Month: February 2011

Under Pressure

“Pressure pushing down on me
pressing down on you no man ask for
under pressure”

(lyrics from “Under Pressure”)

Pressure is the ratio of force applied per area covered:

P= \frac{F}{A}

The unit of pressure is the pascal:

The pascal is also a unit of stress and the topics of pressure and stress are connected.

Pressure in a uniform fluid.

  • The gauge pressure in a uniform fluid at a particular depth is directly proportional to …
    • the density of the fluid ρ,
    • the acceleration due to gravity g, and
    • the depth h.

The absolute pressure in a uniform fluid at a particular depth is given by:

P=P_0+\rho gh

Atmospheric pressure

Atmospheric pressure is defined as the force per unit area exerted against a surface by the weight of the air above that surface.

Boyle’s Law(after Robert Boyle, Irish scientist, around 1600)

Boyle’s law states that, at a constant temperature, the volume of a given mass of gas varies inversely with pressure. For two states of pressure (P1, P2) and two corresponding volumes (V1, V2), this is stated mathematically:

P_1V_1=P_2V_2

Charles’ Law (after Jacques Charles, French scientist, around 1790)

By warming the balloon up, we increase the speed of the moving gas molecules inside it. This in turn increases the rate at which the gas molecules bombard the skin of the balloon. Because the balloon’s skin is elastic, it expands upon this increased pushing from inside, and the volume taken up by the same mass of gas increases with temperature. In consequence, the density [=mass/volume] decreases with rising temperature. Cooling the balloon down again will make the balloon shrink.

Thus Charles’s law states that at a constant pressure, the volume of a given mass of gas is directly proportional to its (absolute) temperature. For two states with temperatures (T1, T2) and two corresponding volumes (V1, V2):

 

The Ideal Gas Law or Equation of State

The example used to illustrate Charles’s law probably does not follow Charles’s law exactly. It is very likely that, during the heating process, when the rate of collisions by the gas molecules increased, the pressure increased as well as the volume. Thus, in practical situations all three variables involved in Boyle’s and Charles’s law are linked and both principles are in action at the same time:

Pressure: P
Temperature: T
Density: r = m/V

These variables describe the state of the gas at any one time and are combined in the single relationship known as the ideal gas law or the equation of state:

Dalton’s Law of Partial Pressure:

The pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented as:

PressureTotal = Pressure1 + Pressure2 … Pressuren

Pascal’s Principle:

Pascal’s principle states that a pressure applied to an enclosed fluid is transmitted everywhere in the fluid. Hence, if a pressure is applied to one side of an enclosed fluid, all the other walls containing the fluid feel the same pressure. The pressure is transmitted without being diminished.

In physics, if a pressure is applied to a compressible gas, Pascal’s principle still applies, but the volume of the gas will change. For Pascal’s principle to be useful to hydraulics, the fluid should be an incompressible liquid, which will transmit the applied pressure without changing its volume.

Mathematics and Physics in Movies and Tv

This is a collection of movie titles in which Mathematics and Physics appear.

  • The Dam Busters (1955): On the use of Congruent triangles to measure distances. Also some applied math problems on bouncing balls on water and detonations in water. Thanks to Craig Smorynski for the suggestion;
  • The Ice Storm (1997): Its when they say 2*2 is equal to 4, it is not numbers, it is space. It is perfect space. But only in your mind. You can not draw perfect squares in the material world;
  • The Bank (2005): The multiplication table and the compound interest formula;
  • Cranford (2007): On addition of income numbers and a sentence on teaching mathematics or geography;
  • The Wild Blue Yonder (2005): Chaotic transport in the solar system and Rotating system;
  • The Killer Inside Me (2010): A brief moment sanity in this dark, dark movie when Lou solves some integrals. It is an extremely disturbing movie because the dark side of Lou Ford, the psychotic killer, is not visible. Why the police men Lou does some math in this scene is unexplained in the movie;
  • Deskset (1957): The roof scene of this charming Tracy/Hepburn movie features some “mathematical” questions;
  • Rites of Love and Math( 2009): In this movie of Edward Frenkel mathematical formulas are written onto skin;
  • Artificial Intelligience (A.I.) (2001): About the fabric of space time and how humans have tried to find the meaning of life in art, poetry or mathematical formulas;
  • Drowning by Numbers  (1988): Counting the stars. Once you counted the hundred, all the other are the same;
  • In July (2000): Theoretical and applied computation of a free fall problem;
  • The Knack …and How to Get it (1965):The angle of incidence is equal to the angle or reflection;
  • Rain man (1988): 3*82=246 = 250-4;
  • A Serious man (2009): The Uncertainty Principle in Quantum Mechanics. The entire movie is a celebration of this principle starting with the dead/alive cat scene, unsharp boundaries singing and TV receiption, accepting mysteries, culture clashs, quantum tunneling between relationships etc,etc. One of the best Cohen brother movies;
  • Three O’ Clock High (1987): Some algebra problems are visible in a quiz. To determine who cheated, buddy has to solve 2 blackboard problems on square roots;
  • G.I. Joe – Rise of the Cobra (2009): The shadow determines the lattitude where the picture was taken. Compare the idea of Eratostenes to measure the shadows of a stick on different locations to get the radius of the earth;
  • The Hangover (2009): Mathematical thoughts of Allen, when winning at Vegas: from simple arithmetics to Fourier theory;
  • Time Machine (2002): Mathematical work on a black board;
  • Breaking the Code (1996): The enigma and its complexity appears in this movie about Alan Turing;
  • Star Trek (2009): Young Spock learns Math. He memorizes the formula (4pi/3) r3 for the volume of the sphere, the square root of 2396324 and the definition of dimensionality log(n)/log(d);
  • Star Trek, the New Generation (2002): Probably the most hilarious statement about dimension in the galaxy appears in the episode “Where silence has Lease”: “Is the lack of a dimension a dimension by itself?” Negative dimension. Mathematicians have not yet come up with this idea, but mathematicians have used also some time to come up with negative numbers;
  • Night at the Museum II (2009): What number is at the heart of a Pyramide? Pi=3.1415926;
  • Up in the Air (2009): E is just a number;
  • Flatland: the Movie (2007): Spherius shows Arthur the third dimension;
  • Flatland (1965): The sphere shows the third dimension. This movie was done at the animation workshop at the Carpenter Center for the Visual Arts at Harvard University. A production based on an idea by the American animator John Hubley (1914-1977) and directed by Eric Martin;
  • The Pink Panther Strikes Again (1976): Torture, finger nails on a blackboard filled with wrong mathematical computations like 3×3=7;
  • Parenthood (1989):  this commedy with Steve Martin, a kid takes the square root of a large number;
  • Bedazzled (2000): The devil first assigns Fermats theorem but then cancels all homework;
  • Fermat’s Room (2007): This brilliant movie is essentially about math only. A few famous math puzzles appear in this movie, where 4 mathematicians are trapped in a room where the walls slowly crush them;
  • Phantom Tollbooth (1970): The dodecahedron asks some riddles to get to Digitopolis. Fibonnacci series, vectors and scalars, equivalence relations and 4827659 hairs;
  • Pay it Forward (2000): Powers of three in a good pyramid scheme: select 3 people to do good things for and then those 3 each select 3 more people, etc;
  • For a Few Dollars more (1965): Counting dead gangsters;
  • Smilla’s Sense of Snow( 1997): Smilla reads from Euclids book to Isaiah;
  • Reality Bites (1994): About the Math in Astronomy;
  • Smilla’s Sense of Snow (1997): Natural numbers, negative integers, fractions;
  • Merry Andrew (1958): In this musical comedy, Danny Kaye as Merry Andrew teaches Newton’s law, geodesics and Pythagoras;
  • Butterfly Dreaming (2008): On the probability that two raindrops hit the same leaf;
  • The Oxford Murders (2008): Lecture on Wittgensteins pessimistic view on absolute truth followed by rather shallow sound bites: the beauty and harmony of numbers, the golden ratio, Fibonnacci, snowflakes and cancer, the secret meaning of numbers, the butterfly which flaps its wings to produce a hurricane which nobody can predict, logic and chance;
  • October Sky (1999): Free fall differential equations as used in rocketry;
  • Little Big Man (1970): A lier dilemma leads to the defeat of general Coster at the battle of big horn;
  • Run Lola Run (1998): Beside the main theme of “sensitive dependence on initial conditions”, there is a “run of Lola” in which she wins in roulette twice betting on the same number 20. The first time, the initial input of 100 mark is multiplied by 35. The second bet multiplies the now 3600 by 35 leading to a total win of 3500+126’000 = 129’500 has an element of Grass’s Blechtrommel cry, mathematically related to “resonance”;
  • It’s a Mad, Mad World (1963): Some division problems appear in this oscar winning comedy when eight motorists try to figure out how to split the not yet found treasure;
  • A Walk to Remember (2002): A tutoring scene with equilateral and isosceles triangles;
  • Old School (2003): This comedy not only shows shots of Harvard college but also some rather tough math test problems: like Harriet’s method of solving cubics, Diophantine equations or integration problems;
  • Last Year in Marienbad (1961): In this rather enigmatic movie, the enigmatic game of NIM with a 7-5-3-1 initial condition is played twice;
  • Shrek, the Third (2007): Mathematical logic in sentences;
  • The Happening (2008): During one of the “happenings”, Julian tries to divert the attention to a math problem;
  • Apocalypse Now (1979): Surrounded by horror, forms of poetry, physics and math appear in a mad form too. Photojournalist: “this is dialectics, simple dialectics. It is very simple dialectics: 1 through 9, no maybes, no supposes, no fractions. You can’t travel to space. You can not go to space with fractions. What do you land on: on one quarter or 3/8th? What do you do when you go to venus or something. Thats dialectic. Physics;
  • How Green was my valley(1941): A 100 gallon bath tub is filled from A with 20 gal/min and from B with 10 gal/min and leaks 5 gal/min;
  • Alice in Wonderland (1951): Riddle: Why is a raven like a writing desk? Carols own answer given in 1896: Because it can produce a few notes, tho they are very flat; and it is nevar put with the wrong end in front!Fooling around with complements. The unbirthday. Its a small world, most people share an unbirthday. Carol might have been inspired by the birthday paradox: in a class of 23 the chance to have two kids with the same birthday is already more than 1/2;
  • National Treasure (2004): Cracking a password by knowing the letters used;
  • National Treasure Code (2004): The Ottendorf Cipher, a book Cipher;
  • The Wizard of Oz (1939): The scare crow theorem: in an isoscele triangle, the sum of the square roots of two sides is the square root of the third side;
  • The Number 23 (2007): Numerology with the number 23;
  • 23 (1998): A true story about German Hackers/Spies. Numerology as in the movie “The number 23”. Bach as a hacker composing palindromic music;
  • Antonia’s Line (1995): An algebraic topology class;
  • 21 (2008): The Newton method; Cauchy plagiarism?
  • Colossus: the Forbin Project (1970): The mighty US defense computer “Colossus” develops calculus to communicate with its buddy in the Soviet union;
  • The Office: Season 5, Episode 9 (2008): Explaining a surplus to a 5 year old;
  • Little Big League (1994): Joe can paint the house in a=5 hours, Sam can paint the house in b=3 hours;
  • The Bank (2001): Predicting the stock market using complex dynamics;
  • Revolutionary Road (2008): A  mathematician appears in this though provoking movie;
  • Harold and Kumar (2008):Solving an integration problem in calculus. A poem about the number square root of 3;
  • Back to the Future, Part III (1990): Dok Brown: Clara was one in a million, one in a billion, one in a googolplex;
  • Once upon a time in the west (1968): Counting horses; Thousands of Thousands. One calls them Millions;
  • Jane Eyre (2006): Some glimpses of mathematics appear in the BBC drama: Jane Eyre grades Adeles homework;
  • Mansfield Park (1996): Reciting a scene with Fanny, Edmund and Mary, mentioning teaching of mathematics. The sceene is also a play in a play where the dialog refers to the actual situation;
  • The Prophecy (1995): Simon: “See you kids. Study math. Its the key to the universe”;
  • Father of the bride (1991): How to get 8 hotdogs and 8 hotdog buns if hotdog buns are bundled in 12;
  • Mean Girls (2004): A scene showing a Highschool calculus class; A scene showing a calculus contest in which a system of linear equations as well as a limit problem appears;
  • The Clan of the Cave Bear (1986): Teaching of mathematics at the time of the Neanderthals maybe 100’000 years ago;
  • Bedazzled (1967): The lier’s paradox in this Faustian comedy in which Elliot sold his soul to have 7 wishes fulfilled;
  • The Code Conspiracy (2001): The ulam prime spiral appears. One could overlook that almost nothing connected with codes, physics or math does make sense in this movie, but that the blue picture of the Ulam spiral is fake is slightly annoying;
  • The Island (2005): Discovering a deterministic system for the lottery on the island;
  • Cast Away (2000): First scene: Lecture on search area on a rock. Second scene: the path of the sun on the rock used as a calendar;
  • Eleventh Hour: Kryptos(2006): Ian Hood, the special scientific troubleshooter for the British government has to solve a riddle from a friend;
  • Marius (1931): Bartender Cesar lectures Marius on mixing a picon-citron-curacao: one very small third of curacao, one third of citron, then a large third of picon. And to finish, a large third of water;
  • Ma and Pa Kettle(1949): Different proofs that 25/5 = 14;
  • Cube (1997):People are trapped in a giant cube puzzle. A permutation riddle has to be solved;
  • Hypercube (2002): People are trapped in a hypercube which implodes at the end. Also time is mixed up in this cube;
  • It’s my turn (1980):A lecture on the Snake lemma in homological algebra in which a student pretends to know things better;
  • Simpsons treehouse of Horror, VI (1995): Homer enters a 3D world with different mathematical topics;
  • Sneakers (1992):  A lecture on computational number theory. A method superior to the number field sieve is announced;
  • Enigma (1991): About cracking “Shark” a refinement of the Enigma code;
  • Simpsons, First Season (1989): Bart Simpson solves a math problem at the learning center;
  • Straw Dogs (1971): A blackboard with mathematical astrophysical formulas;
  • P.S. (2004): A blackboard in Columbia University with mathematical formulas written by astrophysisist Peter, the ex-husband of the main character Louise;
  • Stand and Deliver (1988): Drop out student learns calculus. TicTacToe method for integration by parts; The giggolo problem;
  • Proof (2005): Work on the Riemann hypothesis;
  • Abbott and Costello: in the Navy (1941): Abbott and Costello do a Calculation trick to show that 7*13 = 28;
  • Pi (1998): Numerology, mathematics is everywhere;
  • Monty Pithon’s Flying Circus (2005): Football game, the mathematicians Leibniz on the german team, Archimedes on the greek team;
  • The Saint (1997): Piece of paper with mathematical formulas for cold fusion;
  • Indiana Jones and the Raiders of the Lost Ark (1981): Blackboard with some physics formulas;
  • Good Will Hunting (1997): Will Hunting writes down Cayley’s formula stating that the number of labeled trees on n nodes is nn-2. Then lists 8 different unlabeled trees with 10 nodes; Blackboard in linear algebra lecture at MIT on Parseval’s identity in Fourier theory;
  • Via Panisperna boys (1989): the story of a  group of young scientists led by Enrico Fermi.
  • A beautiful Mind (2001): Multivariable calculus lecture;
  • Dimensions (2008): An educational movie by Jos Leys Etienne Ghys and Aurelien Alvarez;
  • Donald in Mathmagicland (1959): Donald learns the Math of Billiards;
  • Death of a Neapolitan Mathematician (1992): This movie was inspired by the mathematician Renato Caccioppoli (1904-1959);
  • Blaise Pascal (1972);
  • Einstein and Eddington (2008);
  • The Mirror has Two Faces (1996): Calculus lecture but the actors mumble about prime twins;
  • Infinity (1996): Abakus scene and explanation how to compute the third roots;
  • Jurassic Park (1993): Chaos theory;
  • Contact (1997): Information is encoded in a cube;Prime numbers as contact;
  • Like Mike (2002): Supersized triangles;
  • Big (1988): Josh helps a kid with algebra;
  • Mission Impossible III(2006):Pendulum swing;
  • The Count of Monte Cristo (2002):  offer something priceless. I offer knowledge. Abbe Faria teaches Edmond Dantesphilosophy, mathematics and economics;
  • Clueless (1995): The math problem 7×7;
  • The Da Vinci Code (2006): The Fibonnacci sequence 1 1 2 3 5 8 13;
  • Chaos (2005): The popular book of James Gleick on Chaos;
  • Casino Royale (2006): Some mathematical themes and patterns motivated by mathematics appear in the intro;
  • Mr. Hollands Opus (1995): If I’m forced to choose from Mozart or Reading and Writing and Long divisions, I choose long division. – You can cut the arts, but the kids will have nothing anymore to read and write about;
  • Numb3rs (2005): Mathematics is everywhere. It is also used to solve crimes;Using statistics to find location of criminal and the odds to win the lottery;
  • Yakitate Japan (2004): Encoding a message as a number to base 26;
  • Fahrenheit 451( 1966): Gray suited students recite multiplication tables;
  • The Big Bang Theory (2007): Much of the show focuses on science, particularly physics; Leonard is an experimental optical physicist;Sheldon is a theoretical physicist;Howard is an aerospace engineer; Raj is an astrophysicist;
  • Caddyshack (1980): In one physical model, the shortest distance between two points is a straight line – in the opposite direction;
  • Frankenweenie (2012): it’s a 3D stop-motion animated film, a heartwarming tale about a boy and his dog. This animated film introduces children to the Science education: circuits and electrical currents; static electricity; conductors and insulators; electromagnets and so on; 
  • Fringe (2008): it’s a science fiction television series, focused on fringe science and genetic engineering;
  • V for Vendetta (2005):  Newton’s Third Law.

The World is our Classroom: Online Tutoring!

Learn from wherever you are in the world!

Majority of the students have lesser interest in Math and in Physics. I can help you in solving arithmetic problems, brain games and in understanding mathematical sentences. Teachers strive hard to bring back students’ interest in Mathematics and in Physics. The purposes of stimulating the student’s interest are:

  • attract students;
  • keep students active;
  • increase students’ enthusiasm for the course.

If the studying is not boring, the student will be keen to study and will be “happy” to study.

Solving Math (and Physics) problems is not easy! A lot of students have difficulty with Math/Physics questions. I will work with you in an environment to help you understand Math/Physics concepts better thereby ensuring that you are able to solve Math/Physics problems. So, get help FAST with your mathematics and physics questions!

Many students connect with personal teachers for conversation in any subject, on the web. There are many tutoring websites which provide such services at an affordable rates. The services are also good and available round the clock. One such company is BuddySchool, a company that has students all over the world and is one of the largest and reputed company in the field of education (another company is Tutorvista). Buddyschool.com provides help in all subjects like Math, Science, English, Statistics, History and so on. Teachers and students meet to study online; the teachers give a systematic explanation to solving problems in a step by step method and they are available round the clock 24 x7. They can get help with solving your homework problems.

Online tutoring

I have been looking at online tutoring adventures as I feel that I could help others to learn. This would be a different and interesting way to earn more money. You can chose to study through online learning, full time or part time. I answer your pre-algebra, algebra, trigonometry, calculus and statistics homework questions with step-by-step explanations. There are a lot of online math calculators and solvers to help calculate and solve your exercises.

Why must you learn Mathematics?

Technology is everywhere around us, and you need mathematics to master it!

 

 

 

Most jobs need good math skills:

  • Doctors
  • Engineers
  • Scientists (The physical sciences require mathematics for the development of their theories) 
  • Software Developers
  • Marketing Analysts
  • Financial Officers
  • Investment Managers (Statistics provides the theory and methodology for the analysis of wide varieties of data) 
  • and more…

Mathematics is also useful in everyday life:

  • Investing money
  • Estimating costs
  • Shopping
  • Understanding Computers (the mathematics of error-correcting codes is applied to CD players and to computers)
  • Designing rooms and gardens
  • Planning journey(Voyager’s journey to the planets could not have been calculated without the mathematics of differential equations)

Math is not about reading pages (so don’t think “I read 2 pages today”): it is about building concepts in your mind. Thus, it is more important to know the ideas than to remember the formulas.

Scientists are inclined to believe that mathematics and the mathematical rules which underpin nature are universal, so that all intelligent races in space have at least this much in common. Since the fundamental properties of numbers are the same everywhere, these can be used as the basis of interstellar messages.The main reason for studying mathematics to an advanced level is that it is interesting and enjoyable.People like ist challange and the solutions of a problem has an excitement and a satisfaction. Let me first say that everyone studies differently and there is no one right way to study for a math class.

Whether you need answers to specific Math Problems or just some help before a Math test or quiz, I will help you.