CTK Insights

Archive for the 'Homeschooling' Category

20 Dec

Beautiful Geometry

And this is how it goes: 51 chapters that combine pedagogically meaningful artwork together with informative, and often eye opening, text. The book ends with a short Appendix which lays foundations for several mathematical concepts mentioned in the text.

This is truly an enjoyable, simple book that meets if not exceeds the author's expectations. It's a good seasonal present, too.

17 Oct

Elementary Problems that Beg for Generalization

TweetIn a well known puzzle, a father willed to his three sons camels, with the proviso that of the inheritance should go to the oldest among them, with being due to the middle one and to the youngest. Shortly after the father's death, a wise man riding on his camel through the village noticed the […]

12 Mar

Why cats land on their feet - a problem of 80 years standing!

Now, the thing that surprised me most in the course of the investigation was a wikipedia reference to the 1969 article by T. Kane and M. P. Scher "A dynamical explanation of the falling cat phenomenon" (International Journal of Solids and Structures 5 (7): 663–670. doi:10.1016/0020-7683(69)90086-9), as the solution as "originally due to (Kane & Scher 1969)." This appears to imply that the problem remained (officially, at least) unsolved for about 80 long years - quite on a par with the, say, better known Poincaré conjecture. But think of it, most probably the members of the Académie des sciences in Paris were not the first to ponder the question, which leads to a conclusion that the question has a much longer history. Hmm, I would never guess.

19 Sep

A Magical Incident due to the Paypal's Policy

I believe that the discrete variant makes the solution more transparent. For example, think of coffee and cream not as liquids but as collections of molecules. Since the number of molecules in the two glasses remains the same even after repeated iterations, cream molecules in the "water" glass come at the expenses of the water molecules in the "cream" glass and, therefore, the two quantities are equal.

14 Aug

The 5 Elements of Effective Thinking

Be as it may, I find it significant that the two math professors chose a venue other than employing Algebra as a tool for improving their readers' thinking. Had the book been written around an algebra course it would have no competitors.

08 Aug

Leonardo's Petals

Leonardo da Vinci's Notebooks contain many examples of geometric designs with circles and squares. Here's two design patterns obtained as a combination of a circle and four circles half its size. If r is the radius of the big circle, the small ones have radius r/2 and touch pairwise between themselves and also the big circle. Petals and flowers are formed. What is their area?

19 Jun

Children, parents and puzzles

I wonder whether the girl in the story was naturally scared of mental exercises, disliked puzzles or math, or, perhaps, her mom's injunction played a role in setting the girl into a wrong mood. I had a very clever classmate who - likely for that very reason - felt under pressure to perform well at examinations, but never had.

18 Jun

The Euclid Debate from 1869

TweetI am reading Lewis Carroll in Numberland by Robin Wilson that I reported buying earlier. The book is an extended professional - so to speak - biography of Charles Dodgson, better known as Lewis Carroll. Here's a passage from the book (pp 89-90) that adds another pair of quotes to the two I posted not […]

15 Jun

Two quotes on math education

TweetThere is a firmly held belief that study of mathematics has a benevolent effect on brain development. I am not aware of any research that supports this thesis. The evidence is mostly anecdotal, like that expressed in the following quote: To those of us who have not pursued the study of mathematics since college days […]

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.

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