dominated by arithmetic, with an emphasis on measurement and calculation in geometry. With their vast knowledge of geometry, they were able to correctly calculate the areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. They were also able to build the Grea
• Carl Gauss
Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world. Carl Gauss was born Johann Carl Friedrich Gauss, on
• Symbolism Of Albrecht Durer?s ?master Engravings?
Symbolism Of Albrecht Durer?s ?master Engravings? Albrecht Durer completed the "Master Engravings" in the years 1513 and 1514. With these three engravings (Knight, Death, and Devil, St. Jerome in His Study, and Melencolia I) he reached the high point of his artistic expression and concentration. each print represents a different philosophical perspective on the "worlds" respectively of action, spirit, and intellect. Although Durer himself evidently did not think of the three as a set, He sometim
• Clock Arithmetic
Clock Arithmetic Clock Arithmetic The topic of time has always been one of interest to me at least on a philosophical basis. Through the works of Einstein, ancient timepieces and calendars such as Stonehenge, and even theories on past and present, time is everywhere. I chose this topic to perhaps explore further the relevance of clocks and timepieces in mathematics and arithmetic. To gain a better understanding of the mathematical features of time would be rewarding knowing that philosophy and m