CTK Insights

Archive for June, 2010

28 Jun

Most elementray aha! moments

TweetThe identity although simple, is rather surprising. It could be verified by raising the right-hand side to the power of 3: One way of accidently running into this identity is by means of Cardano's cubic formula applied to the third degree equation The formula will produce terms that include cubic roots. On the other hand, […]

27 Jun

Gambling Crusade

TweetIn a recent post I have opined that an engaging book on the follies of gambling well deserves to be included in the classic Extraordinary Popular Delusions and the Madness of Crowds by Charles Mackay, LLD. In fact the latter mentions (p. 425) that gambling was a matter of concern during the third crusade (led […]

24 Jun

Regarding the Disagreements

TweetAs I just mentioned a collection of articles Judgement under uncertainty: Heuristics and biases edited by D. Kahneman et al, I thought that perhaps it would be worth adding a quote or two from the text, especially because some ideas appear to have bearing on what is happening with math education. Here's one from an […]

24 Jun

Gambling and Penchant for Irrational Behavior

TweetI have just finished a review of Joseph Mazur's What's Luck Got to Do with It? As far as gambling is concerned I claim complete innocence. Perhaps this is the reason the book appeared to me as a concise encyclopedia of gambling. The book traces the history of gambling from the prehistoric times to the […]

19 Jun

Math teachers at play carnival

TweetI'll be hosting the next Math teachers at play blog carnival. A blog carnival is a publisher's way of networking. By now, there are hundreds if not thousands of various blog carnivals. Submit your article if the scope of this particular one suits your interests. The dead line for the next issue is July 14, […]

18 Jun

Square in a circle inscribed in a square

Tweet Here's a square inscribed in a circle which in turn is inscribed in a larger square. What is the ratio between the areas of the two circles? Two and a half millennia ago, Socrates already new the answer.

16 Jun

Euclid's Game

TweetDenise of the superb blog Let's Play Math has streamlined my online version of Euclid's game. The game provides a playful practice for the divisibility, gcd and some counting. The game (more accurately, the Java applet) has been written more than a decade ago when I just began to learn the Java language. At the […]

15 Jun

Sad news

TweetSteve Fisk, 63, passed away on January 31, 2010 after a long battle with leukemia. Fisk earned his PhD from Harvard and accepted a post-doctoral teaching postion at MIT. He moved to Bowdoin College in 1977 where he remained until his death. Many in the mathematics community will remember him through his proof of the […]

14 Jun

A Chain of Circles in a Sangaku and a Generalization

TweetA nice sangaku was listed by Fukagawa and Pedoe as Problem 1.3.3. Points O1, O2, and O3 are collinear points and the circles O1(r), O2(r), and O3(r) touch each other, the first touching the second and the second the third. The circle O(R) circumscribes the three given circles, touching the first and the third internally. […]

11 Jun

Areas in a Regular Hexagon

TweetHere's a simple problem that I found at the site of St. Ann's school in Brooklyn. The midpoints of the sides of a regular hexagon are joined to form a smaller hexagon. Find the ratio of the areas of the two shapes. One solution has been discovered by the students at the school and posted […]

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