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Visual Math Learning Center

This site is focused on college and precollege math resources for learning with a focus on visual and applied techniques. Math Contributors are welcome to register!

Math is a logical language to describe and visualize the vast order of the natural world. Visualization and imaging skills can be used to enhance our understanding and application of math.

Interactive online private tutoring services, fun learning and teaching of visual math center, beginning algebra, equations, questions, tutorials, tutoring, word problems, worksheets, homework help, tutorials and activities

 

Big Bang Math!

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Hubble's Velocity-Distance relationship

v = H.d

established that the Universe is expanding. Edwin Hubble made a plot of recession velocity vs distance for galaxies that he had observed he found a straight line relationship. The slope of this line, known as the Hubble Parameter, H 20 (km/s)/million l.y., has units of 1/time. It is easy to see that, if the Universe is expanding at the present time, then at some point in the past, all matter was once together. Thus, 1/H, called the Hubble Time is an estimate of the Age of the Universe, about 15 billion years.

If we rewind the motion picture representing the history of the Universe, we can understand a great deal about its early state, just after the Big Bang. In its early stages the Universe was simpler than it has ever been. It was very hot and in a state of Thermal Equilibrium, that is its temperature determined all its other properties. Just after the Big Bang, temperatures were so high that particle pairs could be created purely out of the heat energy present. For example, a pair of thermal photons - which would be gamma-rays at these temperatures - might react to form an electron/positron pair:

+ e+ + e-

During its early phases the Universe was radiation dominated, that is the photons dominated the energy and pressure of the Universe. As the Universe expanded, it cooled, T 1/R, where R is some measure of the "scale of the Universe".

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The Big Bang Model

Let's review the observational evidence:

  • Distance/velocity relationship: distant galaxies are moving away from us, with speeds which increase linearly with distance
  • Chemistry: the universe is almost entirely hydrogen and helium, in a mixture of roughly 12 H atoms to 1 He atom
  • Cosmic Microwave Background: no matter where we look in the universe, we see radio waves which look like those radiated by a blackbody at about 2.7 degrees above absolute zero. There are tiny (one part in 10,000) variations in the brightness of this radiation on scales of a degree or so

Is there any way to tie all these pieces of data together? Yes! One model which can explain them all is called the Big Bang model. The name was coined by a scientist who didn't like the theory and tried to make it sound silly.

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Last Updated on Friday, 10 July 2009 22:19
 

Puzzling Adventures: Snow Walkers

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Puzzling Adventures: Snow Walkers--How to Clear Streets of Snow More Effectively

A fictional city grapples with the white stuff

By Dennis E. Shasha   

 

 Grid City is a small planned city laid out on a completely regular six-by-five grid with streets going north-south and east-west. There is one building per city block.Grid occasionally suffers major snowstorms. The Grid City Snow Clearing Department (GridClear) wishes to make it possible for residents to move about on paved roads

The head of GridClear consults you to help plan the path.

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Last Updated on Wednesday, 22 April 2009 05:44
 

Hidden Dimensions

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A Radical Mind

A Radical Mind
Benoit Mandelbrot is a true maverick, as his interview reveals.

The Most Famous Fractal

The Most Famous Fractal
What exactly is the Mandelbrot set? Find out in this excerpt from the book Fractals: The Patterns of Chaos.

Design a Fractal

Design a Fractal
Create and save your own wildly colorful fractals using our generator.

Sense of Scale

A Sense of Scale
Explore the infinite detail of a Mandelbrot set as you zoom to a magnification of

 

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Chicks do arithmetic

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Recently hatched fowls appear to add and subtract

Count your chickens after they hatch, and they may do a little arithmetic themselves.

Chicks only 3 or 4 days old manage an animal version of adding and subtracting, says Rosa Rugani of the University of Trento Center for Mind/Brain Sciences in Rovereto, Italy.

 
Last Updated on Wednesday, 22 April 2009 05:56
 
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Math Stories

Scientific American - Math
Science news and technology updates from Scientific American
Scientific American
  • When should a scientist's data be liberated for all to see?

    When researchers make an exciting discovery, the data behind it are often closely guarded until they can be examined, developed and then revealed--at least in part--in a peer-reviewed journal with all of the proverbial fanfare. [More]

  • Is the cure (geoengineering) worse than the disease (global warming)?

    If there's one thing more potentially contentious than the international politics of global warming (which the world has spent at least the past 20-plus years dithering about), it's the politics of the most radical suggestion to solve it: geoengineering . After all, he who controls Earth's thermostat...

  • Manipulation of the Crowd: How Trustworthy Are Online Ratings?

    Web sites such as Amazon, TripAdvisor and Yelp have long depended on customers to rate books, hotels and restaurants. The philosophy behind this so-called crowdsourcing strategy holds that the truest and most accurate evaluations will come from aggregating the opinions of a large and diverse group of people. Yet a...

  • When I'm 64: Identification with 'Future Self' Helps with Successful Financial Habits

    How much money do you put away each month toward retirement? Maybe you sock away all you can, already dreaming of that Florida condo. Or maybe you can’t even imagine where you’ll be then, what you’ll want to use the money for, even what you’ll be like: when you think...

  • Design Boosts Chances for Air-Powered Motorcycle

    Die-hard advocates of alternate energy might fantasize about cars that could one day run on water. But scientists in India have gone a step further. They’ve mathematically modeled an engine that should allow a motorcycle to run on air--compressed air, that is. Their design is described in the Journal...

  • Readers Respond on "Reform or Re-Reform?"

    Reform or Re-reform? In “ Numbers War ” [News Scan], Linda Baker’s treatment of our inquiry-based Discovering Mathematics series is filled with errors and naive claims. For instance, there was no “three-year pilot” of our texts, contrary to what Baker reported. The article repeats many unfounded criticisms of...

  • Shifty Science: Programmable Matter Takes Shape with Self-Folding Origami Sheets

    Researchers at Harvard University and the Massachusetts Institute of Technology (M.I.T.) have invented a real-life Transformer, a device that can fold itself into two shapes on command. The system is hardly ready to do battle with the Decepticons--the tiny contraption forms only relatively crude boat and airplane shapes--but the concept...

  • Paul Dirac: "The Strangest Man" of Science, Part 2

    Award-winning writer and physicist Graham Farmelo talks with podcast host Steve Mirsky (pictured) about The Strangest Man, Farmelo's biography of Nobel Prize–winning theoretical physicist Paul Dirac. [More]

    Add to digg "The Strangest Man" of Science, Part 1

    Award-winning writer and physicist Graham Farmelo talks with podcast host Steve Mirsky (pictured ) about The Strangest Man, Farmelo's biography of Nobel Prize-winning theoretical physicist Paul Dirac. [More]

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  • Soccer Players Ranked with Network Analysis

    (Announcer’s call of “GOAL!”)

    That’s a shout World Cup enthusiasts don’t hear too frequently. Soccer’s known for low-scoring games, which makes it difficult to find an objective means of measuring the skill of top players. In a given game, a couple might nail a goal or have an assist. But who’s...

  • Fact or Fiction: The Days (and Nights) Are Getting Longer

    The summer solstice that falls this year on June 21 marks the longest day of the year in the Northern Hemisphere, sunlight-wise. Almost imperceptibly, however, Earth's day–night cycle --one rotation on its axis--is growing longer year by year, and has been for most of the planet's history.

    Forces from afar...

  • Get Serious about Budget Deficits

    The continuing economic crisis in the U.S. and Europe is quickly sharpening the debate over public finances. Several countries have budget deficits around 10 percent of national income or larger, and their governments must show their publics and the financial markets that they have a plan for dealing with these...

  • A Quarter Century of Recreational Mathematics, by Martin Gardner

    Edit or's note: In light of the recent death of Martin Gardner, we are republishing this article from the August 1998 issue of Scientific American. Gardner wrote the "Mathematical Games" column for Scientific American from 1956 to 1981, and continued to contribute columns on...

  • Science Maps Explore New Ways of Displaying Information [Slide Show]

    Data visualization is something of a cottage industry these days--witness Edward Tufte, an emeritus professor of political science at Yale University, who has built a mini empire founded on his well-received books, which bear titles like Visual Explanations; Envisioning Information; and The Visual Display of Quantitative Information...

  • Martin Gardner: A Major Shaping Force in My Life

    Editor's Note: Douglas Hofstadter gave permission to Scientific American to post this essay in light of the death of Martin Gardner, who wrote the magazine's "Mathematical Games" column for 25 years and published more than 70 books. Gardner died May 22, at 95.

    I've been trying to...

  • Scholars and Others Pay Tribute to "Mathematical Games" Columnist Martin Gardner

    Editor's Note: Martin Gardner , who wrote the "Mathematical Games" column for Scientific American magazine for 25 years and published more than 70 books, died May 22 at 95. Scientific American editor Steve Mirsky solicited the following tributes and remembrances of Gardner from various colleagues. We...

  • Remembering Martin Gardner, with Douglas Hofstadter

    Martin Gardner died May 22nd at 95. [More]

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  • Hermits and Cranks: Lessons from Martin Gardner on Recognizing Pseudoscientists

    Editor's note: In light of the recent death of Martin Gardner, we are republishing this column from the March 2002 issue of Scientific American.

    In 1950 Martin Gardner published an article in the Antioch Review entitled "The Hermit Scientist," about what we would today call pseudoscientists. It...

  • Three puzzles from Martin Gardner (1914-2010)

    News of Martin Gardner's death began circulating on Saturday night. For those of you who are unfamiliar with his work, here's a taste of the kinds of puzzles he was famous for bringing to the world. Of course, he did much more: 15 years ago, I had the great honor...

  • Profile: Martin Gardner, the Mathematical Gamester (1914-2010)