# CTK Insights

• ## Pages

25 Dec

### Math Associations on a Trip to Longwood Gardens, PA

TweetInterference A projectile / an arrow Circle packing Ball packing Bifurcation Hairy Ball Theorem Two parabolas Paraboloid Up and Down Sunset Just watching this sunset was worth the trip

30 Aug

### Math Associations on a Field Trip

I am just back from a wonderful 10 day trip to the central Alaska. It was cloudy and rainy for the first two days; low clouds common to Alaska were covering mountain peaks and even tree tops. But then the skies have cleared, the visibility was perfect, and the imagery of mountain ridges and jagged portions of glaciers easily evoked the idea of fractals. On a flight from Anchorage to Coldfoot it was fascinating to observe that many clouds had perfectly smooth flat bottoms that at a distance projected into straight lines.

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.

02 Jul

### An Engaging Algebraic Identity

One of the posts at linkedin pointed to a solution of an engaging algebraic identity by the Stevens Society of Mathematicians. What follows is a slight simplification of that proof.

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.

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 […]

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 […]

04 May

### Let Them Count by My Boys

Tweet This is a small book written by one of my boys and illustrated by the other. The idea is along the lines discussed in my previous post. Any group of objects has an associated attribute that reflects on the size of the group. This attribute is called Number; its presence and uniqueness is what […]

18 Feb

### Math Teachers at Play - a Blog Carnival, February 2011

TweetThe Math Teachers at Play blog carnival had several articles that especially drew my attention. The visual for explaining and using Equivalent Fractions, Sue Downing found at the Wikiversity website is indeed wonderful. It requires hardly an explanation and beautifully applies to explain the division of fractions process: It is a pity the Wikiversity page […]

13 Feb

### The myth of declining U.S. schools: another sane voice.

TweetJay Mathews from the Washingtom Post wrote a follow up on a recent report by the Brookings Institution scholar Tom Loveless. Loveless is one of the nation's leading experts on PISA and TIMSS. He has been part of the cohorts of specialists who advise those programs. In his report he says the first international test […]