# CTK Insights

• ## Pages

27 Mar

### Weekly report, March 21-27, 2016

TweetThis week a discussion on tweeter, brought to mind a quote by Underwood Dudley I used years ago Can you recall why you fell in love with mathematics? It was not, I think, because of its usefulness in controlling inventories. Was it not because of the delight, the feeling of power and satisfaction it gave; […]

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.

24 Jul

### Sphereland: The movie

At the space Portal where all spaces and universes cross, Hex observes a ship carrying a parallel Her and her Grandfather and wonders what it was those did differently over there that did not cause A. Square's heart to break.

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 […]

20 Feb

### Probability of Two Integers Being Coprime

TweetFor a prime , two integers are both divisible by with the probability , because this only happens when the two integers have the residue 0 (one out of available residues) modulo . Two integers are mutually prime if they have no common nontrivial factors, prime facors in particular. Assuming divisibility by one prime is […]

17 Jan

### Can you miss the New Year moment?

Tweet Indeed, is it possible to miss the New Year moment? The question is not meant to account for a possible tragic circumstance and is being asked plainly and candidly. Assuming you are in good health on December 31 of one year and remain healthy on January 1 of the next year, is it possible […]

21 Dec

### Star of David Theorems in Pascal Triangle

TweetI am not sure who coined the term "The Star of David Theorem" to designate the identities discovered in the early 1970s. There are in fact two of them, both related to the "Star of David" configuration in Pascal triangle (The diagram is courtesy wikipedia.org.) The first result discovered by Hoggatt and Hansell in 1971 […]

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 […]

18 Oct

### Curvy Dissections

TweetNowadays, finding the area of curvilinear shapes falls in the purview of calculus. But the problem of finding areas draw much interest in antiquity and preoccupied mathematicians ever since. One of the acknowledged results by Hippocrates of Chios (470-410 B.C.) is the Squaring of a Lune. The problem of squaring a shape refers to a […]

21 Mar

### Happy Purim!

Tweet (Borrowed from http://www.boingboing.net/2011/03/21/how-to-make-a-hamant.html)