CTK Insights

Archive for the 'geometry' Category

18 Nov

It Never Stops with Pythagoras

TweetIn the previous blog I described a discovery of Hirotaka Ebisui and an observation by Thanos Kalogerakis, both concerning what's known as Vecten's configuration. Vecten's configuration is a generalization of the famous Bride's Chair that underlies Euclid I.47, generally identified as the proof of the Pythagorean Theorem, although by now there are hundreds of them. […]

11 Nov

A Discovery of Hirotaka Ebisui And Thanos Kalogerakis

TweetToday's communication from Thanos Kalogerakis brought to mind an insightful one page note by Alan Alda - a chapter in a collection This Explains Everything by John Brockman. With every door into nature we nudge open, 100 new doors become visible, each with it own inscrutable combination lock. On a rather small scale that Alan […]

17 Oct

A pizza with a hole

TweetThe editorial in the Crux Mathematicorum (43(8), October 2017) posed an interesting problem; how to equally share a pizza with a hole. To make the problem solvable, we need to assume a degree of abstraction. For example, if the hole makes it more difficult to divide a pizza, the assumption that it is possible to […]

04 Apr

Weekly report, the week of March 28, 2016

The present collection supplies a perfect illustration to the fact that even the most simplest of the problems may be looked at from various angles. I wish that the authors of school textbooks that often include only answers or "solutions to the odd-numbered problems" paid more attention to the possibility of alternative view points.

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 […]

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 Aug

Distance to the Horizon on the Fourth of July

TweetI had the luck to celebrate the past 4th of July with our friends in their newly acquired home just above the marina in Atlantic Highlands, NJ. The view from their backyard was absolutely breathtaking. The ambient light that appeared to blur the background made the view even more enchanting. Here is a map that […]

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.

19 Jun

Climbing Pyramidal Slopes

It is not very steep and may be even tedious, but - at the end - the answer (summit) proves to be somewhat simpler than the climb that led there.

I slipped once and got an answer that included the golden ratio. Since the latter commonly pops up in unexpected situations, I was not at all surprised. However, I noticed in time that the golden ratio would lead the path downhill.

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