Bernoulli Kette Roulette

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From `A Short Account of the History of Mathematics' (4th edition, 1908)by W. W. Rouse Ball.

James Bernoulli John Bernoulli Daniel Bernoulli

The Bernoullis (or as they are sometimes, and perhaps more correctly,called, the Bernouillis) were a family of Dutch origin, who weredriven from Holland by the Spanish persecutions, and finally settledat Bâle in Switzerland. The first member of the family whoobtained distinction in mathematics was James.

James Bernoulli

Jacob or James Bernoulli was born atBâle on December 27, 1654; in 1687 he was appointed to achair in mathematics in the university there; and occupied it untilhis death on August 16, 1705.

He was one of the earliest to realize how powerful as an instrumentof analysis was the infinitesimal calculus, and he applied it toseveral problems, but did not himself invent any new processes.His great influence was uniformly and successfully exerted in favourof the use of the differential calculus, and his lessons on it,which were written in the form of two essays in 1691 and arepublished in the second volume of his works, shew how completelyhe had even then grasped the principles of the new analysis. Theselectures, which contain the earliest use of the term integral, werethe first published attempt to construct an integral calculus; forLeibnitz had treated each problem by itself, and had not laid downany general rules on the subject.

The most important discoveries of James Bernoulli were his solutionof the problem to find an isochronous curve; his proof that theconstruction for the catenary which had been given by Leibnitz wascorrect, and his extension of this to strings of variable densityand under a central force; his determination of the form taken byan elastic rod fixed at one end and acted on by a given force atthe other, the elastica; also of a flexible rectangularsheet with two sides fixed horizontally and filled with a heavyliquid, the lintearia; and lastly, of a sail filled withwind, the velaria. In 1696 he offered a reward for thegeneral solution of isoperimetrical figures, that is, of figuresof a given species and given perimeter which shall include a maximumarea: his own solution, published in 1701, is correct as far as itgoes. In 1698 he published an essay on the differential calculusand its applications to geometry. He here investigated the chiefproperties of the equiangular spiral, and especially noticed themanner in which various curves deduced from it reproduced theoriginal curve: struck by this fact he begged that, in imitationof Archimedes, and equiangular spiral should be engraved on histombstone with the inscription eadem numero mutata resurgo.He also brought out in 1695 an edition of Descartes'sGéometrie. In his Ars Conjectandi,published in 1713, he established the fundamental principles ofthe calculus of probabilities; in the course of the work he definedthe numbers known by his name and explained their use, he also gavesome theorems on finite differences. His higher lectures weremostly on the theory of series; these were published by NicholasBernoulli in 1713.

John Bernoulli

John Bernoulli, the brother of James Bernoulli, wasborn at Bâle on August 7, 1667, and died there on January 1,1748. He occupied the chair of mathematics at Groningen from 1695to 1705; and at Bâle, where he succeeded his brother, from1705 to 1748. To all who did not acknowledge his merits in a mannercommensurate with his own view of them he behaved most unjustly:as an illustration of his character it may be mentioned that heattempted to substitute for an incorrect solution of his own onthe problem of isoperimetrical curves another stolen from hisbrother James, while he expelled his son Daniel from his house forobtaining a prize from the French Academy which he had expected toreceive himself. He was, however, the most successful teacher ofhis age, and had the faculty of inspiring his pupils with almostas passionate a zeal for mathematics as he felt himself. Thegeneral adoption on the continent of the differential rather thanthe fluxional notation was largely due to his influence.

Leaving out of account his innumerable controversies, the chiefdiscoveries of John Bernoulli were the exponential calculus, thetreatment of trigonometry as a branch of analysis, the conditionsfor a geodesic, the determination of orthogonal trajectories, thesolution of the brachistochrone, the statement that a ray of lightpursues such a path thatis a minimum, and theenunciation of the principle of virtual work. I believe that hewas the first to denote the accelerating effect of gravity by analgebraical sign g, and he thus arrived at the formulav² = 2ghthe same result would have been previously expressedby the proportion.The notationx to indicate a function of x was introduced by him in1718, and displaced the notation X orproposed by him in1698; but the general adoption of symbols like f, F,...to represent functions, seems to be mainly due toEuler and Lagrange.

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The Younger Bernoullis

Several members of the same family, but of a younger generation,enriched mathematics by their teaching and writings. The mostimportant of these were the three sons of John; namely Nicholas,Daniel, and John the younger; and the two sons of John the Younger,who bore the names of John and James. To make the account completeI add here their respective dates. Nicholas Bernoulli, theeldest of the three sons of John, was born on Jan. 27, 1695, andwas drowned at St. Petersburg, where he was professor, on July 26,1726. Daniel Bernoulli, the scond son of John, was born onFeb. 9, 1700, and died on March 17, 1782; he was professor firstat St. Petersburg and afterwards at Bâle, and shares with Eulerthe unique distinction of having gained the prize proposed annuallyby the French Academy no less than ten times.John Bernoulli, the younger, a brotherof Nicholas and Daniel, was born on May 18, 1710, and died in 1790;he also was a professor at Bâle. He left two sons, Johnand James: of these, the former, who was born on Dec. 14,1744, and died on July 10, 1807, was astronomer-royal, and directorof mathematical studies at Berlin; while the latter, who was bornon Oct. 17, 1759, and died in July 1789, was successively professorat Bâle, Verona, and St. Petersburg.

Daniel Bernoulli

Daniel Bernoulli, whose name I mentioned above, and who wasby far the ablest of the younger Bernoullis, was a contemporaryand intimate friend of Euler, whose works are mentioned in the nextchapter. Daniel Bernoulli was born on Feb. 9, 1700, and died atBâle, where he was professor of natural philosophy, on March 17,1782. He went to St. Petersburg in 1724 as professor of mathematics,but the roughness of the social life was distasteful to him, andhe was not sorry when a temporary illness in 1733 allowed him toplead his health as an excuse for leaving. He then returned toBâle, and held successively chairs of medicine, metaphysics,and natural philosophy there.

His earliest mathematical work was the Exercitationes,published in 1724, which contains a solution of the differentialequation proposed by Riccati. Two years later he pointed out forthe first time the frequent desirability of resolving a compoundmotion into motions of translation and motions of rotation. Hischief work is his Hydrodynamique, published in 1738;it resembles Lagrange's Méchanique analytiquein being arranged so that all the results are consequences of asingle principle, namely, in this case, the conservation of energy.This was followed by a memoir on the theory of the tides, to which,conjointly with the memoirs by Euler and Maclaurin, a prize wasawarded by the French Academy: these three memoirs contain all thatwas done on this subject between the publication of Newton'sPrincipia and the investigations of Laplace. Bernoullialso wrote a large number of papers on various mechanical questions,especially on problems connected with vibrating strings, and thesolutions given by Taylor and by D'Alembert. He is the earliestwriter who attempted to formulate a kinetic theory of gases, andhe applied the idea to explain the law associated with the namesof Boyle and Mariotte.

This page is included in acollection of mathematical biographies taken fromA Short Account of the History of Mathematicsby W. W. Rouse Ball (4th Edition, 1908).

Transcribed by

D.R. Wilkins
(dwilkins@maths.tcd.ie)
School of Mathematics
Trinity College, Dublin

Sector Betting Using Matrix Holy Grail System!

We all know that Matrix system is one of the most brilliant roulette systems today. Matrix system has given us an extremely important tool in the invention of matrix. There is an American Matrix and a European Matrix. I have had a great amount of success using matrix to formulate my bets. Many people have asked me how I use this tool. I have demonstrated below.

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✗ Track 24 spins.

✗ Record them as shown in Figure 2.

✗ Bet using the matrix sector layout as labeled 1-6 and A-F.

The Matrix (European)

ABCDEF
13215194212
225173462713
336113082310
45241633120
514319221829
67281235326

The Matrix (American) (Fig.1)

ABCDEF
12892630117
220321752234
31532436131
420102529128
519311862133
61642335142
Bernoulli kette roulette online

(Recording Chart) (Fig. 2)

ABCDEF
XXXXXXXXXXXXXXXXXXX
XXXXX
123456
XXXXXXXXXXXXXXXXXX
XXXXXX

HOW TO TRACK AND SELECT YOUR BET

As I said earlier, you will track 24 spins. You enter an “X” mark in the appropriate column of the tracking chart for each spin. There will be one “X” mark in the letter column, and one “X” mark in the number column for each number spun. I have labeled each matrix sectors with a letter and a number as you can see in Figure 1.

Example

Let’s say the following 24 numbers are spun:

5,31,11,14,29,7,31,31,17,18,28,4,8,24,34,28,14,19,2,33,12,32,4,14,8

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The first number is 5, so you you refer to Figure 1 and find 5 in the matrix. As you can see it is in Row 2, Column D. You would now place one “X” in Row 2, and 1 “X” in Column D. You will do this for all 24 spins. After 24 spins, you will count up the X’s in each row and column. The row and column with the least number of X marks are the row and columns that you will bet. You will always have 11 numbers to bet. If there is a tie, you will refer to the last number spun in one of the tie columns. For example, if Column “A” and Column “C” each have 3 “X” marks, you will trace back the numbers and the column that hit last will be ruled out and the other column will be your column to bet.

In the example above, I have recorded all of the spins and now it is time to add them up. You simply total up the X marks in each column.

Bernoulli Kette Roulette Game

A314
B524
C331
D244
E656
F565

As you can see in the table above, Column “D” has the least amount of “X” marks with 2. Row “3” has the least amount of hits also, so our sectors to bet are Column D, Row 3. We now find the corresponding numbers in our matrix (Fig.1) and they are 30,5,36,29,6,35,15,3,24,36,13,1. One of the numbers will appear twice. In this case it is 36. That leaves 11 numbers to bet. I bet using the following 7 stage progression until I get a hit. 1,1,2,3,5,7,10. After I get a hit, I repeat the process. That is how I use Matrix!

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