# 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; […]

01 May

### A wrapping surprise

As you may surmise, the path will behave - if I may say so - in a more rational way. Given the incommensurate dimensions of the box it was rational to expect an endless path. This is what you get on the second attempt. But there remains a question to ponder: Why was the first path so short? Jim Henle leaves to his readers to find the answer.

01 Apr

### Why Learn Mental Math Tricks?

I strongly believe that those tricks are more than anything else convey to the early learners the essence of practicing mathematics. Presh Talwalkar's book may also open the eyes of an older generation on what they missed in the early grades.

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 […]

07 Jun

### Dynamic Software as Serendipity Enhancement

Checking the "Extra" box will suggested a few more properties: angle MAN is not the only angle in the diagram that equals 45 degrees (e.g., angle ADN and angle CMD; angle NLM=90 degrees; some intersections (N,D,L,E,M) are concyclic; there are several similar triangles (e.g., ALN and NLD).)

There are probably other properties. Should you find any, please let me know

02 Jul

### Fibonacci Numbers Trick

TweetWilliam Simon was probably the first to employ a property of Fibonacci's recursion Xn+1 = Xn + Xn-1 as a professional magic trick. This is best described in Hilton, Holton, Pedersen: Consider the following number trick — try it out on your friends. You ask them to write down the numbers from 1 to 10. […]

27 Jun

### Bags, Coins, and Questions

There are 31 bags placed in a row with 100 identical coins each. One bag is selected and one coin is moved from the selected bag to every bag to the right of it. A question can be asked for a total number of coins in any group of bags. How many questions are needed to determine the chosen bag?

08 May

### Spilling Molasses and Defying Conservation Laws

TweetAs Galileo has famously said, "Mathematics is the language with which God has written the universe." But what problems! The new book is a collection of physical puzzlers, often with counter intuitive manifestations, which, for all that, admit rigorous explanation supported by physical intuition. Say, you are in a spacecraft orbiting a planet. You turn […]

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 […]

19 Feb

### Thought Provokers to Start a Class With, VI

TweetHere are a few engaging problems that many a student will be able to solve and, if not, would be able to appreciate the simplicity of a missed solution. Without a measuring tape, is it possible to cut a half-meter piece from the rope of 2/3 m length? Solution What is the digital root of […]