John Napier

John Napier, Inventor of Logarithms
John Napier, ahir at Merchiston Castle, near Edinburgh, Scotland. Son of Sir Archibald Napier of his first wife, Janet Bothwell. When the age of 14, Napier sent to the university St. Andrews to study theology. After traveling to foreign countries, Napier returned to my hometown in 1571 and married Elizabeth Stirling and had two children. In 1579, his wife died and remarried to Agnes Chisholm. This second marriage gave him ten children.

The second child of his second wife, Robert, later became his father's translator works. Sir Archibald died in 1608 and John Napier succeeded him, lives in Merchiston castle all his life.

Napier is not a professional mathematician. stateless Scotland, he was a baron who lived in Murchiston and has plenty of land but also has a hobby of writing the various topics that interested her. He is only interested in researching any aspect of mathematics, particularly relating to the calculation and trigonometry. The term "framework Napier" (Napier frame) refers to the multiplication tables and "Napier's analogies" and "Law sections Napier circle" is a tool to remember in connection with the trigonometric circle. Napier said that the research and findings on the logarithm happened twelve years ago before it was published. This statement points out that the basic idea occurred in 1594. Although invented by Napier but there is the role of its predecessor. Stifel wrote Arithmetica integra in 50 years ago with the guidelines for the works of Archimedes. Numbers with power of two is essentially, though not be used for purposes of calculating the difference because there is too big and way of interpolation does not give accurate results.
Influence of the ideas Dr. John Craig could not be ruled out, the influence of John Napier. Meeting this accident happened, happened when the group Craig on his way to Denmark by boat, a storm that made this group to stop not far from the observatory of Tycho Brahe, not far from where Napier. While waiting for the storm to pass, they discussed ways of calculation used in the observatory. This discussion is more motivated to make Napier in 1614 published the book description of the rules in the logarithm (A Description of the Marvelous Rule of Logaritms).



Logarithm
Early discoveries of Napier is actually very simple. Using a geometric progression and integral simultaneously. Take a certain number close to 1. Napier using the 1-107 (or .9999999) as numbers. Now, the term progression of ever-increasing power until the end result is close - very little difference. In order to achieve "balance" and avoid going (number) decimal multiplied by 107.

N = 107 (1 - 1/107) L, where L is the logarithm of Napier so the logarithm of 107 is equal to zero, ie: 107 (1-1/107) = 0.9999999 is 1 and so on. If the number is divided by 107 and logarithms, will be found - virtually - the system of logarithms as base 1 / e, for (1-1/107) 107 approached Lim n → ∞ (1 - 1 / n) n = 1 / e.

Keep in mind that Napier did not have the concept of logarithms as a basis, as we know it today. Napier working principles will be more clearly by using the concept of geometry below.

A___________________P____________B___________________



C_______________________D__________Q_______________________E


The line AB is half of the line CE. Imagine a point P set out from point A, passing along the line AB with a velocity comparable with the proportion decreasing with distance from point B; at the same point Q moves from CE line ... with the same moving speed as the point P. Napier called CQ distance variable is the logarithm of the distance PB is the geometric definitions Napier. For example: PB = CQ = x and y. If AB be 107, and if the rate it is also P 107, is obtained in modern calculus notation dx / dt =-x and dy / dt = 107, x0 = 107, y0 = 0. So dy / dx = - 107 / x, or y = -107 ln cx, where c is the initial condition to be 10-7. The result, y = -107 ln (x/107) or y/107 = log 1 / e (x/107).

Eccentricity
Although Napier made great contributions in the fields of mathematics, but the greatest interest in the field of religion precisely Napier. He was a strong Protestants who wrote his views in the book description of the discovery of the resurrection of St. John (A Plaine Discovery of the Whole Revelation of Saint John (1593), who bitterly attacked the Catholic church and insulting the King of Scots, James VI (later James I, king of Britain) by calling an atheist.

Another area that interests Napier, a landlord, is managing the farm. To improve soil fertility, Napier tried to provide fertilizer in the form of salt. 1579, Napier found a hydraulic pump to raise water from the well. In the military field, Napier plans to create a giant mirror in order to protect Britain from invasion of the navy of King Philip II of Spain. Both Napier invention is not unlike the discovery of Archimedes.
There is an anecdote, that as a landlord, Napier is often at odds with the tenants (land) and its neighbors. An event, Napier was disturbed by a neighbor who felt the dove was too much. The threat that the pigeons will not be addressed neighbors arrested, because he felt convinced that Napier may not arrest all the pigeons. The next day, the neighbors were surprised to find all the pigeon flounder - not dead - slumped in front of the house. Napier seems to have been feeding the first corn was soaked with wine.

Last service
As soon as the first book was published, the enthusiasm of mathematicians broke so many of their visit to Edinburgh. One of the guests was Henry Briggs (1516 - 1631), which at the time of Briggs informed the meeting about the modifications made to Napier. Transform into a logarithmic basis, rather than 107, the result is zero and use the base 10 (decimal). Finally found the log 10 = 1 = 10 º.
Napier died in his castle on April 3, 1617, and was buried in the church of St. Cuthbert, Edinburgh. Two years later, 1619, published a book of beauty logarithm Construction (Construction of the wonderful logarithms), compiled by Robert, son.


Contributions
Find the basic concept of logarithms, before being developed by other mathematicians - especially Henry Briggs - so it can provide benefits. This discovery brought a big change in mathematics. Johannes Kepler helped, because the logarithm, calculated able to increase capacity for the astronomer. "Miracle" was later called by the logarithm of [Florian] Cajori as one of the three important discoveries of mathematics (the other two are notation-based Arabic numerals and ten fractions / decimals).