# Wonders of Math - The Game of Life

What is the Game of Life? by Paul Callahan Rules of the Game of Life Life is played on a grid of square cells--like a chess board but extending infinitely in every direction. A cell can be live or dead. A live cell is shown by putting a marker on its square. A dead cell is shown by leaving the square empty. To apply one step of the rules, we count the number of live neighbors for each cell. A dead cell with exactly three live neighbors becomes a live cell (birth). Note: The number of live neighbors is always based on the cells before the rule was applied. In Life, as in nature, we observe many fascinating phenomena. The rules described above are all that's needed to discover anything there is to know about Life, and we'll see that this includes a great deal. Life Patterns A good way to get started in Life is to try out different patterns and see what happens. The R-pentomino is the first pattern Conway found that defied his attempts to simulate by hand. How Complex Can Life Get?

Critical thinking web We have over 100 online tutorials on different aspects of thinking skills. They are organized into modules listed below and in the menu above. Our tutorials are used by universities, community colleges, and high schools around the world. The tutorials are completely free and under a Creative Commons license. roots Typesetting math: 8% John Baez December 15, 2011 Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4: Click on the picture for bigger view. Roots of quadratic polynomials are in grey; roots of cubics are in cyan; roots of quartics are in red and roots of quintics are in black.

Banach-Tarski Paradox Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using rigid motions only, form TWO solid balls, EACH THE SAME SIZE AND SHAPE as the original? This theorem is known as the Banach-Tarski paradox. So why can't you do this in real life, say, with a block of gold? If matter were infinitely divisible (which it is not) then it might be possible. But the pieces involved are so "jagged" and exotic that they do not have a well-defined notion of volume, or measure, associated to them. In fact, what the Banach-Tarski paradox shows is that no matter how you try to define "volume" so that it corresponds with our usual definition for nice sets, there will always be "bad" sets for which it is impossible to define a "volume"!

Math Monday: Hula Hoop Geometry, Part 1 By Glen Whitney for the Museum of Mathematics Math Mondays have so far featured a wide array of different items from which one can make a tremendous variety of geometric constructions, but there has not yet been one on hula hoops. This week and next we’ll remedy that oversight. Also, the postings so far have almost entirely shown the constructions as fait accompli, so this series will also try to give a bit of insight into the process of devising a new creation. First, why hula hoops?

Graphs of Functions and Algebra - Interactive Tutorials Free tutorials using java applets to explore, interactively, important topics in precalculus such as quadratic, rational, exponential, logarithmic, trigonometric, polynomial, absolute value functions and their graphs. Equations of lines, circles, ellipses, hyperbolas and parabolas are also explored interactively. Graph shifting, scaling and reflection are also included. The definition and properties of inverse functions are thoroughly investigated. A graphical approach to 2 by 2 systems of equations is included. Math Calculator Perform mathematics calculations online : arrays, matrix, integrals, trigonometry functions, linear equations, differential equations, financial functions, polynomials, function solver, math equation solver, variables, products, inequalities, approximations, root-finding for algebraic functions, integrate functions numerically, find local extrema, analysis of a function and more. It can solve various mathematical problems in areas of calculus, algebra, discrete mathematics, numerical algorithms, applied mathematics and engineering mathematics. Use of variables, definitions, pi, exponential functions, products, symbols, sets, logic is allowed and possible.

The Socratic Method The Socratic Method:Teaching by Asking Instead of by Tellingby Rick Garlikov The following is a transcript of a teaching experiment, using the Socratic method, with a regular third grade class in a suburban elementary school. I present my perspective and views on the session, and on the Socratic method as a teaching tool, following the transcript. Blog : Twisted Architecture I didn’t set out to tie knots in Norman Foster’s Hearst Tower or wrinkle his Gherkin, but I got carried away. It’s one of the occupational hazards of working with Mathematica. It started with an innocent experiment in lofting, a technique also known as “skinning” that originated in boat-building.

What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree Clever student: I know! Now we just plug in x=0, and we see that zero to the zero is one! Algebra II - Math for Morons Like Us As of July 1, 2013 ThinkQuest has been discontinued. We would like to thank everyone for being a part of the ThinkQuest global community: Students - For your limitless creativity and innovation, which inspires us all. Teachers - For your passion in guiding students on their quest.

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