Full text

... the cycles can easily be seen. Regarding the fractal geometry of the triangle, the results can be observed for small n and generalized for higher ones. For example, if we take a look at the PT2r, we see that the row 2r - 1 contains only ones. This leads us to an easy proof of the well-known fact tha ...

... the cycles can easily be seen. Regarding the fractal geometry of the triangle, the results can be observed for small n and generalized for higher ones. For example, if we take a look at the PT2r, we see that the row 2r - 1 contains only ones. This leads us to an easy proof of the well-known fact tha ...

Unit 8 - Intro to Pascal's Law - Hydraulics

... The hydraulic pump transmits mechanical energy into hydraulic energy. This is done by the movement of fluid which is the transmission medium. There are several types of hydraulic pumps including gear, vane and piston. All of these pumps have different subtypes intended for specific applications such ...

... The hydraulic pump transmits mechanical energy into hydraulic energy. This is done by the movement of fluid which is the transmission medium. There are several types of hydraulic pumps including gear, vane and piston. All of these pumps have different subtypes intended for specific applications such ...

Slide 1

... volume of the fluid) has no net angular velocity. This condition eliminates the possibility of whirlpools and eddy currents. (The flow is nonturbulent.) ...

... volume of the fluid) has no net angular velocity. This condition eliminates the possibility of whirlpools and eddy currents. (The flow is nonturbulent.) ...

The P=NP problem - New Mexico State University

... abstractly outcome of a random event. • Formalized the classical definition of probability: If the total number of possible outcomes, all equally likely, associated with some actions is n and if m of those n result in the occurrence of some given event, then the probability of that event is m/n. • E ...

... abstractly outcome of a random event. • Formalized the classical definition of probability: If the total number of possible outcomes, all equally likely, associated with some actions is n and if m of those n result in the occurrence of some given event, then the probability of that event is m/n. • E ...

Probability Theory

... 2000(BC) - Games of chance played in ancient civilizations 1494 - Fra Luca Paccioli wrote the first printed work addressing probability called Summa de arithmetica, geometria, proportioni e proportionalita. 1550 - Geronimo Cardano wrote a book about games of chance called Liber de Ludo Aleae 1654 - ...

... 2000(BC) - Games of chance played in ancient civilizations 1494 - Fra Luca Paccioli wrote the first printed work addressing probability called Summa de arithmetica, geometria, proportioni e proportionalita. 1550 - Geronimo Cardano wrote a book about games of chance called Liber de Ludo Aleae 1654 - ...

Problem 12 : Odd Numbers in Pascal`s Triangle

... Since we are only interested in odd terms, these two problems are now equivalent. One method of constructing Sierpinski’s triangle, is to take three copies of the first 2k rows, adjoin them corner to corner creating a larger triangle, and lastly fill in the remaining positions with zeroes. We can us ...

... Since we are only interested in odd terms, these two problems are now equivalent. One method of constructing Sierpinski’s triangle, is to take three copies of the first 2k rows, adjoin them corner to corner creating a larger triangle, and lastly fill in the remaining positions with zeroes. We can us ...

Lecture 26 - Pascal`s Principle

... h = Patmos / ρg = 105 / (1000 x 9.8) ~ 10 m! That's why the jar+sheet demo works - atmospheric pressure can balance 10 m of H2O. Pascal's Principle Lastly, we consider what happens when an external pressure is applied to a confined fluid. We already know that the pressure varies locally with positio ...

... h = Patmos / ρg = 105 / (1000 x 9.8) ~ 10 m! That's why the jar+sheet demo works - atmospheric pressure can balance 10 m of H2O. Pascal's Principle Lastly, we consider what happens when an external pressure is applied to a confined fluid. We already know that the pressure varies locally with positio ...

File

... • The weight of the water in the upper part of the tin can is pressed down on the water in the lower part. – The more water above the hole, the more pressure. ...

... • The weight of the water in the upper part of the tin can is pressed down on the water in the lower part. – The more water above the hole, the more pressure. ...

The Particle Model (Topic 1)

... Solutes and solvents Sugar (solute) dissolves in water (solvent). Why is water considered the universal solvent? What does it mean if something is insoluble? How can you speed up dissolving (hint: there are four things that can affect the rate of dissolving) ...

... Solutes and solvents Sugar (solute) dissolves in water (solvent). Why is water considered the universal solvent? What does it mean if something is insoluble? How can you speed up dissolving (hint: there are four things that can affect the rate of dissolving) ...

File

... a)__6_ writeln(): 1) Doing a problem by hand so you understand what to do. b) _11__ readln(); 2) A decision construct used when you want to a chunk of code only when something is true.. c) _8__ for..do 3) The section of a program where you declare variables. d) _2__ if 4) Writing out, in English, in ...

... a)__6_ writeln(): 1) Doing a problem by hand so you understand what to do. b) _11__ readln(); 2) A decision construct used when you want to a chunk of code only when something is true.. c) _8__ for..do 3) The section of a program where you declare variables. d) _2__ if 4) Writing out, in English, in ...

# Blaise Pascal

Blaise Pascal (/pæˈskæl, pɑːˈskɑːl/; French: [blɛz paskal]; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Christian philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. Pascal also wrote in defense of the scientific method.In 1642, while still a teenager, he started some pioneering work on calculating machines. After three years of effort and fifty prototypes, he built 20 finished machines (called Pascal's calculators and later Pascalines) over the following ten years, establishing him as one of the first two inventors of the mechanical calculator.Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of 16, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646, he refuted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted.In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism. His father died in 1651. Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the Lettres provinciales and the Pensées, the former set in the conflict between Jansenists and Jesuits. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659 he wrote on the cycloid and its use in calculating the volume of solids.Pascal had poor health, especially after his 18th year, and his death came just two months after his 39th birthday.