Friday, September 25, 2009

Wolfram Mathematica Demos

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The above picture is not a bizzarre test pattern or color palette, but is a "Geometric pattern of Congruence" produced using Wolfram Mathematica.

So What exactly is Wolfram Mathematica ?

The full blown "Wolfram Mathematica" is powerful computer software that has to be purchased for several hundred US dollars.

However there are some great pre-made free demonstrations which can be downloaded to our own PC, and then played using the free Wolfram Player.

(We also have to download the Wolfram Player as detailed later).

From their own website, they describe Wolfram as follows:

Founded by Stephen Wolfram in 1987, Wolfram Research is one of the world's most respected software companies, and a well known powerhouse of scientific and technical innovation.

At the center is “Mathematica”: Wolfram’s core product that launched modern technical computing and has now become the world's most powerful global computation system. With millions of dedicated users throughout the technical and educational communities, “Mathematica” represents a unique blend of major research breakthroughs, outstanding user-oriented design, and world-class software engineering.


The "Wolfram Demonstrations" website page is at:

http://demonstrations.wolfram.com/

These mathematical demonstrations can be previewed and then downloaded.

However, to play them and use their control sliders, we need the "Wolfram Mathematica Player" installed, and this can be easily downloaded for free on the demonstrations page.

On the demonstration we are viewing, in the top right hand corner, there should be a clickable download symbol that looks like this:

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We can click this symbol and download and install the free player onto our computer.


For Mathematics Teachers:

The idea is to search and find a demonstration that is useful, and then download that file.

If it is your first time downloading a demonstation, then you will also need to download the free player and install it onto your computer.

Here are some screen shots of some useful demonstrations that I have downloaded and used:


Addition of Fractions

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Using the slider controls we can create many diferent denominators and numerators to visually show how a fractions sum answer is derived.



Multiplication of Fractions

This demonstration allows any fraction to be multiplied by a whole number.

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This can be used to identify equivalent fractions.



Get The Equation of the Line in Record Time

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This is a mathematical activity designed to help students practice finding the equation of a line in slope-intercept form. Press the "go" button to start the game. A green line will appear; select the button with the equation that describes the green line before the time runs out.

Selecting the correct button will give you a new line, but less thinking time.

This activity is designed to work well with interactive boards, as a classroom activity. (It will not work on this blog post, because it is only a screen dump).



The Gambler's Ruin

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The gambler starts with an "i" unit stake and the casino or house starts with "c" units. They repeatedly play a game for which the gambler has a fixed probability "p" of winning and the winner gets 1 unit from the loser.

Play continues until the gambler "succeeds"
by acquiring i+c units or is "ruined" by dropping to 0 units.

This Demonstration computes the probability that the gambler will succeed by breaking the bank. Subtracting this probability from 1 gives the gambler's ruin probability. The theoretical expected number of plays of the game until success or ruin is also computed and a simulation gives empirical results for the various parameter values.

In the example shown above we used p=0.474, the player's
probability of winning an "even money" bet in American roulette.


There are many other free demonstrations available from Wolfram.

So take Little Red Riding Hood and all her friends along to see
the Big Math Wolf.


Enjoy,
Big Passy Wasabi

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