Geometry And Mathematics In The Renaissance

Geometry And Mathematics In The Renaissance Renaissance is one of the historical ages that truly had an impact on the modern civilization in terms of development in education, design and many other fields and also it did not ignore presenting out the most important figures during this age which had the same impact on modern civilization. This period of age started from the 14th century and ended on the 17th century starting in Florence in Italy and ending to the rest of Europe. Filippo Brunelleschi was one of its most important figures, shortly, the Renaissance style started to spread across Italian cities and some other countries like France, Germany, England, Russia and other parts of Europe at different dates and with varying degrees of impact. This paper will be discussing the impact of Renaissance on the development of mathematics and geometry in the modern age, its relation and the important figures that truly had an impact on this period. It will also discuss the important drawings and buildings that got affected by suc h innovations in this period of time. Renaissance is one of the periods that had an impact on mathematic and geometry due to the brilliant figures that have been in this period of time which will be discussed in this paragraph. First of all, Geometry is simply a branch of mathematics that is concerned with shapes, size, position of figure, and properties of a space like for example, a square have a property of the flat equal-distance lines from all sides that gives it, its shape and the same goes for the other shapes like rectangle, hexagon, circle etcà ¢Ã¢â€š ¬Ã‚ ¦Mathematics in general is the study of any types of structure, a space like a house, any designs etc., changes in velocity of an object, in general, anything that has to do with equations and calculations is categorized under mathematics. The most important figures that appeared in this period of age and had a true impact on Geometric and mathematics are Filippo Brunelleschi dating from 1377 1446 he is the inventor of the mathematics of perspective in painti ng. Paolo dal Pozzo Toscanelli dating from 1397-1482 creating a huge sundial and making astronomical calculations and also giving a higher accuracy in calculating latitude at the sea and luca pacioli who wrote a number of theories and developed the geometrical proportions. (Fletcher, 2000-11) Renaissance buildings heavily relied on the use of geometry and the mathematics in their design which heavily impacted other modern designs till now. Renaissance type of buildings relied on curves, arches, triangle, circles and squares, which are the main elements of geometry, also needs to be defines as buildings like churches, castles and much more relied on those basic elements and developed it into arches, domes, rectangular segments inside and outside the buildings as many floor plans could describe it. Renaissance building construction and how it was affected by such basic elements of geometry. The Renaissance great thinkers took the human being as a model for the universe being the perfect being made by god and used it in geometry and mathematics. This idea was developed by simply drawing this perfect figure which is the Vitruvian man standing in a square figure stretching his arms and legs forming a perfect circle around him. Based on these ideas, Leonardo made his own drawings based on the use of human proportions and the Vitruviuss theory. In the renaissance age, it was their aim to put such ideas developed into practice in real buildings .What was done is that he blended the use of circles and squares much in his general layout of his plan and in the plan itself he divided it further into spaces through the use of columns plus having the advantage of supporting the roof and as for the circular part, he used it to act as a domes which was one of the most important figures in th is period of time which gives the building its texture and unique style. In this drawing, Leonardo made some adjustments to the Vitruvius measurement of the human figure which was inspired by his own studies and observation. Finally after adjustments and his own studies, he created the perfect image of the human figure with the best proportions. Leonardo had the belief that god was the perfect geometer and the one who created the universe based on proportions and numbers, he believed that the human body was one of his perfect creation, based on Leonardos thought, he drawn the Vitruvian man stretching his own legs and arms to form a perfect revolving circle around him and a square. However, in order to make this work, he had to place the circle centered but the center on the square is a bit lower. Through adjustments and researches of his own measurements based on studies of life models, the Vitruvian figure is not recognized as an ideal image and proportion of the human body. Proportion is not only to be found in numbers and measures, but also in sounds, weights, intervals of time, and in every active force in existence. stated by Leonardo da Vinci (University of the Arts). The development of mathematics and calculations in the renaissance period is for sure one of the most important matters in this age. During the Renaissance, mathematicians and artists wrapped their arms around the questions of perspective, infinity, symbolic algebra and quartic equations, producing treatises on these subjects and offering fresh insights into the field of mathematics. The 15th through 17th centuries saw mathematical innovations in European countries like France and Italy, the impact of which extends to this day. These calculations were divided into different categories such as: Analysis vs. synthesis where the Renaissance saw the advancement of symbolic algebra. In his Artem Analyticem Isogoge of 1591, Franà §ois Vià ©te took the ideas of Ancient Greeks Euclid, Diophantus and Pappus and sought to explain and clarify them through systematic algebraic notation. In doing so he could explain the concepts of analysis and synthesis. Analysis, or an assumption of something that is looked for and the arriving at something admitted to be true through its consequences, was to be distinguished from synthesis, which is an assumption of something that is admitted (conceded) and the arriving at something admitted to be true through its consequences. Moreover, he applied rules for calculating species Vià ©te further established rules for species, as opposed to numerical calculations. His first rule stipulates to add a magnitude to a magnitude, or to add only homogeneous magnitudes, such as apples to apples; his third and fourth rules instruct to multiply and divide magnitudes, respectively, which will result in heterogeneous kinds. For example, a side multiplied by a side is a plane, not another side. Expressed through species, operators and units, equations could now be handled more easily. Also, in the development of equations, cubic and quartic was main ingredients Two breakthroughs during the Renaissance in mathematics involved the solving of both cubic and quartic equations, which had beguiled mathematicians before and during the Renaissance. Although the work was not his own, Girolamo Cardano is credited with giving general solutions to both types of equations in the form of radicals. Previously, equations of the second degree were solved in this manner, but not cubic or higher equations. He published these findings in his work, Artis Magnae, in 1545. Finally, the imaginary and complex numbers, another advance for mathematics during the Renaissance period was the acknowledgment of the validity of imaginary or complex numbers. Cardano, in solving cubic equations, came upon the appearance of negative numbers under the radical sign. Predecessors either brushed these aside or were not able to solve such numbers. Cardano, although he incorporated these numbers in his calculations, admitted that he did not fully understand them. Nonetheless, his work with these new numbers brought mathematics to a higher level of abstraction. After knowing the impact of mathematics and geometry in this period of time, renaissance did also impact modern age building design even though this period of age is so old but till nowadays it still impact us not in the design of the faà §ade but in certain designs. We can see how did the Renaissance influenced architecture and its design all around us. The Use of symmetry, columns, and balance of windows in modern architecture, whether at a bank or courthouse, or even in an expensive home, all point to the influences of Renaissance architecture on modern buildings. Hence to effectively study the influence of Renaissance architecture on more modern architecture one should begin by more closely examining the elements and impact of Renaissance architecture and how those elements have been incorporated into architecture today. Renaissance architecture followed the Gothic period of architecture, which gave us the cathedral at Notre Dame, and was succeeded by the Baroque period, which i s marked by highly ornate architectural designs and furnishings, and is often associated with the King Louis of France. The Renaissance period strongly emphasized the following elements: Geometry which relied on having buildings, windows, and doors in square and rectangular shapes. Proportion, balance was critical in the Renaissance, and elements of the structure needed to be designed in proportion to other elements of the building. Symmetry relied on the use of geometric figures came an emphasis on symmetry and clean lines. Regularity which means that there is a little about the Renaissance style that is random or impulsive. A building must have recurring themes and elements. To accomplish these design goals, the Renaissance style employs many recurring elements, including: Columns, Pilasters, Lintels, Arches and arcades, Domes, Symmetrical windows and doors and finally Niches with sculptures. Each of these elements is used in proportion and with much attention given to order and balance. Influence of the renaissance period came strongly in the 18th and early 19th centuries, which still many of these buildings still stand till today. Even later, in the 20th century, architects are reverting back to Renaissance designs when building grand homes much like the palaces found in Renaissance Italy and France. Various aspects of modern architecture find their roots in the Renaissance style. The features can include: Cube-shaped structure, Symmetrical faà §ade, Smooth stone walls, made from finely-cut stone or with smooth stucco, Low-pitched roof, Roof topped with balustrade, Wide eaves with large brackets, Horizontal stone banding between floors, Segmental pediments, Ornately-carved stone window trim varying in design at each story, Smaller square windows on top floor and Quoins (large stone blocks at the corners). (What Influence Has Renaissance Architecture had on More Modern Architecture, 2011) We could also see many of these elements every day, all around you. Nowadays, designers do seek to blend the use of columns and style that dated 600 years old to use it till now . Finally, to sum up, Renaissance time period showed a great improvement in the geometric and its use in the buildings as described in the paper and also the mathematical calculations used and how they were innovated and the name of the scientists who developed it. Moreover, we truly see the impact of geometry and proportions of space applied in their designs and how they made use of the basic elements such as circle, square, line etcà ¢Ã¢â€š ¬Ã‚ ¦which later on impacted the modern age designs

Environment Pollution Essay

As you know, China is well known on its 5000 years history, and it’s also famous for producing poisonous food and the worst environment pollution. Living in a developing country, Chinese develop industry and handicraft industry, and making money as much as they can. Compare with environment pollution, Chinese business man more care about how much money they could make per day. There are millions of factories in China mainland. And thousands of factories are being built right now. Before factories were built, owner or designer usually choose the factory location which nearby the river or lake. Locals usually drink and take water from the river or lake. Some rivers even provide water to several cities. Usually, an industry factory could produce poisonous waste water 350 m? /h and exhaust gas or smog 14000m? /h. But each factory could treat poisonous waste water 30m? /h. that means over 300m? /h poisonous waste water cannot be treated and be discharged into river or lake. In each factory, the equipment for exhaust treatment is required, but the most factories discharge exhaust treatment into air without treatment. Industry community usually is the high incidence area of cancer and oaf. Animals which are living nearby or living in the rivers and lakes, are bigger or with strange appearance. Farmers who are local, usually take water from river or lack for irrigation and raising livestock. Locals get disease on drinking poisonous water, eating poisonous food, and breathing in seriously polluted area. In China, living healthier become people’s dream and hope. Everybody hopes long live and having a healthy life. Over 70% Chinese are not covered by health insurance, and medical bill is going higher and higher, over 85% locals cannot handle it. People usually stay at home and wait for death when they get disease. Living in polluted area make people more worry about their descendants. People start to move to foreign country for a better environment. Let descendants have a chance to live in a healthier living environment also become their goal.

The Insider Secret on Revise Essays Online Revealed

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World War II in the Pacific - New Guinea, Burma, China

Previous: Japanese Advances Early Allied Victories World War II 101 Next: Island Hopping to Victory The Japanese Land in New Guinea In early 1942, following their occupation of Rabaul on New Britain, Japanese troops began landing on the north coast of New Guinea. Their objective was to secure the island and its capital, Port Moresby, in order to consolidate their position in the South Pacific and provide a springboard for attacking the Allies in Australia. That May, the Japanese prepared an invasion fleet with the goal of attacking Port Moresby directly. This was turned back by Allied naval forces at the Battle of the Coral Sea on May 4-8. With the naval approaches to Port Moresby closed, the Japanese focused on attacking overland. To accomplish this, they began landing troops along the islands northeast coast on July 21. Coming ashore at Buna, Gona, and Sanananda, Japanese forces began pressing inland and soon captured the airfield at Kokoda after heavy fighting. Battle for the Kokoda Trail The Japanese landings preempted Supreme Allied Commander, Southwest Pacific Area (SWPA) General Douglas MacArthurs plans for using New Guinea as a platform for attacking the Japanese at Rabaul. Instead, MacArthur built up his forces on New Guinea with the goal of expelling the Japanese. With the fall of Kokoda, the only way to supply Allied troops north of the Owen Stanley Mountains was over the single-file Kokoda Trail. Running from Port Moresby over the mountains to Kokoda, the trail was a treacherous path that was seen as an avenue of advance for both sides. Pushing his men forward, Major General Tomitaro Horii was able to slowly drive the Australian defenders back up the trail. Fighting in terrible conditions, both sides were plagued by disease and a lack of food. Upon reaching Ioribaiwa, the Japanese could see the lights of Port Moresby but were forced to halt due to a lack of supplies and reinforcements. With his supply situation desperate, Horii was ordered to withdraw back to Kokoda and the beachhead at Buna. This coupled with the repulse of Japanese attacks on the base at Milne Bay, ended the threat to Port Moresby. Allied Counterattacks on New Guinea Reinforced by the arrival fresh American and Australian troops, the Allies launched a counteroffensive in the wake of the Japanese retreat. Pushing over the mountains, Allied forces pursued the Japanese to their heavily defended coastal bases at Buna, Gona, and Sanananda. Beginning on November 16, Allied troops assaulted the Japanese positions and in bitter, close-quarters, fighting slowly overcame them. The final Japanese strongpoint at Sanananda fell on January 22, 1943. Conditions in the Japanese base were horrific as their supplies had run out and many had resorted to cannibalism. After successfully defending the airstrip at Wau in late January, the Allies scored a major victory at the Battle of the Bismarck Sea on March 2-4. Attacking Japanese troop transports, aircraft from SWPAs air forces managed to sink eight, killing over 5,000 soldiers that were en route to New Guinea. With momentum shifting, MacArthur planned a major offensive against the Japanese bases at Salamaua and Lae. This attack was to be part of Operation Cartwheel, an Allied strategy for isolating Rabaul. Moving forward in April 1943, Allied forces advanced towards Salamaua from Wau and were later supported by landings to the south at Nassau Bay in late June. While fighting continued around Salamaua, a second front was opened around Lae. Named Operation Postern, the attack on Lae began with airborne landings at Nadzab to the west and amphibious operations to the east. With the Allies threatening Lae, the Japanese abandoned Salamaua on September 11. After heavy fighting around the town, Lae fel l four days later. While fighting continued on New Guinea for the rest of the war, it became a secondary theater as SWPA shifted its attention to planning the invasion of the Philippines. The Early War in Southeast Asia Following the destruction of Allied naval forces at the Battle of the Java Sea in February 1942, the Japanese Fast Carrier Strike Force, under Admiral Chuichi Nagumo, raided into the Indian Ocean. Hitting targets on Ceylon, the Japanese sank the aging carrier HMS Hermes and forced the British to relocate their forward naval base in the Indian Ocean to Kilindini, Kenya. The Japanese also seized the Andaman and Nicobar Islands. Ashore, Japanese troops began entering Burma in January 1942, to protect the flank of their operations in Malaya. Pushing north towards the port of Rangoon, the Japanese pushed aside British opposition and forced them to abandon the city on March 7. The Allies sought to stabilize their lines in the northern part of the country and Chinese troops rushed south to aid in the fight. This attempt failed and the Japanese advance continued, with the British retreating to Imphal, India and the Chinese falling back to the north. The loss of Burma severed the Burma Road by which Allied military aid had been reaching China. As a result, the Allies began flying supplies over the Himalayas to bases in China. Known as The Hump, the route saw over 7,000 tons of supplies cross it each month. Due to the hazardous conditions over the mountains, The Hump claimed 1,500 Allied aviators during the war. Previous: Japanese Advances Early Allied Victories World War II 101 Next: Island Hopping to Victory Previous: Japanese Advances Early Allied Victories World War II 101 Next: Island Hopping to Victory The Burmese Front Allied operations in Southeast Asia were perpetually hampered by a lack of supplies and the low priority given the theater by Allied commanders. In late 1942, the British launched their first offensive into Burma. Moving along the coast, it was quickly defeated by the Japanese. To the north, Major General Orde Wingate began a series of deep penetration raids designed to wreak havoc on the Japanese behind the lines. Known as Chindits, these columns were supplied entirely by air and, though they suffered heavy casualties, succeeded in keeping the Japanese on edge. Chindit raids continued throughout the war and in 1943, a similar American unit was formed under Brigadier General Frank Merrill. In August 1943, the Allies formed the Southeast Asia Command (SEAC) to handle operations in the region and named Admiral Lord Louis Mountbatten as its commander. Seeking to regain the initiative, Mountbatten planned a series of amphibious landings as part of a new offensive, but had to cancel them when his landing craft were withdrawn for use in the Normandy invasion. In March 1944, the Japanese, led by Lieutenant-General Renya Mutaguchi, launched a major offensive to take the British base at Imphal. Surging forward they encircled the town, forcing General William Slim to shift forces north to rescue the situation. Over the next few months heavy fighting raged around Imphal and Kohima. Having suffered high numbers of casualties and unable to break the British defenses, the Japanese broke off the offensive and began retreating in July. While the Japanese focus was on Imphal, US and Chinese troops, directed by General Joseph Stilwell made progress in northern Burma. Retaking Burma With India defended, Mountbatten and Slim began offensive operations into Burma. With his forces weakened and lacking equipment, the new Japanese commander in Burma, General Hyotaro Kimura fell back to the Irrawaddy River in the central part of the country. Pushing on all fronts, Allied forces met with success as the Japanese began giving ground. Driving hard through central Burma, British forces liberated Meiktila and Mandalay, while US and Chinese forces linked up in the north. Due to a need to take Rangoon before the monsoon season washed away the overland supply routes, Slim turned south and fought through determined Japanese resistance to take the city on April 30, 1945. Retreating east, the Kimuras forces were hammered on July 17 when many attempted to cross the Sittang River. Attacked by the British, the Japanese suffered nearly 10,000 casualties. The fighting along the Sittang was the last of the campaign in Burma. The War in China Following the attack on Pearl Harbor, the Japanese launched a major offensive in China against the city of Changsha. Attacking with 120,000 men, Chiang Kai-Sheks Nationalist Army responded with 300,000 forcing the Japanese to withdrawal. In the wake of the failed offensive, the situation in China returned to the stalemate that had existed since 1940. To support the war effort in China, the Allies dispatched large amounts of Lend-Lease equipment and supplies over the Burma Road. Following the capture of the road by the Japanese, these supplies were flown in over The Hump. To ensure that China remained in the war, President Franklin Roosevelt dispatched General Joseph Stilwell to serve as Chiang Kai-Sheks chief of staff and as commander of the US China-Burma-India Theater. Chinas survival was of paramount concern for the Allies as the Chinese front tied down large numbers of Japanese troops, preventing them from being used elsewhere. Roosevelt also made the decision that US troops would not serve in large numbers in the Chinese theater, and that American involvement would be limited to air support and logistics. A largely political assignment, Stilwell soon became frustrated by the extreme corruption of Chiangs regime and his unwillingness to engage in offensive operations against the Japanese. This hesitancy was largely the result of Chiangs desire to reserve his forces for fighting Mao Zedongs Chinese Communists after the war. While Maos forces were nominally allied with Chiang during the war, they operated independently under Communist control. Issues Between Chiang, Stilwell, Chennault Stilwell also butted heads with Major General Claire Chennault, the former commander of the Flying Tigers, who now led the US Fourteenth Air Force. A friend of Chiangs, Chennault believed that the war could be won through air power alone. Wishing to conserve his infantry, Chiang became an active advocate of Chennaults approach. Stilwell countered Chennault by pointing out that large numbers of troops would still be required to defend US airbases. Operating parallel to Chennault was Operation Matterhorn, which called for the basing of new B-29 Superfortress bombers in China with the task of striking the Japanese home islands. In April 1944, the Japanese launched Operation Ichigo which opened a rail route from Beijing to Indochina and captured many of Chennaults ill-defended airbases. Due to the Japanese offensive and the difficulty in obtaining supplies over The Hump, the B-29s were re-based to the Marianas Islands in early 1945. Endgame in China Despite having been proven correct, in October 1944, Stilwell was recalled to the US at Chiangs request. He was replaced by Major General Albert Wedemeyer. With the Japanese position eroding, Chiang became more willing to resume offensive operations. Chinese forces first aided in evicting the Japanese from northern Burma, and then, led by General Sun Li-jen, attacked into Guangxi and southwestern China. With Burma retaken, supplies began to flow into China allowing Wedemeyer to consider larger operations. He soon planned Operation Carbonado for the summer of 1945, which called for an assault to take the port of Guandong. This plan was cancelled following the dropping of the atomic bombs and Japans surrender. Previous: Japanese Advances Early Allied Victories World War II 101 Next: Island Hopping to Victory