» Part 1
Logarithms initially originated in an early form along of logarithm tables published by the Augustinian Monk Michael Stifel when he published ’Arithmetica integra’ in 1544. In the same publication, Stifel also became the first person to use the word ‘exponent’ and the first to indicate multiplication without the use of a symbol. In addition to mathematical findings, he also later anonymously published his prediction that at 8:00am on the 19th of October 1533, the world would end and it would be judgement day. However the Scottish astronomer, physicist, mathematician and astrologer John Napier is more famously known as the person who discovered them due to his work in 1614 called ‘Mirifici Logarithmorum Canonis Descriptio’. The reason they were created is to present and express numbers in a new form that was easy to work with. He was successful, as logarithms can be applied in many functions which are used commonly today. They were even more useful back around the time they were created however, as there were no calculators in existence. Scientists (astronomers in particular) had to do massive amounts of calculations on paper which was very time consuming and inconvenient. When logarithms were introduced to them, they weren’t obliged to spend so much time on tedious arithmetic. Logarithms are essentially just exponents, as they show values by using a base number that is raised to a given exponent. Stifel created his logarithm tables to change complicated multiplication and division problems into addition and subtraction equations.
» Part 2
Logarithms have the ability to replace a geometric sequence with an arithmetic sequence because they raise a base number by an exponent. A simple example can be provided with a geome...
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...1.254 = 2.4414
(1+1/5)5 = 1.25 = 2.4883
(1+1/10)10 = 1.110 = 2.5937
(1+1/100)100 = 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
http://www.recoveredscience.com/constanteofgrowth.htm
http://www.mathworksheetscenter.com/mathtips/logarithms.html
http://www.zyra.org.uk/log-e.htm
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Abstract: This paper gives an insight into the Mathematics used by the American Indians. The history of American Indians and how they incorporated mathematics into their lives is scarce. However from the information retrieved by Archeologists, we have an idea of the type of mathematics that was used by American Indians.
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Pierre de Fermat Pierre de Fermat was born in the year 1601 in Beaumont-de-Lomages, France. Mr. Fermat's education began in 1631. He was home schooled. Mr. Fermat was a single man through his life. Pierre de Fermat, like many mathematicians of the early 17th century, found solutions to the four major problems that created a form of math called calculus. Before Sir Isaac Newton was even born, Fermat found a method for finding the tangent to a curve. He tried different ways in math to improve the system. This was his occupation. Mr. Fermat was a good scholar, and amused himself by restoring the work of Apollonius on plane loci. Mr. Fermat published only a few papers in his lifetime and gave no systematic exposition of his methods. He had a habit of scribbling notes in the margins of books or in letters rather than publishing them. He was modest because he thought if he published his theorems the people would not believe them. He did not seem to have the intention to publish his papers. It is probable that he revised his notes as the occasion required. His published works represent the final form of his research, and therefore cannot be dated earlier than 1660. Mr. Pierre de Fermat discovered many things in his lifetime. Some things that he did include: -If p is a prime and a is a prime to p then ap-1-1 is divisible by p, that is, ap-1-1=0 (mod p). The proof of this, first given by Euler, was known quite well. A more general theorem is that a0-(n)-1=0 (mod n), where a is prime...
The population of the world is growing extremely fast. Eventually there is going to be overpopulation and resources are going to run out if something is not done. We know earth is overpopulated and that a control over population can be made or at least something can be done so there is not a catastrophe. Population growth can be determined using exponentials which directly relate to derivatives. This is a tool that can be very helpful for anthropologist and sociologists in the world (which have nothing to do with mathematics). Not only to know population numbers in ten or twenty years but to have control over other things. For example will there be enough food for five billion people in the world, will there be enough mineral supply for five billion people in the world or will there be enough fuel supply for five billion people in the world. Many of those types of investigations can be determined with the application of derivatives.
from his tables, which showed powers of 10 with a fixed number used as a base.
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In 1886 Dorr D. Felt (1862 - 1930) invented the "comptometer". This was the first calculator where the operands are entered by just pressing keys. In 1889 in also invents the first printing desk calculator.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
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