tag:blogger.com,1999:blog-42804517352902145902024-03-08T15:49:09.668-08:00Daily MatherciseSimple mathematical exercises for fun each day (excluding Sundays).Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-4280451735290214590.post-10595945483804452482010-03-24T17:43:00.000-07:002010-03-24T17:44:08.656-07:00The EndThis daily blog was an experiment, but it's not working for me. So sorry. Don't expect any new posts here.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com2tag:blogger.com,1999:blog-4280451735290214590.post-67406007603044435832010-03-16T18:57:00.000-07:002010-03-16T19:00:21.188-07:00Knots<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://karenswhimsy.com/public-domain-images/celtic-knots/celtic-knots-6.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 324px; height: 478px;" src="http://karenswhimsy.com/public-domain-images/celtic-knots/celtic-knots-6.jpg" border="0" alt="" /></a><br />Try drawing some knots. This is not as easy as it may sound at first. Tying knots is much more natural and intuitive than drawing them.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-82412020148967916612010-03-15T19:25:00.000-07:002010-03-15T19:26:23.885-07:00More Prime NumbersIf p is a prime number that is bigger than 3 can you see why either p+1 or p-1 is divisible by 6?Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-29509352950259590932010-03-13T12:57:00.000-08:002010-03-13T12:57:00.075-08:00RandomnessRandomness is a tricky thing. Open up a text document and put your a finger on two different keys (for instance 1 and 0). Now <span style="font-style: italic;">very</span> rapidly type a sequence of those two characters (taking about five seconds to do so), but try to make the sequence as random as possible.<br /><br />Here is what I got:<br /><br />1010100000100001010100100101011010101011<br /><br />How random is your sequence? (Mine is pretty nonrandom.) Think about ways of measuring its randomness.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com2tag:blogger.com,1999:blog-4280451735290214590.post-8118603932695717982010-03-12T18:20:00.000-08:002010-03-12T18:20:00.702-08:00Joke Chess ProblemsYou may have heard of <a href="http://en.wikipedia.org/wiki/Chess_problem">chess problems</a>: puzzles involving the game of chess. Have you heard of a joke chess problem?<br /><br />If not check them out: <a href="http://en.wikipedia.org/wiki/Joke_chess_problem">Joke chess problems on Wikipedia.</a><br /><br />Source: <a href="http://en.wikipedia.org/wiki/Main_Page">Wikipedia.</a>Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-9365151944862727492010-03-11T19:48:00.000-08:002010-03-11T19:48:00.097-08:00Number Sense + Working MemoryThis exercise is meant to be done in your head to give your working memory a workout.<br /><br />Think of four four-digit numbers. Let's say the year you were born, the last four digits of your social security number, the last four digits of your telephone number and the number 1234 (but feel free to come up with your own). <br /><br />First arrange them in your head in ascending order.<br /><br />Next arrange them so that the third digits are in descending order.<br /><br />Finally, with the numbers in the order of step two, think of the four-digit number whose first digit is the first digit of the first number, whose second digit is the second digit of the second number and so on.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-3550942803316589042010-03-10T19:40:00.000-08:002010-03-10T19:40:00.825-08:00Geometry + Working MemoryHere is one to exercise your <a href="http://en.wikipedia.org/wiki/Working_memory">working memory</a> while your <a href="http://en.wikipedia.org/wiki/Spatial_reasoning">spatial reasoning</a> is engaged.<br /><br />Imagine four or five solids (I used the sphere, cube, tetrahedron [a triangle-based pyramid] and cylinder, but don't let that influence you).<br /><br />Now visually moving them around and scaling them, put the first inside the second inside the third inside the fourth. Now reverse the order of the nesting.<br /><br />Too easy-peasy? Do it with more solids.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-7113205153272402382010-03-09T18:54:00.000-08:002010-03-09T18:54:00.258-08:00Fuse PuzzleOK, this should take you more than a few seconds, it's a tough puzzle, but give it a go:<br /><br />I'm quoting verbatim from the Web page: <a href="http://www.tanyakhovanova.com/Puzzles/#miscellaneous">My Favorite Puzzles</a>:<br /><br />"You have two fuses that both last one hour, and you have no other ways of telling time. The fuses may be thicker at some points, so in half an hour, the amount of fuse that has burned may or may not be half the length of the whole fuse. How do you measure 45 minutes worth of time?"<br /><br />Source: <a href="http://www.tanyakhovanova.com/">Tonya Khovanova</a>Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com3tag:blogger.com,1999:blog-4280451735290214590.post-21252558850251922662010-03-08T18:47:00.000-08:002010-03-08T18:47:00.265-08:00159 match sticksI have 159 match sticks that got wet and are now useless as matches. I want to cut the heads off of them and make a mathematical sculpture, but I haven't decided what to make yet. What would you make with 159 match sticks? If you have a good idea please share it.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-80243041973025663512010-03-06T18:08:00.000-08:002010-03-06T18:08:00.247-08:00More Fundamental MathematicsTopology is like geometry, but with a little less structure. (Don't confuse <a href="http://en.wikipedia.org/wiki/Topology">topology</a> with <a href="http://en.wikipedia.org/wiki/Topography">topography</a>. They are not the same thing.) In topology you don't care about actual distances, just a more abstract notion of "nearness". Planar topology is sometimes called rubber-sheet geometry, because two-dimensional figures can be deformed without their topology changing (though their geometry certainly changes) as if they were drawn on a rubber sheet. Topology developed as a mathematical subject much later than geometry, probably because it is more abstract and it's ideas are more slippery, but topology can be thought of as a stripped down version of geometry. Today topology itself is a full-blown branch of mathematics.<br /><br />I know that you probably won't come up with a whole new branch of mathematics in the next few seconds, but try anyway. Think of a branch of mathematics that you know (maybe number-theory or sequence patterns) and try to strip it down to something more fundamental and abstract. Don't stress. Success is not expected. It's the journey that is important.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-85458768893038541602010-03-05T17:55:00.000-08:002010-03-05T17:55:00.267-08:00Base ThreeComputers are designed around the fact that it is easy to store and manipulate bits with components that have two states (e.g. 1 or 0, on or off, high voltage or low voltage). It is just possible that at some point it will become more efficient to work with components that naturally have three states. Then computers will work base three (or <a href="http://en.wikipedia.org/wiki/Ternary_numeral_system">ternary</a>). If that happens then the sequence of numbers starting with three and continuing by multiplying by three to get bigger and bigger numbers will become very important to computer scientists:<br />3 -> 9 -> 27 -> 81 -> etc.<br />Continue this sequence as far as you can mentally, or as far as you have time on paper.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-90675666832535224902010-03-04T18:04:00.000-08:002010-03-04T18:04:00.459-08:00Powers of TwoOne plus one is two. Two plus two is four. Four plus four is eight. Continue this sequence as far as you can mentally.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-92109188117636783072010-03-03T17:48:00.000-08:002010-03-03T17:48:00.222-08:00Three-Dimensional FormsYou know some solids (or three-dimensional figures) such as cubes, spheres, pyramids. Name as many solids as you can think of. Think of some that don't have names (and think up your own names for them).Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-57163565351052610752010-03-02T17:29:00.000-08:002010-03-02T17:29:00.403-08:00Kaprekar RoutineStart with any whole number (but it should have more than one digit. Four digits works well.) I'll start with 5820. Make a new number by writing the digits in descending order:<br />8520<br />and another by writing them in ascending order:<br />0258 = 258<br />Now subtract the two:<br />8520-258 = 8262<br />This process is called the Kaprekar routine. Notice that you start with one number and end up with a new number. From there you can repeat the process if you wish.<br />Here's the sequence I get:<br />8520 -> 8262 -> 6354 -> 3087 -> 8325 -> etc.<br />If you continue long enough what do you notice?<br /><br />Source: <a href="http://mathworld.wolfram.com/">Wolfram MathWorld</a>:<a href="http://mathworld.wolfram.com/KaprekarRoutine.html">Kaprekar Routine</a>Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0tag:blogger.com,1999:blog-4280451735290214590.post-84550950607917970392010-03-01T14:28:00.000-08:002010-03-01T14:28:00.832-08:00Large PrimesName the largest prime number that you can come up with off the top of your head. No calculating. No in-depth thinking about. Just name the biggest prime number you can think of right now.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com1tag:blogger.com,1999:blog-4280451735290214590.post-74360492075160318452010-02-23T13:58:00.000-08:002010-02-27T18:21:04.135-08:00What is Daily Mathercise?Daily Mathercise is your source for a fun daily (excluding Sundays) mathematical exercise. These are simple exercises that should either take only a few seconds or be something to keep in the back of your mind all day. They are meant to get your mathematical juices flowing and are targeted at the general public (primarily), math students, math teachers, mathophobes and professional mathematicians or other technically trained people alike.<br /><br />I'm planning on getting started with daily posts on March 1, 2010.Jamiehttp://www.blogger.com/profile/16414506576878819208noreply@blogger.com0