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03 May

No Need To Lose the Battle

In passing, I totally disagree with Tanya's thesis that "People who think make better decisions, whether they want to buy a house or vote for a president." That's factually wrong. This would be rather presumptuous to assume that the ones who disagree with one's choice of a president give their vote thoughtlessly. I am certain Tanya did not mean that.

18 Jan

Kordemsky's Palindrome Problem

In his last book Mathematical Allurments (Matematicheskie Zavlekalki), published posthumously in 2000, he tells a story of a 7th grade girl who got tempted to solve that problem and found a solution, too. She informed Kordemsky that her solution was different from the one in the book. Kordemsky encouraged her to look further, for other solutions. Several of her classmates get involved in the search that eventually produced more than 120 solutions. I can imagine Kordemsky's delight in seeing his efforts at attracting young minds to mathematics being born fruit. The kids even came up with something unexpected: many of the numbers they came up lead to other solutions when some pairs of their digits get swapped.

10 Jun

Dominoes and Chessboard Activities

Tiling a chessboard with dominoes is uniquely suitable as an entertaining and edifying activity even for young children. Both implements are widely available, while experimentation with them leads to a good number of problems. Some of the problems admit simple (albeit ingenious) proofs that I would classify as the "very first," in the sense that they require minimal (if any) knowledge of mathematics.

09 Jun

Archimedes' Law of Buoyancy

Every body has a shape. Bodies may have the same or different shapes. We visualize a shape as separate from any connection to any physical body. Shapes have volume.

There are various forces that act on a physical body: gravity, air pressure, surface tension, forces due to the possible interaction of the surface of the body with the surrounding environment. For a derivation of Archimedes' law, we make an assumption that, excluding the weight, the force total that acts on a body in a given environment depends solely on the shape of the body. This is a reasonable assumption, especially because we shall be only interested in the bodies of the same shape that occupy a fixed volume, i.e., the bodies that may occupy the same physical space.

21 May

Engaging Math Activities for the Summer Break

TweetBelow is a growing collection of resources I designate as "Summer Math Activities". These deal with various (mostly non-computational) aspects of early mathematics and are suitable for young children. There is no good reason not to try these activities at any other time of the year. During summertime, with the kids out of school or […]

21 May

Parity Games

TweetParity is the simplest mathematical concept after counting. 1 is an odd number, 2 is even, and then they come intermittently: 3, 5, 7, ... are odd, 4, 6, 8, ... are even. A pile of an even (but not odd) number of items can be divided into two piles of equal sizes. An odd […]

19 Mar

What Is Origami?

TweetOrigami is an ancient Japanese art of paper folding, with adherents all over the world. Origami has a mathematical side to it and, as a tool of geometric construction, is more powerful than the Euclidean straightedge and compass. (For example, angle trisection is possible by paper folding.) Is it silly to ask, How much folding […]

24 Nov

Thought Provokers to Start a Class With, IV

TweetThe Bottleneck Principle The Bottleneck Principle is a problem-solving strategy according to which it may be useful to look into the circumstances in which the conditions of a problem at hand are either hardly or not at all satisfied. It is different from the Worst-Case Scenario in that the latter looks at the problem as […]

11 Nov

Thought Provokers to Start a Class With, III

TweetThe Extreme Principle The Extreme Principle is a misnamed problem-solving tactic akin to the Worst-Case Scenario often used in combinatorics and computer science. It does not make any claim (like, say, the Pigeonhole Principle) per se, but only suggests that, for some problems, looking into extreme circumstances or elements within the conditions of the problem […]

23 Oct

Wrapping a Cube

TweetThis puzzle comes from a wonderful Russian site, where its solution is presented as a sequence of animations. (A later remark: through the efforts of Colm Mulcahy who approached David Singmaster an earlier reference has been found: Martin Gardner describes the puzzle at the end of Chapter 5 of his New Mathematical Diversions - a […]