Euler number theory has been an interesting topic as it is complex and difficult to understand. To make this topic easy to understand for me, I decided to explore Euler number. Euler number is used in many different situations like trigonometry, logarithms and my favourite integration. These are some areas which we have studies in IB Math SL. There is more importance to Euler number than the IB curriculum has taught me. This is one reason I wanted to explore this topic.
The concept of irrational numbers and their usage makes the topic more interesting to me. Moreover, Euler e is one irrational number which is equal to its derivative and integral. Math has surrounded the world with calculation and there we have
Introduction:
Originally e was constantly used by many mathematicians in 17th and 18th century. It was denoted by Swiss mathematician, Leonhard Euler as e.
Constant e= 2.71828182845904523536028747135266249775724709369995…
The history of e starts with John Napier who aimed to simplify logarithms multiplication into addition. Today, this is almost equivalent to
y=log_bx and only if b^y=x
Constant e is also the base of all logarithms Gottfried Leibniz, in his works identified constant e as b. however; Leonhard Euler used e as constant in his works. Moreover, he brings the relevance of constant e in application and host. This application is in modern mathematic and choice of symbol e is said to have been retained in his honour. Importance of constant e is alongside 0, 1, π and symboli. Alongside, there are other alphabets which have values like π, γ and symbol e. π and constant e are irrational numbers. However, difference between π and constant e is that π is used in basic maths. Whereas, constant e is used in mor...
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...den ratio. Constant e can be represented in continued fraction which gives some more realistic data. The usage of constant e is been diversified to different field with different mathematicians and scientists; Leonhard Euler using word e for all his works then Jacob looking for the numerical value of constant e.
Bibliography
http://formulas.tutorvista.com/physics/decay-formula.html radioactive
http://en.wikipedia.org/wiki/E_(mathematical_constant)
http://prezi.com/czaf7e8kgkm-/the-mathematical-constant-e/
http://math.stackexchange.com/questions/28558/what-do-pi-and-e-stand-for-in-the-normal-distribution-formula
http://www.mathsisfun.com/money/compound-interest-periodic.html
http://en.wikipedia.org/wiki/Exponential_function
"The Normal Distribution." MATHEMATICS STANDARD LEVEL. Ed. Fabio Cirrito. 4th ed. N.p.: IBID, n.d. 521-34. Print.
In many applications, the natural base e is the most convenient base in an exponential equation. The value e is approximately 2.718281828. The natural base e works exactly like any other base. It is easy to think of e as a substitution for a in f (x) = ax. Its graph looks as so:
In the beginning of the course, we discussed “NGD”. The two areas of “NGD” that we focused on were number and geometry. Number is discrete, finite, time, or sound. Geometry is continuous, infinite, space, or vision. Bronowski mentioned how “it’s said that science will dehumanize people and turn them into numbers” (374). This tragically became true during the Holocaust where people were no longer considered human beings, but rather numbers. We discussed various mathematical topics concerning numbers like the well-ordering pair. In the well-ordering pair, ever subset has a least member. There are also figurative numbers, squared numbers, and even Pythagorean triples.
Leonhard Euler was born in Basel, Switzerland as the first born child of Paul Euler and Marguerite Brucker on April 15, 1707. Euler’s formal education started in Basel where he was sent to live with his maternal grandmother on his father’s orders. Euler's father wanted his son to follow him in working for the church and sent him to the University of Basel to prepare him in becoming a pastor. He entered the University in 1720 to gain general knowledge before moving on to more advanced studies. Euler’s pastime was used for studying theology, Greek, and Hebrew in order to become a pastor like his father. During that time at the age of thirteen Euler started gaining his masters in Philosophy at the University of Basel, and in 1723 he achieved his master degree. On his weekends, Euler was learning from Bernoulli in several subjects because Bernoulli noticed that Euler was very intelligent in all types of mathematics and it also helped that Euler’s father was a friend of the Bernoulli Family, at the time Johann Bernoulli was Europe’s best mathematician. Bernoulli would later become one of ...
The contemporary world is full of marvels. Technological advances have enabled mankind to fly in the heavens, instantaneously communicate with distant relatives thousands of miles away, construct buildings that are able to withstand many natural disasters, cure deadly diseases, and even travel to and study areas beyond the confines of planet Earth. While there are many factors that contributed to man’s ability to overcome what many once thought were impossible feats, it is the study of engineering that has enabled one to study the elements and leverage all that they have to offer. Mathematics lies at the heart of all science, including engineering. Without progressions in mathematical concepts, engineering principles and applications would not have advanced as quickly as they have throughout history.
Chapter two of The Universe and the Teacup deals with exponential numbers. More precisely, it deals with the difficulty humans have in processing very large and very small numbers. The term the book uses to describe this difficulty is "number numbness."
...eas that had been around for a long time but had also been thought to be different. He put together the concept of mass and the concept of energy and showed that they are actually the same thing when you think about them correctly. So his equation, E = mc2, theE is for energy and the m is for mass, and he showed that given a certain amount of mass you could calculate the amount of energy it contains. Or, alternatively, given an amount of energy, you can determine how much mass you can create from it. So mass and energy, he showed, are the ultimate convertible currencies. They are different carriers of some fundamental stuff that you can call energy, with mass simply being one manifestation of energy. But there are other manifestations: heat and light, radiation, and so forth. These are now recognized to all be different facets of one idea, one entity called energy.
While studying the golden mean it becomes evident just how relevant this number is in the world. Many architects and artists have used this ratio as a scale and proportion sequence. The sequence is also relevant in music, nature and even the human body. Ancient mathematicians were so fascinated in the ratio because of its frequency in geometry. The first person to provide a written definition was Euclid. He stated “A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less” this has been studied thoroughly by many mathematicians but the most relevant was the studies of Leonardo Fibonacci. Fibonacci is famous for the work he put in to come up with the Fibonacci sequence.
The great field of mathematics stretches back in history some 8 millennia to the age of primitive man, who learned to count to ten on his fingers. This led to the development of the decimal scale, the numeric scale of base ten (Hooper 4). Mathematics has grown greatly since those primitive times, in the present day there are literally thousands of laws, theorems, and equations which govern the use of ten simple symbols representing the ten base numbers. The field of mathematics is ever changing, and therefor, there is a great demand for mathematicians to keep improving our skills in utilizing the numeric system. Many great people, both past and present, have made great contributions to the field. Among the most famous are Archimedes, Euclid, Ptolemy, and Pythagoras, all of which are men. This seems to be a common trend in mathematics, for almost all classical mathematicians were male.
Perkowitz, Sidney. "E = Mc2 (equation)." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 26 Dec. 2013. .
1.01100 = 2.7048 (1+1/1000)1000 = 1.0011000 = 2.7169 (1+1/10000)10000 = 1.000110000 = 2.7181 (1+1/) = (1+) = 2.7182818284590452353602874713526624977572470936. = e. Works Cited http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/. http://oakroadsystems.com/math/loglaws.htm http://www.physics.uoguelph.ca/tutorials/LOG/ http://en.wikipedia.org/wiki/Michael_Stifel http://en.wikipedia.org/wiki/John_Napier http://www.ndt-ed.org/EducationResources/Math/Math-e.htm http://www.thocp.net/reference/sciences/mathematics/logarithm_hist.htm http://mathforum.org/dr.math/faq/faq.pi.html
By 1904 Ramanujan had begun to undertake deep research. He investigated the series (1/n) and calculated Euler's constant to 15 decimal places. He began to study the numbers, which is entirely his own independent discovery.
Have you ever put thought of who is responsible for all these mathematical equations you see daily in school or throughout life? John Napier is a mathematician who is the creator of logarithms, the decimal’s modern notations, and the popular invention of napier bones. He was born in 1550 in Edinburgh, Scotland, and was the son of Sir Archibald Napier. They were a family of privilege and wealth, so he had a more than adequate education and lifestyle. He used his brilliant mind not only for math, but also contributed to the Spanish conquest by building weapons. John Napier is regarded as a genius in mathematics, and is respected greatly for his inventions and contributions to mathematics.
The history of the computer dates back all the way to the prehistoric times. The first step towards the development of the computer, the abacus, was developed in Babylonia in 500 B.C. and functioned as a simple counting tool. It was not until thousands of years later that the first calculator was produced. In 1623, the first mechanical calculator was invented by Wilhelm Schikard, the “Calculating Clock,” as it was often referred to as, “performed it’s operations by wheels, which worked similar to a car’s odometer” (Evolution, 1). Still, there had not yet been anything invented that could even be characterized as a computer. Finally, in 1625 the slide rule was created becoming “the first analog computer of the modern ages” (Evolution, 1). One of the biggest breakthroughs came from by Blaise Pascal in 1642, who invented a mechanical calculator whose main function was adding and subtracting numbers. Years later, Gottfried Leibnez improved Pascal’s model by allowing it to also perform such operations as multiplying, dividing, taking the square root.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
"programming" rules that the user must memorize, all ordinary arithmetic operations can be performed (Soma, 14). The next innovation in computers took place in 1694 when Blaise Pascal invented the first “digital calculating machine”. It could only add numbers and they had to be entered by turning dials. It was designed to help Pascal’s father who