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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
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