CTK Insights

Archive for October, 2010

27 Oct

That Divergent Harmonic Series

TweetThe harmonic series, i.e., the series of the reciprocals of integers is a prototypical divergent series: the sums grow, albeit very slowly, without bound. There is no finite value S that could be ascribed as its sum. Assuming that such a value exists leads to a contradiction. A contradiction could be achieved in a multitude […]

27 Oct

Cannibalism makes grasshoppers stick together!

TweetThe latest Maths by Email newsletter from CSIRO Education has brought some remarkable research news; and mathematics is at the center of it. Scientists from around the world have spent many years researching locusts. A lot of the research had looked at what locusts like to eat. Locusts will eat almost anything they can find, […]

25 Oct

How much math do we really need?

TweetMr. Chase of the Random Walks blog came across an article by G.V. Ramanathan, a professor emeritus of mathematics, statistics and computer science at the University of Illinois at Chicago. The author beautifully argues a few obvious (to me) facts to which the establishment intentionally or not remains blind. Unlike literature, history, politics and music, […]

23 Oct

An Equation in Rational Numbers

TweetJust last week I received a request for a permission to use a picture from my Introduction to Graphs page in a forthcoming book. I gave the permission but noted that the picture is not mine and that I had lifted it from an old book years ago. None of the references listed on the […]

21 Oct

A. Soifer's Book, P. Erdos' Conjecture, B. Grunbaum's Counterexample

TweetA variant of Helly's Theorem states that if any three from an infinite sequence of convex planar sets have a nonempty intersection, the same holds for the intersection of all the sets, provided all of them are closed and at least one is compact. Neither closedness or compactness of at least one set can be […]

20 Oct

What a difference a minus one makes!

TweetThe FLT - Fermat's Last Theorem - states that for n ≥ 3, the Diophantine equation xn + yn = zn has no solutions. We now know this is true due to the 1995 result of Andrew Wiles. The theorem was conjectured by Pierre de Fermat in 1637 and thus withstood the many attempts during […]

20 Oct

Golden Ratio - Another Sighting

Tweet We'll be looking into a chain of circles all tangent to a given line and to the two immediate predecessors in the chain. The chain starts with two circles tangent to each other of radii a and b. For three circles, we have the following well known result, obtained yet in one of the […]

19 Oct

A Combinatorial Gem: Sum Multisets

TweetA combinatorial result due to Paul Erdös and John Selfridge has been discussed by R. Honsberger in his In Pólya's Footsteps. The problem was also included by Savchev and Andreescu in the wonderful Mathematical Miniatures. I reported these results elsewhere. More recently an extension of the discussion was posted in the problem section of the […]

19 Oct

Benoit Mandelbrot Dies at 85

TweetIt was probably in 1983 that I got my first depiction of the Mandelbrot set. I have just installed a black-and-white IBM PC with the screen resolution of 320×200, spent 5 minutes writing a Basic program and let it run for the whole night. In the morning, the results of my very first program written […]

14 Oct

October 2010 Math Fact

TweetHere's a message I received: There is an interesting fact about October 2010. The month is unusual in that it has 5 Fridays, 5 Saturdays, and 5 Sundays. This happens once in 823 years. Such a month is considered propitious of a good fortune. Send this note to 8 good people and in 4 days […]

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