MATH 1)NUMBER SYSTEMS 2)PYTHAGOREAN BROTHERHOOD 3)BOOK 'HOW TO SOLVE Essay

MATH 1)NUMBER SYSTEMS 2)PYTHAGOREAN BROTHERHOOD 3)BOOK 'HOW TO SOLVE IT' 4) JOHN NAPIER - Essay Example Napier was one of the first, if not the first, to use the decimal point in expressing decimal fractions in a systematic way and according to the modern system of decimal notation[1]. The first tables of logarithms were published independently by the Scottish mathematician John Napier in 1614 and the Swiss mathematician Justus Byrgius in 1620. The first table of common logarithms was compiled by the English mathematician Henry Briggs [1]. Henry Briggs (1561-1630) was born at Warley Wood, near Halifax at Yorkshire and educated at St. John's College, in Cambridge. He is notable for changing Napier's logarithms into common/Brigessian Logarithms [2]. In the year 1616, Henry Brigss visited John Napier in his home in Edinburgh to discuss the suggested change to Napier's work [2]. The next year, Henry again visited John regarding the same matter. He proposed the alteration of the scale of logarithms from the hyperbolic 1 / e from which John Napier had given to that which unity is assumed as the logarithm of the ratio of 10 to 1 [2]. During their conversation, the alteration proposed by Briggs was agreed upon by Napier and published the first chiliad of his logarithms du ring his second visit to Edinburgh in 1617. In 1624 Henry Briggs gave a numerical approximation to the base 10 logarithm. The Pythagorean Brotherhood is one of Greece's ancient societies. ... settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism.. There he founded the famous Pythagorean school in the south of Italy, which in addition to being an academy for the study of philosophy, mathematics, and natural science, developed into a closely knit brotherhood with secret rites and observances (Eves, 54). The Pythagoreans adhered to certain mysteries, observed bedience and silence, abstinence from food, simplicity in dress and possessions. The Pythagoreans believed in immortality and in the transmigration of souls. The brotherhood became so great that the democratic forces of the south of Italy destroyed the school buildings and caused the society to disperse (Eves, 55). According to Eves, the Pythagorean philosophy rested on the assumption that whole number is the cause of the various qualities of matter, which led to the exhaltation and study of number properties and arithmetic along with geometry, music and spherics constituted the fundamental liberal arts of the Pythagorean program of study(Eves, 55). The brotherhood dispersed after Pythagoras was said to have died through murder. Although scattered in different places, not only in Italy, the brotherhood continued to exist for at least two (2) more centuries. For the reason that Pythagoras' teaching was entirely oral, and also because of the custom of the brotherhood to refer all discoveries back to the revered founder, it is now difficult to know which mathematical findings should be credited to Pythagoras himself, and which to other members of the society (Eves, 55). How to Solve It How to Solve It is a book in small volume describing the methods in problem solving [3]. George Plya was

Research Assignment Essay Example | Topics and Well Written Essays - 500 words - 1

Research Assignment - Essay Example Tell customers: If you want a V-8 rumble, you’ve gotta buy a V-8 that costs more, gets worse gas mileage and hurts the Earth†¦You’re fabricating the car’s sexiness. You’re fabricating performance elements of the car that don’t actually exist. That just feels deceptive to me† (Brauer cited in Harwell). (Migliore) predicts that V6 engines will be more popular compared to the V8 engines for the 2015 Ford F – 150. The article sums up the benefits provided by V6 engines over V8 engines to back up the prediction; â€Å"In the truck business, its historically been about the most horsepower, the most towing power and the most torque† (Scott cited in Migliore). The main difference between V6 and V8 engine is the number of cylinders. V6 has six cylinders whereas V8 has eight cylinders. The number of cylinders in an engine usually affects the engine’s total displacement volume. Smaller engines they are more cost effective. Since they have less cc, they require less gas to run. However, certain comforts are also offered by bigger engines e.g. more power and better performance, but they require more fuel in order to run the car. Generally, V6 engine provides more economical benefit whereas V8 engine provides more power benefits. Which engine comforts the customers more de pends upon the preferences of the customers. If they are looking for saving, they should go for V6 engines. If they are looking for power and performance, then V8 engines is the choice for them. (Att Training Ltd. and Denton) have introduced a blended learning approach to the engineering of cars in their book. Their book covers all technological and theoretical sections needed by students. Together with ATT online resources, this book offers a comprehensive package comprising video footage, activities, and assessment. They say that the comfort of customers is also determined by their need. If they need larger vehicles, V8 engine would provide them with more comfort whereas if they are looking

Car Difting Essay Example | Topics and Well Written Essays - 500 words

Car Difting - Essay Example I am fascinated by high speed endeavors; high speed car drifting is one of them, though not very many people like or approve it. Car drifting improves my abilities to concentrate and control. I like car drifting because of a host of reasons. Since I was born, I have always liked to express myself in motorsports. I have watched racing movies and racing competitions for so long. I wished time would come when I get to position myself at the steering wheel and maneuver through corners at speeds not many people would dare. When I finally got a car that could enable me to drift with the least negative consequences, I made car drifting a routine activity. My liking is so great that I am willing to overlook the costs of burned tires and damaged car parts. Though it is an extremely dangerous and costly affair, I am always thrilled to step in the car and drift my way around corners or other bent parts of the road. I also like drifting because of it, I have leant many drifting techniques and the physics of racing. The feeling I get when adrenaline is rushing through my blood is great. I’ve always wanted to be in control. I like control that comes from concentrating on a particular activity. Once I realized that car drifting improves my levels of concentration and helps me gain a lot of control in driving, I have never been detached from it. This, among other aforementioned reasons is why I like car drifting even if it is dangerous and non-appealing to the majority of the population. It is clear to me that I not only get thrilled by car drifting, but also learn to control and concentrate. Quite frankly, my judgment derived from car drifting enables me to control other vehicles despite the terrain. I can have my way with many cars as a result of my liking for car drifting. Evidently, my liking for car drifting surpasses the consideration for negative effects of car drifting. This is

Macro Econ Assignment Example | Topics and Well Written Essays - 250 words

Macro Econ - Assignment Example For assistance with your assignment, please use your text, Web resources, and all course materials. Proponents of the benefits of free markets argue that markets create â€Å"efficiency† in the distribution of goods and services. A great example of the increased efficiency in distribution by increasing the scope of market mechanisms is the impact of internet markets in used goods, such as Ebay and Craigslist. Items that might have once only been able to be resold for rock-bottom prices at garage, garden and stoop sales are now valued in a more universal fashion as they find a wider potential market on the web. Items which might be of interest to only a very few people can be much more easily located by these select few customers. In both cases, the consolidation of many small markets into a single large one increases the efficiency of valuation and distribution. On the other hand, the stock market has provided of the pitfalls of market mechanisms, which has fuelled criticism o f markets. The ongoing economic recession was launched when market speculation in real estate caused inflation of home prices and created incentives at every level of the market, from real estate agents, to mortgage brokers to stock sales to sell and buy at prices far beyond the value of the properties or homeowners ability to pay.

Illustrate techniques that influence performance Essay

Illustrate techniques that influence performance - Essay Example These are personalities who like to be sensually animated and sexually roused. They regard eroticism as an abundant source of pleasure and prompt their romanticism through cuddling, tenderness and amorous care. They enjoy living one day at a time and prefer interruption to solemn work. These incoporate people motivated by Financial Incentive strive for a huge pay-off that comes as the fruit of their labor. They need to feel that their income and benefits equal the value of the time and energy they invest in their work. While it is a shared motivator, most people identify with high income earners, (those who do not want to work for peanuts), these individuals place more importance on remuneration than the average worker. This is not to say they are only after the big bucks; their main concern is having the money to afford a specific lifestyle that gives them the drive to succeed. They are willing to invest themselves, but will not do so without significant pay-off (Pandey, 2005). Apart from a desire to make an extremely high salary within a short time to feel happy upon employment, they would also want to see the long-term reward for the personal investment they put into their

The Story of an Hour Essay Example for Free

The Story of an Hour Essay The Story of an Hour is a work of short fiction by southern regionalist writer Kate Chopin. Originally published in Vogue magazine in 1984, this widely read story by Chopin did not receive strong recognition until it was rediscovered during the height of the feminist movement back in the 1960’s. This work of the author greatly reflects and represents Chopin’s personal view on women’s roles in society which very much shocked her reading audience at the time. As a writer, Chopin was highly influenced by the southern environment she grew in. She was raised in a household of intelligent, independent, pioneering women for she was raised by her French-Creole mother and grandmother (who was the first woman in Kansas to be legally separated from her husband) after being orphaned of her father at the young age of four. Toth in her biography notes that Chopin â€Å"†¦also smoked cigarettes in public and revelled in wandering around alone, drinking beer. † Like in many of her other writings, in The Story of an Hour she illustrates to the reader [some of] the concerns faced by women and their plight to have their own identity. The Story of an Hour is a story set in the late 19th century when women’s duties were basically to keep house, bear children and present themselves as faithful loving wives and not much more. It tells the story of a married southern woman, Louise Mallard, who receives news of her husband’s (Brently Mallard) death. Being of frail condition, those around her (sister Josephine and family friend Richards) took great care in gently revealing to her the disastrous news. At first the heroine takes the reception of the news like any other loving wife of the time: with despair and grief. However, when Louise isolates herself from her sister and Richards to deal with her feelings in private, she realizes something quite surprising to herself. To her surprise [and the reader’s], â€Å"a monstrous joy†¦held her† (Chopin) and it was during this moment of epiphany she realizes her overwhelming desire for freedom. Empowered by her new realization, Louise ends her brief isolation and decides to go down from her room to welcome her future filled with â€Å"days that would be her own† (Chopin). However, with a sudden twist of faith, her erroneously reported deceased husband walks into the house to the surprise of everyone. As a result, Louise ended up dying ironically â€Å"of heart diseaseof the joy that kills† (Chopin). This short fiction by Chopin tackles the issue of identity and self-discovery of women. Written in a time where numerous social and ethical questions were in the minds of most Americans, Chopin’s take on the â€Å"Woman Question† proved to be quite controversial for the period. Rejected initially for its feminist message, The Story of an Hour is a prime example of how the author tackles female self-assertion. In the story, the author subtly hints at the social oppression of women. During the period at which the story was originally written, the standards upheld by general society for women were that of selfless wives and mothers. This is reflected in the way the lead character Louise Mallard doesn’t even receive a name at the beginning of the story. She is only referred to as Mrs. Mallard and in pronouns until much later in the story. Ironically her husband Brently, a minor character, is named at the beginning of the story. By the simple omission of Louise’s name early in the story the author manages to imply how women at the time were mere â€Å"property† of men – that they were â€Å"attachments† to their father’s and husbands.

Increase Of Concentration Of Ethyl Acetate

Increase Of Concentration Of Ethyl Acetate Firstly the aim of the experiment is to determine the yield, conversion and reaction rate by employing the principles of material balance with chemical reaction for batch reactions. The purpose of the experiment is to find out the factors affecting the rate of reaction to increases the conversion rate the yield of product produced. The hypothesis of the experiment is that the increase of concentration of Ethyl Acetate would also increase the rate of reaction. From two different concentrations of Ethyl Acetate (0.01M and 0.02M) have shown that the 0.02M of Ethyl Acetate shows a increase in the rate of reaction and conversion rate of Sodium Hydroxide to Sodium Acetate. Secondly the theory part shows the definitions of terms like saponification, batchwise reactions and factors that affect the rate of reaction. The most important definition is the saponification which is the hydrolysis of an ester under basic conditions to form an alcohol and the salt of a carboxylic acid. Thirdly, the procedure section shows how to carry out the 3 major steps which are preparation of the reactant, the experimental setup and the procedures to carry out the experiment. This is followed by the results and calculations which is about the calculation of the conversion percentage and yield of the reactions of different concentrations of Ethyl Acetate carried out in the experiment. After the results and calculations, is the discussion part which discusses the results obtained, states some precautions to be taken while carrying out the experiment and the factors that affect the results. Lastly the conclusion concludes the report by stating if the aim of the experiment had been reached and it also states that the hypothesis that the higher the concentration of the reactant, the faster the rate of reaction and conversion, has been proven. REPORT ON MATERIAL BALANCE WITH CHEMICAL REACTION 1. Introduction 1.1 Background Literature Conversion of sodium hydroxide into sodium acetate is called saponification. It is the process of making soap. It is the reaction between an ester with a metallic base and water. It is also related to the process used to convert natural fats into soap. (Donohue 2009) An alkali is a soluble salt of an alkali metal like sodium. It is used in soap-making whereby it was obtained from the ashes of plants. Now, the term alkali describes a base which neutralizes an acid. (Donohue 2009) Alkalis used in soap making are sodium hydroxide (NaOH), also called caustic soda; and potassium hydroxide (KOH), also called caustic potash. (Donohue 2009) Example: An example of the reaction is: (Therese Lotts Saponification Calculator Standalone spreadsheet for calculating saponification values in handmade soapmaking. ) (http://www.freepatentsonline.com/6751527.html) 1.2 Aim The aim of this experiment is to determine the yield, conversion and reaction rate by employing the principles of material balance with chemical reaction for batch reactions. This will also enable us to find out factors to improve the yield and the rate of conversion and reaction. 1.3 Hypothesis The hypothesis of the experiment is that if the concentration is high, the yield together with the rate of conversion and reaction would also increase. Thus, from a 0.02M concentration of Ethyl Acetate and 0.01M concentration of Ethyl Acetate, the 0.02M concentration would have a higher yield, rate of conversion and reaction. This is because at the start of the experiment the conductivity value was high but as the reaction precedes the conductivity value decreases showing the concentration and number of moles. 2. Theory 2.1 Saponification Saponification is the hydrolysis of an ester under basic conditions to form an alcohol and the salt of a carboxylic acid. Saponification is commonly used to refer to the reaction of a metallic alkali with a fat or oil to form soap. Saponifiable substances are those that can be converted into soap. In the experiment the desired product is sodium acetate. (Donohue 2009) 2.2 Batchwise Reaction A batchwise reaction is a reaction where by reactants are put in and the reaction is started. After the reaction has ended, the products are taken out and the equipment and all are washed to be prepared for the next experiment. Unlike steady state reaction it does not have a continuous input and output. (Singapore Polytechnic 2009) 2.3 Percentage Conversion Xa = moles of A reacted Moles of A fed into the reactor x100% It is defined as a fraction of reactants or feed that successfully reacted to form the desired product. The above formula calculates the amount of reacts converted into products. (Singapore Polytechnic 2009) 2.4 Yield of A Product YP = Moles of desired product formed Moles of reactant fed into the reactor Yield has 3 definitions. Firstly it is amount of desired product formed based on the amount of limiting reactants feed into the reaction. Secondly it is the amount of desired product obtained divided by the amount of reactant consumed. Lastly, it is also defined as the amount of product obtained divided by the theoretically amount of limiting reactant consumed. The above reaction calculates the amount yield based on just the limiting reactant. (Singapore Polytechnic 2009) 2.5 Rate of Reaction The rate of reaction is the amount of time taken for the chemicals to react totally. (Singapore Polytechnic 2009) 2.6 Surface Area To Volume Ratio The surface area to the volume ration affects the rate of reaction. The smaller the particle, the larger its exposed surface area. With a larger exposed surface area more particles can collide with one another causing more reactions to take place within a shorter amount of time. (Purchon 2006) 2.7 Presence of a Catalyst If a catalyst is involved in a reaction, the amount of energy needed to start the reaction (activation energy) decreases. Thus, the molecules in the reactions will gain more energy that is equal to or more than the activation energy. The higher amount of energy a molecules has, the more active it will become and more collisions will occur increasing the rate of reaction. However a catalyst is not involved in this experiment. (Purchon 2006) 2.8 Pressure Pressure is another factor that affects the rate of reaction. Pressure mainly affects gases. Gases can be compressed. Thus, as pressure increases, gaseous molecules are closely packed together which allows them to collide more frequently with one another. This is almost the same as changing the concentration as the number of molecules is increased within a specific area. However the reaction is a liquid-liquid reaction so pressure does not affect the reaction in this experiment. (Purchon 2006) 2.9 Concentration Concentration affects the rate of reaction. The higher the concentration, the number of particles within a specific area increases. Thus, molecules are closely packed together and this increases the number of collisions between molecules so the rate of reaction increases. Concentration is similar to pressure where by the number of molecules in a specific area increases. (Purchon 2006) 2.10 Temperature Temperature also affects the rate of reaction. If the temperature is higher, the energy levels of the molecules increases and they would tend to more faster. Thus, this results in more effective collisions in a shorter amount of time. (Purchon 2006) 2.11 Conductivity Unlike Sodium Hydroxide, Ethyl acetate, Ethanol and Sodium acetate have negligible conductivity. Thus the conductivity value of the reaction is measured by the conductivity of Sodium Hydroxide. The conductivity is used to find the concentration of Sodium Hydroxide as the reaction proceeds. (Singapore Polytechnic 2009) Fig.1) Graph of conductivity values of Sodium Hydroxide against the concentration of Sodium Hydroxide.) 3. Procedure 3.1 Preparation of chemicals The MSDS of sodium hydroxide and ethyl acetate was read and the handling and disposal of the chemicals must be familiarized before the start of the experiment. Disposable gloves and chemical goggles were put on when preparing and handling the chemicals.500 ml of 0.01 M sodium hydroxide solution and 500 ml of ethyl acetate solution to the required concentration as discussed in Questions 1 and 2 of Pre-experiment Assessment was prepared. (CP4047 Lab Manual) 3.1.1 Preparing 500 ml of 0.01 M sodium hydroxide solution: The required volume of 0.1 M NaOH stock solution was measured using a measuring cylinder and pour into the 500 ml volumetric flask. The solution in the volumetric flask was topped up with de-ionized water to the 500 ml-mark. A Stopper was placed on the flask, and it was shaken and inverted to mix the solution. (CP4047 Lab Manual) 3.1.2 To prepare 500 ml of ethyl acetate solution: About 250 ml de-ionized water was poured into a 500 ml volumetric flask first. The required volume was measured using the micropipettor. The stock solution was dispensed into the 500 ml volumetric flask.The solution in the volumetric flask was topped up to the 500 ml-mark. A stopper was placed on the flask, and was shaken and inverted to mix the solution. (CP4047 Lab Manual) 3.2 Experimental setup (CP4047 Lab Manual) 3.3 Carrying out the Experiment The prepared sodium hydroxide solution was poured into the reactor. The reaction conditions were adjusted to the predetermined levels (based on experimental methodology discussed with Lecturer). The reaction conditions were recorded, Eg. temperature, stirring speed, concentrations and volumes of reactants. Conductivity meter probe was positioned into the reacting mixture. The ethyl acetate solution was poured in and the timer was started immediately. The conductivity values (mS/cm) at a regular interval of 1 minute for 30 minutes of reaction time was recorded. After 30 minutes of reaction, the stirring device was stopped and the magnetic stir bar was removed from the mixture using the magnetic rod. The conductivity probe was also removed and rinsed thoroughly with de-ionised water. The reaction product mixture was poured into the plastic waste container. The glassware was rinsed and the experiment was repeated based on experimental methodology discussed with the Lecturer. At the end of the experiment, the conductivity probe was removed from the reacting mixture and rinsed thoroughly with de-ionised water. All chemicals were disposed in the plastic waste container and were brought to the waste together with any unused reactants to W314 for proper treatment and disposal. All the used glass-wares was rinsed and tidied up the work space. (CP4047 Lab Manual) 4. Results and Calculations 4.1 Determining the Yield of Sodium Acetate at 15 Minutes The yield of Sodium Acetate at 15minutes is determined with the concentration of Sodium Hydroxide as with the concentration, the number of mole of sodium hydroxide can be found out. Also, with the molar ratio of Sodium Hydroxide and Ethyl Acetate, the number of moles of Ethyl Acetate can be determined. With the use of the yield formula, the yield of Ethyl Acetate can be calculated. 4.2 Yield When 0.01M of Ethyl Acetate Used 5. Discussion 5.1 Factors Affecting Rate of Reaction Firstly the concentrations of Ethyl Acetate used were 0.01M and 0.02M which means that for 0.01M of Ethyl Acetate was obtained by diluting 0.49cm3 of pure Ethyl Acetate and 0.02M was obtained by diluting 0.92cm3 of pure Ethyl Acetate. By comparing the graphs (Fig 3 and 4) above, the reaction (0.02M) was the fastest. This was due to the concentration factor. The higher the concentration, the faster the rate of reaction as the increase in concentration means that there are more molecules in a specific area. Other factor like temperature and pressure were keep at a constant (standard room conditions). There was no catalyst involved the experiment. Thus, these other factors did not affect the rate of reaction. 5.2 Factors Affecting Conversion and Yield The conversion of Sodium Hydroxide and the yield of Sodium Acetate will never be a 100% due to the technical equipment and unforced human errors. It is also due to constrains in the lab like equipment or the duration of the experiment. The longer the reaction, more conversion and yield could have been produced. 5.3 Factors Affecting the Conductivity Values The concentration of Sodium Hydroxide affects the conductivity value of the reaction. If the concentration of Sodium Hydroxide is high, the conductivity value will also be high. Thus, as the reaction proceeds, the conductivity drops as the concentration of the Sodium Hydroxide decreases as it is being reacted away. For the 0.01M reaction, Fig 4.2.2 show that the concentration decreases significantly. However, for the 0.02M reaction, Fig 4.3.2 shows some fluctuations in the drop of the concentration of Sodium Hydroxide. This could be because of the equipment. The equipment, the conductivity probe and the machine has been known to turn off randomly during the reaction. Thus there was some irregularities in the drop of concentration for the 0.02M reaction. 5.4 Precautions to Be Taken During the experiment the Ethyl Acetate should always be handled in the fume hood as it would decompose in the open, thus affecting the concentration of the Ethyl Acetate and to prevent it from spilling anywhere else in the laboratory. Gloves should also be worn to prevent bacteria from contaminating the reaction or chemicals and to also protect our hands from the chemicals. Goggles should also be worn to protect our eyes from chemicals splashing into our eyes. 5.5 Comparison of conversion and yields of different concentration of Ethyl Acetate The yield of the reaction of 0.01M Ethyl Acetate is 0.62 while the yield of the reaction of 0.02M Ethyl Acetate is 0.76. The second reaction of 0.02M has a higher yield due to the higher concentration of Ethyl Acetate. This is because the concentration of the reactants is more due to the increase in concentration of Sodium Hydroxide thus, producing more products whereby the yield of Sodium Acetate increases. However both the experiments did not produce a 100% yield because of human error and constrains of technical equipment. Even if a catalyst was added, the yield will be the same as the catalyst will only increase the rate of reaction and affect the yield. 6. Conclusion In conclusion, the higher the concentration of Ethyl Acetate used, the faster the rate of reaction together with a higher conversion percentage of Sodium Hydroxide. The concentration of Sodium Hydroxide affects the conductivity values of the reaction because the results show that the conductivity decreases as the reaction proceeds because the concentration of Sodium Hydroxide also decreases as the Sodium Hydroxide was being reacted away. Therefore, the hypothesis is proven to be true. The aim of the experiment was met as results state that with a higher concentration of Ethyl Acetate, the rate of reaction together with the rate of conversion increases. The concentration of the Ethyl Acetate reacting with Sodium Hydroxide in a reactor as time passes by was studied. However the experiment could be improved by adding in a catalyst or increasing the temperature to increase the rate of reaction and conversion rate.