It is not known exactly when logarithms were first invented, with evidence of use in 8th century India. However, their invention as an aid to calculations is attributed to John Napier in the early 17th century. He released the first ever log tables in 1614.
JOOST BURGI
Another mathematician, Joost Burgi from Prague, had been working independantly on logarithms at the same time as Napier but had a slightly different approach. He released his log tables in 1920. These took the form of a comparison between a geometric series and an arithmetic series, which clearly show the operation and nature of logs. A very simple example of this can be seen in the table below:
This table shows the geometric series on top and the arithmetic along the bottom. To multiply two numbers on the top, add the two numbers directly below and find the corresponding number on top. For example, to multiply 1/2 and 8, the numbers below (in the arithmetic sequence) are -1 and 3 respectively. Adding these is equal to 2 and the corresponding number (in the geometric sequence) for 2 is 4 (the correct answer.) This process also works for division (subtract the two numbers), and raising 2 to a power (find the power in the arithmetic sequence and look above.) This works because the numbers on top are the number 2 to the power of the corresponding numbers on the bottom. These logarithms are therefore to the base 2. This is how arithmetic processes were made easier by logarithms.
John Napier and Henry Briggs
John Napier was a famous Scottish theologian and mathematician who lived from 1550 to 1617. He was a very intelligent man, considered by many of the locals to be in league with the devil. As well as being educated, Napier was also a baron, nobelman, the 7th Laird of Merchiston and owner of a considerable estate. He defined his logarithms in terms of relative rates, in a different way to Joost.
After the release of Napier's logarithm tables, Henry Briggs, an English mathematican who at the time had been researching astronomy and its applications to navigation, immediately saw the potenial for logarithms to ease astronomical and navigational calculations and so turned his attention to developing the idea. During 1915 and 1916 Briggs travelled to Edinburgh to collaberate with Napier whereby they modified Napier's logarithms, which at the time were to the base 1/e, to the base 10. These were easier to work with and would be more useful for Briggs' astronomical and navigational calculations. Logarithms to the base 10 are known as common logarithms or Briggsian logarithms in his honour. In 1924 Briggs published the "Arithmetica Logarithmica" (common logarithms) which included tables of logs from 1 to 20,000 and 90,000 to 100,000 to 14 decimal places, as well as information about the nature and constuction of logs
JOOST BURGI
Another mathematician, Joost Burgi from Prague, had been working independantly on logarithms at the same time as Napier but had a slightly different approach. He released his log tables in 1920. These took the form of a comparison between a geometric series and an arithmetic series, which clearly show the operation and nature of logs. A very simple example of this can be seen in the table below:
This table shows the geometric series on top and the arithmetic along the bottom. To multiply two numbers on the top, add the two numbers directly below and find the corresponding number on top. For example, to multiply 1/2 and 8, the numbers below (in the arithmetic sequence) are -1 and 3 respectively. Adding these is equal to 2 and the corresponding number (in the geometric sequence) for 2 is 4 (the correct answer.) This process also works for division (subtract the two numbers), and raising 2 to a power (find the power in the arithmetic sequence and look above.) This works because the numbers on top are the number 2 to the power of the corresponding numbers on the bottom. These logarithms are therefore to the base 2. This is how arithmetic processes were made easier by logarithms.
John Napier and Henry Briggs
John Napier was a famous Scottish theologian and mathematician who lived from 1550 to 1617. He was a very intelligent man, considered by many of the locals to be in league with the devil. As well as being educated, Napier was also a baron, nobelman, the 7th Laird of Merchiston and owner of a considerable estate. He defined his logarithms in terms of relative rates, in a different way to Joost.
After the release of Napier's logarithm tables, Henry Briggs, an English mathematican who at the time had been researching astronomy and its applications to navigation, immediately saw the potenial for logarithms to ease astronomical and navigational calculations and so turned his attention to developing the idea. During 1915 and 1916 Briggs travelled to Edinburgh to collaberate with Napier whereby they modified Napier's logarithms, which at the time were to the base 1/e, to the base 10. These were easier to work with and would be more useful for Briggs' astronomical and navigational calculations. Logarithms to the base 10 are known as common logarithms or Briggsian logarithms in his honour. In 1924 Briggs published the "Arithmetica Logarithmica" (common logarithms) which included tables of logs from 1 to 20,000 and 90,000 to 100,000 to 14 decimal places, as well as information about the nature and constuction of logs
No comments:
Post a Comment