JAKOB(I) BERNOULLI
BORN: December 27, 1654
DIED: August 16, 1705
BORN: December 27, 1654
DIED: August 16, 1705
Jakob (Jacques) Bernoulli was the 5th child of Nicolaus Bernoulli and older brother to Nicolaus(I) and Johann(I) Bernoulli.
He was able to master the Leibnizian calculus without the assistance of anyone. He was able to develop the calculus further than either Newton or Leibniz were able to, and he was able to apply it to new problems of difficulty and importance.
His contributions to analytical geometry, the theory of probability and the calculus of variations were of the highest importance. It is said that the Calculus of variations is of ancient origin.
According to one legend, when the city of Carthage was founded, a person was granted as much land as he could plough a furrow completely around in one day. The question was: What shape should the furrow be given in order for a person to plough a straight furrow of a certain length in one day?
To state the problem mathematically, the question is asking: What is the figure which has the greatest area of all figures having perimeters of the same length? This is known as an isoperimetrical problem. The answer to this question is the circle - it seems obvious but it is by no means easy to prove.
In 1696, Jakob offered a reward for the general solution of isoperimetrical figures, however no one came up with a suitable answer. Jakob then published his own answer to the problem in 1701 and as far as it goes, it is correct.
Jakob's method of solving this problem was to make a certain integral a maximum subject to one restrictive constraint. He was able to solve this problem and then generalize it.
He also discovered that the answer to the brachistochrone is a cycloid. The fact that the cycloid is the curve of quickest descent, was a discovery made by both Jakob and his younger brother, Johann(I). It was also made by several others at about the same time.
Other work carried out by Jakob shows how far he had developed the differential and integral calculus. Continuing the work of Leibniz, Jakob made a fairly exhaustive study of cantenaries. Cantenaries being the curves in which a uniform chain hangs suspended between two points, or in which weighted chains hang.
Jakob's work on this lives on today when one sees a suspension bridge or high voltage transmission lines.
The first proof for arbitrary positive integral power (m/n = positive integer) seems to be that given by Jakob in his book "Ars conjectandi", which was published in 1713, eight years after his death.
In this same book, Jakob gives the fundamental principles of the calculus of probabilities. He also defines the numbers known by his name and explains their use in this text. Theorems on finite differences are also given.
Jakob was one of the first people to realize how powerful an instrument the calculus was in analysis.
Apart from the fact that Jakob took Leibniz' work on further, the only difference between the two was that Leibniz never laid any general guidelines down for solving problems, instead choosing to solve them independantly of each other.
Jakob was fascinated by a certain spiral which after several geometrical transformations is reproduced in another spiral. He directed that upon his death, an equiangular spiral should be engraved on his tombstone, with the inscription "Eadem mutata resurgo" which translates to "Though changed I shall arise the same".
Jakob's motto in life was "Invito patre sidera verso" which translates to "Against my father's will I study the stars" - this is in ironic memory of his father's futile opposition to Jakob devoting his talents to mathematics and astronomy.
Had his father had his way, Jakob would have been a minister of religion.
Jakob was the professor of mathematics at Basel university from 1687 until his death in 1705.
Jakob died on August 16, 1705 aged 51.
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