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logarithm

history of matematik
by

are fath

on 1 December 2012

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Transcript of logarithm

Logartihm Introduction i) The method of logarithms was publicly propounded by John Napier in 1614

ii)  Joost Burgi independently invented logarithms but published six years after Napier.

iii) Logarithms were originally developed to simplify complex arithmetic calculations.

iv) They were designed to transform multiplicative processes into additive ones.

v) They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily

vi) The present-day notion of logarithms comes from Leonhard Euler

vii) Use is widespread in pure mathematics especially calculus

viii) Logarithmic scales reduce wide-ranging quantities to smaller scopes. History of Logarithms How LOGARITHMS appeared? TIMELINE OF LOGARITHMS Logarithm in a real world Sound intensity Teaching Aid Why use teaching aids? Using History to Teach Logarithms - Good way for students to understand the problem and the achievements of the past

- History of mathematics can help students understand better the mathematical concepts,methods and proofs showing them how they were discovered and developed.

- History of mathematics can help students realize that mathematics is a human and dynamic activity influenced by social and cultural factors and is shaped according to the utilitarian and intellectual needs of each era.

- History of mathematics can help stimulate students’ interest for learning and improve their perceptions of mathematics and attitudes towards it. If at first this seems like no big deal,
then try multiplying
2,234,459,912 and 3,456,234,459. Without a calculator ! Clearly, it is a lot easier to add
these two numbers. People didn’t know how to multiply or divide big numbers. These calculations were necessary not only in Commerce and Business, but also in Astronomy, Engineering, and Science. There were “calculation centers” where people were bringing their problem, paying and coming back after a few days for the answer. announced that from that day on, everybody will be able to solve these problems: the multiplications and divisions will be replaced by simple additions and subtractions John Napier -Born: 1550 in Merchiston Castle, Edinburgh, ScotlandDied: 4 April 1617 in Edinburgh, Scotland

-Napier was born into a wealthy Edinburgh family in 1550 -Napier, who is credited with the invention of logarithms, only considered the study of mathematics as a hobby.

-Napier’s discussion of logarithms appears in his “Mirifici Logarithmorum Canonis Descriptio” (Description of the wonderful canon of logarithms) by Napier published in 1614

-Napier defined his logarithms as a ratio of two distances in a geometric form, as opposed to the current definition of logarithms as exponents

-Napier presented a mechanical means of simplifying calculations in his Rabdologiae in 1617 -John Napier invented logarithms, but many other scientists and mathematicians helped develop

-Napier’s logarithms to the system we use today
Henry Briggs and Napier discovered natural logarithms which first arose as more or less "accidental variations" of Napier’s original logarithms.

-John Napier published his discovery of logarithms in 1614 Joost Burgi He was born in Lichtensteig, a small village of around 400 inhabitants at this time.
Joost Burgi was clockmaker from Switzerland
He was also well known as being a maker of astronomical instruments and mathematician Bürgi's key motivation was not only to facilitate computation, but also to produce a single table that could be applied to all arithmetical operations
He stated that he was able to create one table for a multiplicity of calculations by considering two “self-producing and corresponding progressions”
Bürgi's system was his use of color to emphasize the relationship between the arithmetic and geometric progressions
There is evidence that Bürgi arrived at his invention as early as 1588, six years before Napier began work on the same idea. By delaying the publication of his work to 1620, Bürgi lost his claim for priority in historic discovery 1550 - John Napier1 was born in Edinburgh Scotland
1552 - Jobst Bürgi was born in Switzerland
1588 - Bürgi began working on his logarithms2 independent of Napier (I was unable to find the base to which Bürgi created his logarithms).
1594 - John Napier started work on his tables and spent the next twenty years completing. The tables were for trigonometric applications and gave the logarithms for the sine of angles 30o to 90o. Although Napier did not actually use in his logarithms it could be said his base was roughly 1/e.
1614 - Napier published “Mirifici logarithmorum canonis descriptio” in which he discusses his logarithms.
10 March 1615 - Henry Briggs wrote a letter roughly translating questions Napier’s use of his base (1/e) and why he did not use base 10 and log 1 = 0. Napier replied that he too had the idea but could not create the tables due to an illness.
Summer 1615 - Henry Briggs visited John Napier and they spent a month working on the tables for the logarithms to base 10
1616 - Henry Briggs visited John Napier a second time 4 April 1617 - John Napier passed away
1617 - Briggs published his “Logarithmorum Chilias Prima” which contained his tables for logarithms to base 10
1619 - “Mirifici logarithmorum canonis constructio” is published in which the methodNapier used for constructing his logarithms is discussed
1620 - Bürgis’ were published in his “Arithmetische und Geometrische Progress-Tabulen.” Bürgi’s work went unnoticed due to the beginning of the Thirty Years’ War
1622 - William Oughtred invented the slide rule, which offered an even quicker way of calculating logarithms
1632 - Jobst Bürgi passed away
1675 - Newton discovers the fact that the d/dx ln x = 1/x.
1685 - John Wallis realized that logarithms could be defined as exponents
1694 - Johann Bernoulli also realized that logarithms could be defined as exponents
1694 to present - Logarithms had reached their full potential and most of what was done after 1694 was calculating logarithms to different bases. Richter magnitude scale The richter scale is to scaled to a base 10 logarithm Logartihmic scaling also gives us the measure of acidity The pH of a solution is determined by a logarithmic function relating the hydrogen or H+ ion concentration in a liquid Logarithm are also used to describe sound intensity in decibel

The smallest sound a human can hear is defined as the treshold of hearing or TOH. That volume is defined as zero decibels.

Every sound canbe classified in decibels according to a base 10 logarithmic scale.

Every multiple of 10 from the TOH translates to an increase of 10 on decibel scale Sound intensities table Teaching aids are useful to:
• Reinforce what you are saying
• Ensure that your point is understood
• Signal what is important/essential
• Enable students to visualise or experience something that is impractical to see or do in real life
• Engage students’ other senses in the learning process
• Facilitate different learning styles

• No advanced preparation
required,
• Technology is not dependent on
electricity or other possible
technology.
• Can be used by students for
problem-solving, etc. White Board Mathematical Games Games help students to:
• understand mathematical concepts
• develop mathematical skills
• know mathematical facts
• learn the language and vocabulary of mathematics
• develop ability in mental mathematics. AUDIO TAPES or CDs Use to understand the concept of the topic.
Do the homework
Watch the tutorial examples Songs Overhead
Projector The End! Thank you :)
Full transcript