CTK Insights

Archive for June, 2013

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.

11 Jun

Parallel Chords in Conics

Points A,B,C,D lie on ellipse such that AB||CD. AC and BD meet in H. AD and BC meet in G. Prove that GH crosses AB and CD in their midpoints, E and F. Why this is true? A short answer is truly cryptic: Because this is true for circles

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

05 Jun

Naming Infinity - the book

This is an unusual book that eludes categorization. It's an outline of fundamental mathematical ideas cultivated by human beings, of mathematics as a human endeavor in the most candid sense of the word. It's a collection of biographical sketches - and not only of mathematicians - on a historic background, spread from the Dreyfus affair in France, and over the failed Russian revolution of 1905, the WWI, the October revolution, the Stalinists purges, the WWII, and post-Stalinist experimentations.

The book is a tangle of documented evidence and, likely, anecdotal testimony. It's warm, humane and makes an absorbing reading

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