Showing posts with label Cows in the Maze. Show all posts
Showing posts with label Cows in the Maze. Show all posts
Saturday, 11 September 2010
Sphericon
A while back I got a copy of Ian Stewarts "Cows in the Maze" to review, and did.
Today I was glancing through the links for one of the chapters, "Cone with a Twist", which describes a shape called a sphericon. If you make two equal cones with a 90o angles at the vertices and glue the two bases together then a cross-section cut through the two vertices forms a square, you can slice the shape with a plane through the two vertices, then rotate one 90o and reconnect them and the shape is called a sphericon.
It is sort of a Mobius Strip in 3d since it has one continuous surface...and it rolls with a wobbly gate that makes it fascinating.. See below.
If you want to make one of your own (or many) a nice net for the shape is found here.
The fun really starts when there is more than one.... This site helps you to see how they can roll around each other.
Sunday, 6 June 2010
More Cows... More Math
Well, I did it. A long layover in Chicago and a trans-Atlantic flight left plenty of time to wander through Ian Stewart’s “Cows in the Maze, and other mathematical explorations”. Even with pencil and paper time for a few problems…. But Don’t read it that way… Every chapter offers two or three different but related topics that can be the start of a wonderful mathematical exploration. Plow into them… if you get stuck,,,, read the clues… go to the web references, and in the end, read the answers at the end of the chapter, and then, check the “Further Reading” for each chapter at the end of the book.
I read lots of math books, and yet I kept finding new topics, or new information about old topics I thought I was up to the date on, or a twist I had never seen… it is the kind of stuff that makes a wonderful introduction for the new fan of recreational math, and a wonderful update for those of us who are…ummmm … a little older…. Remember HEX… Stewart rightfully suggests that it is time to re-introduce it to another generation. And you probably have read plenty about knot theory, but now they are playing with a new approach… applied knots so to speak…. Hey, if you don’t know a granny knot from a reef Knot, this is the place…. From Cats Cradle to the Cows in the Maze logic game for which the book is titled, good reading…. Good math…. Check it out.
I read lots of math books, and yet I kept finding new topics, or new information about old topics I thought I was up to the date on, or a twist I had never seen… it is the kind of stuff that makes a wonderful introduction for the new fan of recreational math, and a wonderful update for those of us who are…ummmm … a little older…. Remember HEX… Stewart rightfully suggests that it is time to re-introduce it to another generation. And you probably have read plenty about knot theory, but now they are playing with a new approach… applied knots so to speak…. Hey, if you don’t know a granny knot from a reef Knot, this is the place…. From Cats Cradle to the Cows in the Maze logic game for which the book is titled, good reading…. Good math…. Check it out.
Wednesday, 2 June 2010
Cows in the Maze
Mathematics is SO SERIOUS, that we all need to chill out a bit, and stop getting so uptight about decimal points and fractions and parallelograms." (Ian Stewart)
I just received a copy of Ian Stewart's "Cows in the Maze, And Other Mathematical Explorations" to review from Michelle Rafferty at Oxford University Press. I haven't read it all yet. I'm saving that for the long trip back to England this Friday, but I did thumb through it and got distracted repeatedly by interesting topics. The book is from Stewart's articles in Scientific American. I will save a fuller review, but will advise at the onset that it looks like a wonderful gift for a math student graduating from high school this month.
I do want to mention a topic(game) from the first chapter, which is on dice and dice games. I read a lot of math books, and yet I had never seen the game mentioned. I am going to slightly alter the game (Me altering Stewart's games is like telling Ichiro to try a different stance at the plate to improve his hitting, but hey, here I go)
So here is the idea, and a challenge. A point target is determined, say 15, or 21, or any number that sounds good to you; and a single die is rolled (it doesn't matter by whom). The number showing is the starting value for the running total. Each player in turn will give the die a quarter rotation in any of the four possible directions (for example, if a 1 is on the face, a quarter roll might bring up a 2,3,4, or 5, but not the six on the bottom).This number is added to the running total. The first person who goes over the set target value is the loser (alternate game, make him the winnner).
And my question is... given that each player plays intelligently, is there an advantage to one or the other player based on the value of the opening roll?
I just received a copy of Ian Stewart's "Cows in the Maze, And Other Mathematical Explorations" to review from Michelle Rafferty at Oxford University Press. I haven't read it all yet. I'm saving that for the long trip back to England this Friday, but I did thumb through it and got distracted repeatedly by interesting topics. The book is from Stewart's articles in Scientific American. I will save a fuller review, but will advise at the onset that it looks like a wonderful gift for a math student graduating from high school this month.
I do want to mention a topic(game) from the first chapter, which is on dice and dice games. I read a lot of math books, and yet I had never seen the game mentioned. I am going to slightly alter the game (Me altering Stewart's games is like telling Ichiro to try a different stance at the plate to improve his hitting, but hey, here I go)
So here is the idea, and a challenge. A point target is determined, say 15, or 21, or any number that sounds good to you; and a single die is rolled (it doesn't matter by whom). The number showing is the starting value for the running total. Each player in turn will give the die a quarter rotation in any of the four possible directions (for example, if a 1 is on the face, a quarter roll might bring up a 2,3,4, or 5, but not the six on the bottom).This number is added to the running total. The first person who goes over the set target value is the loser (alternate game, make him the winnner).
And my question is... given that each player plays intelligently, is there an advantage to one or the other player based on the value of the opening roll?
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