# 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; […]

26 May

### The Jeweler’s Observation, a look back

TweetPaul Brown, an Australian math teacher and author of Proof, a book that I may characterize as a well-written guided introduction into that most fundamental activity, has brought to my attention a recent post at the Futility Closet blog, The Jeweler’s Observation, which I fully reproduce below: Prove that every convex polyhedron has at least […]

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.

23 May

### A square in parallel lines

The problem is credited to V. V. Proizvolov and may serve an example where using dynamical software to sketch a diagram proves to be a distraction. I put together a GeoGebra applet and looked at the possible properties of the configuration with several elements added. Meanwhile, Hubert Shutrick pointed out its obvious, salient feature. The solution is a one liner

11 Sep

### Solving Puzzles with Socrates

This remark helps solved the following problem: in the diagram below, sum the areas of the circles in the two squares; which is larger: the sum of the two areas on the left or that of the four circles on the right? Or, may they per chance be equal?

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 […]

05 Apr

### Carnival of Mathematics #85 is out - with a splash

TweetAfter a hiatus of several month, Carnival of Mathematics is back online. Do check the revived carnival at The Aperiodical page by Peter Rowlett, Katie Steckles, and Christian Perfect. The new edition is both edifying and entertaining.

24 Feb

### The Joy of Homogeneity

TweetIn a recent blog A Lovely Observation Gary Davis (@RepublicOfMath) elaborated on an observation of Ben Vitale (@BenVitale) to the effect that In the fractions both numerators and denominators are sums of successive odd numbers: the numerators start with 1, the denominators where the numerators leave off. Thus naturally derivation of the formula for the […]

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 […]

11 Nov

### On the Perimeters of Embedded Polygons

TweetThere are mathematical statements that appear counterintuitive. For example, when it comes to infinities, counterintuitive statements are abundant. At the other extreme, there are statements intuitively obvious that are rather hard to prove. Such, for example, is the famous Jordan Curve Theorem. Naturally, mathematics does not lack in statements of any intermediate kind. Here is […]