Ancient Egyptian mathematics was based on two very elementary concepts.  The first concept was that the Egyptians had a thorough knowledge of the twice-times table.  The second concept was that they had the ability to find two-thirds of any number (Gillings 3). This number could be either integral or fractional.  The Egyptians used the fraction 2/3 used with sums of unit fractions (1/n) to express all other fractions.  Using this system, they were able to solve all problems of arithmetic that involved fractions, as well as some elementary problems in algebra (Berggren).

The science of mathematics was further advanced in Egypt in the fourth millennium BC than it was anywhere else in the world at this time.  The Egyptian calendar was introduced about 4241 BC.  Their year consisted of 12 months of 30 days each with 5 festival days at the end of the year.  These festival days were dedicated to the gods Osiris, Horus, Seth, Isis, and Nephthys (Gillings 235).  Osiris was the god of nature and vegetation and was instrumental in civilizing the world.  Isis was Osiris’s wife and their son was Horus.  Seth was Osiris’s evil brother and Nephthys was Seth’s sister (Weigel 19).  The Egyptians divided their year into 3 seasons that were 4 months each.  These seasons included inundation, coming-forth, and summer.  Inundation was the sowing period, coming-forth was the growing period, and summer was the harvest period.  They also determined a year to be 365 days so they were very close to the actual year of 365 ¼ days (Gillings 235).

When studying the history of algebra, you find that it started back in Egypt and Babylon.  The Egyptians knew how to solve linear (ax=b) and quadratic (ax2+bx=c) equations, as well as indeterminate equations such as x2+y2=z2 where several unknowns are involved (Dauben).

The earliest Egyptian texts were written around 1800 BC.  They consisted of a decimal numeration system with separate symbols for the successive powers of 10 (1, 10, 100, and so forth), just like the Romans (Berggren).  These symbols were known as hieroglyphics.  Numbers were represented by writing down the symbol for 1, 10, 100, and so on as many times as the unit was in the given number.  For example, the number 365 would be represented by the symbol for 1 written five times, the symbol for 10 written six times, and the symbol for 100 written three times.  Addition was done by totaling separately the units-1s, 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 (Berggren).

The original of the oldest elaborate manuscript on mathematics was written in Egypt about 1825 BC.  It was called the Ahmes treatise.  The Ahmes manuscript was not written to be a textbook, but for use as a practical handbook.  It contained material on linear equations of such types as x+1/7x=19 and dealt extensively on unit fractions.  It also had a considerable amount of work on mensuration, the act, process, or art of measuring, and includes problems in elementary series (Smith 45-48).

The Egyptians discovered hundreds of rules for the determination of areas and volumes, but they never showed how they established these rules or formulas.  They also never showed how they arrived at their methods in dealing with specific values of the variable, but they nearly always proved that the numerical solution to the problem at hand was indeed correct for the particular value or values they had chosen.  This constituted both method and proof.  The Egyptians never stated formulas, but used examples to explain what they were talking about.  If they found some exact method on how to do something, they never asked why it worked.  They never sought to establish its universal truth by an argument that would show clearly and logically their thought processes.  Instead, what they did was explain and define in an ordered sequence the steps necessary to do it again, and at the conclusion they added a verification or proof that the steps outlined did lead to a correct solution of the problem (Gillings 232-234).  Maybe this is why the Egyptians were able to discover so many mathematical formulas.   They never argued why something worked, they just believed it did.

  BIBLIOGRAPHY
 Berggren, J. Lennart.  “Mathematics.”  Computer Software.  Microsoft, Encarta 97   Encyclopedia.  1993-1996.  CD- ROM.
 Dauben, Joseph Warren and Berggren, J. Lennart.  “Algebra.”  Computer Software.    Microsoft, Encarta 97 Encyclopedia.  1993-1996.  CD- ROM.
 Gillings, Richard J.  Mathematics in the Time of the Pharaohs.  New York: Dover    Publications, Inc., 1972.
 Smith, D. E.  History of Mathematics.  Vol. 1.  New York: Dover Publications, Inc.,  1951.
 Weigel Jr., James.  Cliff Notes on Mythology.  Lincoln, Nebraska: Cliffs Notes, Inc.,  1991.

Things went quite well at first for Blaise concerning his schooling. His father was amazed at the ease his son was able to absorb the classical education thrown at him and “tried to hold the boy down to a reasonable pace to avoid injuring his health.” (P 74,Bell) Blaise was exposed to all subjects, all except mathematics, which was taboo. His father forbid this from him in the belief that Blaise was strain his mind. Faced with this opposition, Blaise demanded to know ‘what was mathematics?’ His father told him, “that generally speaking, it was the way of making precise figures and finding the proportions among them.” (P 39,Cole) This set him going and during his play times in this room he figured out ways to draw geometric figures such as perfect circles, and equilateral triangles, all of this he accomplished. Due to the fact that Etienne took such painstaking measures to hide mathematics from Blaise, to the point where he told his friends not to mention math at all around him, Blaise did not know the names to these figures. So he created his own vocab for them, calling a circle a “round” and lines he named “bars”. “After these definitions he made himself axioms, and finally made perfect demonstrations.” (P 39,Cole) His progression was far enough that he reached the 32nd proposition of Euclid’s Book one. Deeply enthralled in this task his father entered the room un-noticed only to observe his son, inventing mathematics. At the age of 13 Etienne began taking Blaise to meetings of mathematicians and scientists which gave Blaise the opportunity to meet with such minds as Descartes and Hobbes. Three years later at the age of 16 Blaise amazed his peers by submitting a paper on conic sections. His sister was quoted as having said “that it was considered so great an intellectual achievement that people have said they have seen nothing as mighty since the time of Archimedes.” (I:Pascal) This was his first real contribution to mathematics, but not his last. Note: www.nd.edu/StudentLinks/akoehl/Pascal.html

Pascal’s contributions to mathematics from then on were surmasing. From a young age he was ‘creating science.’ His first scientific work, an essay on sounds he prepared at a very young age. Once at a dinner party someone tapped a glass with a spoon. Pascal went about the house tapping the china with his fork then dissappeard into his room only to emerge hours later having completed a short essay on sound. He used the same approach to all of the problems he encountered; working at them until he was satisfied with his understanding of the problem at hand. A few of his disocoveries stood out more then others, of them his calculating machine, and his contributions to combinatorial analysis have made a signifigant contribution to mathematics.

The mechanical calculator was devised by Pascal in 1642 and was brought to a commercial version in 1645. It was one of the earliest in the history of computing. ‘Side by side in an oblong box were places six small drums, round the upper and lower halves chich the numbers 0 to 9 were written, in decending and ascending orders respectively. According to whichever aritchmatical process was currently in use, one half of each drum was shut off from outside view by a sliding metal bar: the upper row of figures was for subtraction, the lower for addition. Below each drum was a wheel consisting of ten (or twenty of twelve) movable spokes inside a fixed rim numbered in ten (or more) equal sections from 0 to 9 etc, rather like a clockface. Wheels and rims were all visible on the box lid, and indeed the numbers to be added or subtracted were fed into the machine by means of the wheels: 4 for instance, being recorded by using a small pin to turn the stoke opposite division 4 as far as a catch positioned close to the outer edge of the box. The procedure for basic arithmatical process then as follows.To add 315+172, first 315 was recorded on the three (out of six) drums closest to the right-hand side: 5 would appear in the sighting aperture to the extremem right, 1 next to it, and 3 next to that again. To increase by one the number showing in any aperture, it was necessary to turn the appropriate frum forward 1/10th of a revolution. Tus in this sum, the drum on the extremem right of the machine would be given two turns, the drum immediately to its left would be moved on 7/10ths of a revolution, whilst the drum to its immediate left would be rotated forward by 1/10th. Tht total of 487 could then be read off in the appropriate slots. But, easy as thes operation was, a problem clearly arose when the numbers to be added together involved totals needing to be carried forward: say 315 + 186. At the perios at which Pascal was working, and because there had been no previous attempt at a calculating-machine capable of carrying column totals forward, this presened a serious technical challenge.(adamson p 23)

Pascal is also accredited with the advent of Pascal’s triangle; An arrangement of numbers which were originally discovered by the chinese but named after Pascal due to his furthur discoveries into the properties which it possesed. ex. (Pascals Triangle)

1

1 1

1 2 1

1 3 3 1

.

.

.

‘Pascal investigated binomial coefficients and laid the foundations of the binomial theorem.’(adamson p37) ‘A triangular array of numbers consists of ones written on the vertical leg and on the hypotenuse of a right angled isosceled triangle; each other element composing the triangle is the sum of the element directly above it and of the element above it and to the left. Pascal proceeded from this to demonstrate that the numbers in the (n+1)st row are the coeffieients in the binomial expansion of (x+y)n. Due to the ease and clarity of the formation of the problems involved, Pascal’s triangle, although not original was one of his finest achievements. It has greatly influenced mandy discoveries including the theoritical basis of the computer). It has also made an essential contribution to the field of combinatory analysis. It also ‘through the work of John Wallis it led Isaac Newton to the discovery of the binomial theorem for fractional and negative indices, and it was central to Leibniz’s discovery of the calculus.’(adamson p37)

As stated looking closer at the triangle Pascal was able to deduce many properties. First of all, the enteries in any row of the triangle are an equal distance from each other.

He found another property can be derived from the triangle. He discovered that any number in the triangle is the sum of the two numbers directly above it. This hls true for both triangles, the solved and unsolved. (3/1) + (3/2) = (4/2). Similarly, (5/1) + (5/2) = (6/2). The generalization of this property is known as Pascal’s theorem.

Furthur studies in hydrodynamics, hydrostatic and atmospheric pressure led Pascal to many dicoveries still in use today such as the syringe and hydrolic press. Both these inventions came after years of him experimenting with vacuum tubes. One such experiment was to ‘Take a tube which is curved at its bottom end, sealed at its top end A and open its extermity B. Another tube, a completely straight one open at both extermities M and N, is joined into the curved end of the first tube by its extermity M. Seal B, the opening of the curved end of the first tube, either with your finger or in some other manner and turn the entire apparatus upside down so that, in other words, the two tubes really only consist of one tube, being interconnected. Fill this tube with quicksilver and turn it the right way up again so that A is at the top; then place the end N in a dishfull of quicksilver. The whole of the quicksilver in the upper tube will fall down, with the result that it will all recede into the curve unless by any chance part of it also flows through the aperture M into the tube below. But the quicksilver in the lover tube will only partially subside as part of it will also remain suspended at a heright of 26′-27′ according to the place and weather conditions in which the experiment is being carried out.

The reason for this difference is because the air weights down on the quicksilver in the dish beneath the lower tube, and thus the quicksilver which is inside that tube is held suspened in balence.

But it does not weigh down upon the quicksilver at the curved end of the upper tube, for the finger or bladder sealing this prevents any access to it, so that, as no air is pressing down at this point, the quicksilver in the upper tube drops freely because there is nothing to hold it up or to resist its fall.

All of these contibutions have made a lasting impact of all of mankind. Everything that Pascal created is still in use today in someway or another. His primative form of a syringe is still used in the medical field today to administer drugs and remove blood. The work he did on combinatory mathematics can be applied by anyone to ‘figure out the odds’ concerning a situation, which is exactly how he used it; by going to casinos and playing games smart. Something that anyone can do today. The work he did concerning hydrolic pressses are still in use today in factories, and car garages.

The thing that Pythagoras is probably the most famous for is the Pythagorean Theorem. The Pythagorean Theorem is used in the field of mathematics and it states the following: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides. This means that if one makes a square (with all sides equal in length) out of a triangle with a right angle, the areas of the squares made from the two shorter sides, when added together, equal the area of the square made from the long side. Another geometrical discovery made by Pythagoras is that the diagonal of a square is not a rational multiple of its side. The latter discovery proved the existence of irrational numbers and therefore changed the entire Greek mathematical belief that whole numbers and their ratios could account for geometrical properties.

Another contribution of Pythagoras and his follower is that of music. Pythagoras essentially created music in that he discovered the way it works. Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers. After making this discovery, he found that these same ratios could be extended further to other instruments.

Pythagoras was one of the first to teach that the Earth was at the center of the universe. He was also one of the first to teach that the world was round, an idea not to be proven for almost another one thousand years. Pythagoras also discovered that the orbit of the moon is inclined to the equator of the Earth. He also was the first person to make the connection that Venus as the evening star is the same as Venus the morning star.

So, in conclusion, Pythagoras made many contributions to modern society. Thus, making him recognizable as a formidable scientist and mathematician even today. Pythagoras will always be a significant person in history, because of the discoveries made by him, his students in ancient Greece, and the ever growing amount of people studying his teachings today and who will continue to learn and follow his lessons until the end of time.

Although in the popular mind Galileo is remembered chiefly as an astronomer, however, the science of mechanics and dynamics pretty much owe their existence to his findings. Before he was twenty, observation of the oscillations of a swinging lamp in the cathedral of Pisa led him to the discovery of the isochronism of the pendulum, which theory he utilized fifty years later in the construction of an astronomical clock. In 1588, an essay on the center of gravity in solids obtained for him the title of the Archimedes of his time, and secured him a teaching spot in the University of Pisa. During the years immediately following, taking advantage of the celebrated leaning tower, he laid the foundation experimentally of the theory of falling bodies and demonstrated the falsity of the peripatetic maxim, which is that an objects rate of descent is proportional to its weight. When he challenged this it made all of the followers of Aristotle extremely angry, they would not except the fact that their leader could have been wrong. Galileo, in result of this and other troubles, found it prudent to quit Pisa and move to Florence, the original home of his family. In Florence he was nominated by the Venetian Senate in 1592 to the chair of mathematics in the University of Padua, which he occupied for eighteen years, with ever-increasing fame. After that he was appointed philosopher and mathematician to the Grand Duke of Tuscany. During the whole of this period, and to the close of his life, his investigation of Nature, in all her fields, was never stopped. Following up his experiments at Pisa with others upon inclined planes, Galileo established the laws of falling bodies as they are still formulated. He likewise demonstrated the laws of projectiles, and largely anticipated the laws of motion as finally established by Newton. In statics, he gave the first direct and satisfactory demonstration of the laws of equilibrium and the principle of virtual velocities. In hydrostatics, he set forth the true principle of flotation. He invented a thermometer, though a defective one, but he did not, as is sometimes claimed for him, invent the microscope.

Though, as has been said, it is by his astronomical discoveries that he is most widely remembered, it is not these that constitute his most substantial title to fame. In this connection, his greatest achievement was undoubtedly his virtual invention of the telescope. Hearing early in 1609 that a Dutch optician, named Lippershey, had produced an instrument by which the apparent size of remote objects was magnified, Galileo at once realized the principle by which such a result could alone be attained, and, after a single night devoted to consideration of the laws of refraction, he succeeded in constructing a telescope which magnified three times, its magnifying power being soon increased to thirty-two. This instrument being provided and turned towards the heavens, the discoveries, which have made Galileo famous, were bound at once to follow, though undoubtedly he was quick to grasp their full significance. The moon was shown not to be, as the old astronomy taught, a smooth and perfect sphere, of different nature to the earth, but to possess hills and valleys and other features resembling those of our own globe. The planet Jupiter was found to have satellites, thus displaying a solar system in miniature, and supporting the doctrine of Copernicus. It had been argued against the said system that, if it were true, the inferior planets, Venus and Mercury, between the earth and the sun, should in the course of their revolution exhibit phases like those of the moon, and, these being invisible to the naked eye, Copernicus had to change the false explanation that these planets were transparent and the sun’s rays passed through them. But with his telescope Galileo found that Venus did actually exhibit the desired phases, and the objection was thus turned into an argument for Copernicanism.

Galileo was tried by the Inquisition for his writings discussing the Ptolemaic and Copernican systems. In June 1633, Galileo was condemned to life imprisonment for heresy. His writings about these subjects were banned, and printers were forbidden to publish anything further by him or even to reprint his previous works. Outside Italy, however, his writings were translated into Latin and were read by scholars throughout Europe.

Galileo remained under imprisonment until his death in 1642. However he never was a real prisoner for he never spent any time in a prison cell or being treated like a criminal. Instead he spent his time in fancy apartments. The rest of the time he was allowed to use houses of friends as his places of confinement the, always comfortable and usually luxurious.

Bibliography
1. Drake, S. ,Galileo at Work: His Scientific Biography. Greensborough Press, 1995.

2. Finnochiara, Maurice A. ,The Galileo Affair. The University of California Press, 1989.

3. Redondi, P. ,Galileo Heretic. Princeton, N.J.: Princeton University Press, 1987.

4. Reston, J. Jr. ,Galileo: A Life. HarperCollins Publishing, 1994.

5. Segre, M. ,In the Wake of Galileo. New Brunswick Co., 1992.

6. Sharratt, M. ,Galileo: Decisive Innovator., Sanford Publishing 1994

Carl Gauss was born Johann Carl Friedrich Gauss, on the thirtieth of April, 1777, in Brunswick, Duchy of Brunswick (now Germany). Gauss was born into an impoverished family, raised as the only son of a bricklayer. Despite the hard living conditions, Gauss’s brilliance shone through at a young age. At the age of only two years, the young Carl gradually learned from his parents how to pronounce the letters of the alphabet. Carl then set to teaching himself how to read by sounding out the combinations of the letters. Around the time that Carl was teaching himself to read aloud, he also taught himself the meanings of number symbols and learned to do arithmetical calculations.

When Carl Gauss reached the age of seven, he began elementary school. His potential for brilliance was recognized immediately. Gauss’s teacher Herr Buttner, had assigned the class a difficult problem of addition in which the students were to find the sum of the integers from one to one hundred. While his classmates toiled over the addition, Carl sat and pondered the question. He invented the shortcut formula on the spot, and wrote down the correct answer. Carl came to the conclusion that the sum of the integers was 50 pairs of numbers each pair summing to one hundred and one, thus simple multiplication followed and the answer could be found.

This act of sheer genius was so astounding to Herr Buttner that the teacher took the young Gauss under his wing and taught him fervently on the subject of arithmetic. He paid for the best textbooks obtainable out of his own pocket and presented them to Gauss, who reportedly flashed through them.

In 1788 Gauss began his education at the Gymnasium, with the assistance of his past teacher Buttner, where he learned High German and Latin. After receiving a scholarship from the Duke of Brunswick, Gauss entered Brunswick Collegium Carolinum in 1792. During his time spent at the academy Gauss independently discovered Bode’s law, the binomial theorem, and the arithmetic-geometric mean, as well as the law of quadratic reciprocity and the prime number theorem. In 1795, an ambitious Gauss left Brunswick to study at Gottingen University. His teacher there was Kaestner, whom Gauss was known to often ridicule. During his entire time spent at Gottingen Gauss was known to acquire only one friend among his peers, Farkas Bolyai, whom he met in 1799 and stayed in touch with for many years.

In 1798 Gauss left Gottingen without a diploma. This did not mean that his efforts spent in the university were wasted. By this time he had made on of his most important discoveries, this was the construction of a regular seventeen-gon by ruler and compasses. This was the most important advancement in this field since the time of Greek mathematics.

In the summer of 1801 Gauss published his first book, Disquisitiones Arithmeticae, under a gratuity from the Duke of Brunswick. The book had seven sections, each of these sections but the last, which documented his construction of the 17-gon, were devoted to number theory.

In June of 1801, Zach an astronomer whom Gauss had come to know two or three years before, published the orbital positions of, Ceres, a new “small planet”, otherwise know as an asteroid. Part of Zach’s publication included Gauss’s prediction for the orbit of this celestial body, which greatly differed from those predictions made by others. When Ceres was rediscovered it was almost exactly where Gauss had predicted it to be.

Although Gauss did not disclose his methods at the time, it was found that he had used his least squares approximation method. This successful prediction started off Gauss’s long involvement with the field of astronomy.On October ninth, 1805 Gauss was married to Johana Ostoff. Although Gauss lived a happy personal life for the first time, he was shattered by the death of his benefactor, The Duke of Brunswick, who was killed fighting for the Prussian army.

In 1807 Gauss left Brunswick to take up the position of director of the Gottingen observatory. This was a time of many changes for Carl Gauss. Gauss had made his way to Gottingen by late 1807. The following year his father died, and a year following that tragedy, his wife Johanna died giving birth to their second son, who was to die shortly after her. Understandably Gauss’s life was shattered, he turned to his friends and colleagues for support. The next year, Gauss was married a second time. His new wife was named Minna, she was the best friend of Johanna. Although the couple had three children, this second marriage seemed to be somewhat of a expedience for Gauss.

Gauss’s work was not visibly affected by these life altering events. In 1809, he went on to publish his second book Theoria motus corporum coelestium in sectionibus conicis Solem ambientium. This publishing was a profound two volume thesis on the motion of celestial bodies. Gauss’s contributions in the field of theoretical astronomy continued until the year 1817. Gauss himself continued making observations until the age of seventy.

In 1818, Gauss was asked to carry out a geodesic (a study in which predictions are made of exact points or area sizes of the earth’s surface) survey of the state of Hanover, to link with the existing Danish grid. Gauss eagerly accepted the job, and took personal charge of the survey. He made his measurements by day, and reduced them by night, using his incredible mental ability for calculations. To aid him in his survey, Gauss invented the heliotrope, which worked by reflecting the Sun’s rays using a design of mirrors and a small telescope. But inaccurate base lines used for the survey and an unsatisfactory network of triangles.

Gauss often doubted his work in the profession, but over the course of ten years, from 1820 to 1830, published over seventy papers. From the early 1800’s Gauss had had an interest in the question of the possible existence of a non-Euclidean geometry. In a book review of 1816 Gauss discussed proofs which suggested and supported his belief in non-Euclidean geometry (which was later proved to exist), though he was quite vague. Gauss later confined in one of his fellow theoreticians that he believed his reputation would suffer if he admitted to the public the existence of such a geometry.

The period of time from 1817 to 1832 was a particularly hard time for Gauss. He took in his sick mother, who stayed with him until her death twenty-two years later. At the same time he was in a dispute with his wife and her family about whether they should move to Berlin, where Gauss had been offered a job. Minna, his wife, and hr family were enthusiastic about the move, but Gauss, who did not like change, decided to stay in Gottingen. Minna died in 1831 after a long illness.

In 1832, Gauss and a colleague of his, Wilhelm Weber, began studying the theory of terrestrial magnetism. Gauss was quite enthusiastic about this prospect and by 1840, had written three important papers on the subject. These papers all dealt the current theories on terrestrial magnetism, absolute measure for magnetic force, and an empirical definition of terrestrial magnetism.

Gauss and Weber achieved much in their six years together. The two discovered Kirchoff’s laws, as well as building a primitive telegraph device. However, this was just an enjoyable hobby of Gauss’s. He was more interested in the task of setting up a world wide net of magnetic observation points. This vocation produced a great deal of concrete results. The Magnetischer Verein and its journal were conceived, and the atlas of geomagnetism was published.

From 1850 onwards Gauss’s work was that of nearly all practical nature. He disputed over a modified Foucalt pendulum in 1854, and was also able to attend the opening of the new railway link between Hanover and Gottingen, but this outing proved to be his last. The health of Carl Gauss deteriorated slowly and he died in his sleep early in the morning of February 23, 1855.

Carl Gauss’s influence in the worlds of science and mathematics has been immeasurable. His abstract findings have changed the way in which we study our world. In Gauss’s lifetime he did work on a number of concepts for which he never published, because he felt them to be incomplete. Every one of these ideas (including complex variable, non-Euclidean geometry, and the mathematical foundations of physics) was later discovered by other mathematicians. Although he was not awarded the credit for these particular discoveries, he found his reward with the pursuit of such research, and finding the truth for its own sake. He is a great man and his achievements will not be forgotten.

He found areas and volumes of spheres, cylinders and plain shapes. He showed that the volume of a sphere is two-thirds of the volume of the smallest cylinder that can contain the sphere. Archimedes was so proud of this concept that he requested that a cylinder enclosed a sphere, with an explanation of this concept, be engraved on his grave. Archimedes also gave a method for approximating pi. He was able to estimate the value of pi between 3 10/71 and 3 1/7. Math wasnt as sophisticated enough to find out the exact pi (3.14). Archimedes was finding square roots and he found a method based on the Greek myriad for representing numbers as large as 1 followed by 80 million billion zeros.

One of Archimedes accomplishments was his creation of the lever and pulley system. Archimedes proved his theory of the lever and pulley to the king by moving a ship, of the royal fleet, back into the ocean. Then, Archimedes moved the ship into the sea with only a few movements of his hand, which caused a lever and pulley device to move the ship. This story has become famous because Archimedes said, “Give me a place to stand on and I will move the earth. Another invention he invented was the Archimedean screw. This machine was built for raising water to highland areas in Egypt that could not receive water directly from the Nile River. This device is still used today for irrigation purposes even is some countries today.

The most famous story of Archimedes life involves the discovery of Archimedes’ Principle. The story begins when King Hieron asking a goldsmith to construct a gold wreath to the immortal gods. After some time, the king came to suspect that the wreath was not pure gold but rather filled with silver. In order to end his suspicion, the king asked Archimedes to determine whether the wreath was pure gold or filled with gold without destroying it. Archimedes agreed to try to solve the king’s problem. Then one day, while he was taking a bath, Archimedes noticed that the water level rose in the bath as he entered the water. Archimedes was so excited by this discovery that he jumped out of his bath and ran naked through the streets yelling, “Eureka, Eureka!! meaning, I have found it. Archimedes had discovered that a body immersed in a fluid displaces its weight of fluid. This principle in turn helped Archimedes prove that the gold wreath was not solid gold.

Archimedes was probably most famous during the time he lived because he developed techniques defenses for Syracuse against the Romans. Syracuse was able to hold off the invasion for three years due to Archimedess inventions. He invented catapults, which hurled blocks of stone, and cranes, which dropped large stones on approaching ships. Also, he developed scaling ladders, which helped soldiers climb over enemy walls. Archimedes can use mirrors to reflect sunlight on the adversarial ships burning them.

The Romans finally invaded Syracuse and overtook the city Archimedes was drawing circles in the dirt. When a soldier commanded Archimedes to surrender, Archimedes instead drew his sword and told the soldier that he wanted to finish the proof he was working on before surrendering. The soldier became angry and killed Archimedes. This shows that Archimedes was so committed to his expertise that he took the chance to dying in order to work on his last problem. Archimedes was so thoughtful with the study of math, and because of it, it led to many important discoveries and principles for us today.

What helped me the most were encyclopedias, books and the Internet. I think I got enough information to basically point out the general account of it. I cant really think of anything I can do differently. I learned that Archimedes was a very significant man of his time that was perfected pi, his principles and his inventions. He was far beyond any mans thinking capabilities.