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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. […]

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 […]

24 Apr

Environmental impact of power lines

This is to simply document my observation which I've been mulling over for a long time until very recently.

A couple of streets that I daily drive over are lined with trees whose branches seem to exhibit strange growth pattern. While their older branches point unremarkably each other way, the younger ones sprout pretty much vertically

29 Jan

Wizards, Aliens, and Starships

Truth be told, at the outset, when I realized what the book was about, I was a little annoyed. Science is science and fantasy is fantasy, and one may not want to know that there might be something wrong with the concepts in the book one is enjoying. Should everything be laid bare? That's literature we are talking about, for crying out loud, not textbooks or manuals! But Adler's writing is lucid and engaging and it sucks you in. There are so many whys and whats that I eventually developed a feeling that reality may be by far more interesting then any kind of fiction.

19 Sep

Radical Simplification - Not That Simple!

While the cube root of 2+sqrt(5) is in the extension field Q[sqrt(5)], the square root of 2+sqrt(3) is not in Q[sqrt(3)] but rather in Q[sqrt(2), sqrt(3)]

21 May

Area and Perimeter Splitters in a Triangle

It is then meaningful to ask whether a line could be simultaneously an area and a perimeter splitter, and seek a characterization of such lines if they exist. As a matter of fact, they do, and there may be 1, 2, or 3such lines. This was shown by A. Todd a senior at university. In truth, the problem has an interesting history.

15 May

Reflections captured in photo II

When shooting in proximity to a puddle, the reflection of an object comes out sharp is the focus taken is as if you were shooting the object itself. This becomes quite clear when you compare the two pictures below. In the first one focus is on the reflection, in the second it's on the surface of the puddle.

03 Feb

What happens to the area when the radius of circle is doubled?

TweetAssume you work with the kids who do not yet know the famous formula for the area of a circle of radius . How would you explain to the kids that the area of the circle quadruples when the radius doubles? This is the question raised by Linda Fahlberg-Stojanovska at the mathfuture google group. For […]

19 Sep

A Magical Incident due to the Paypal's Policy

I believe that the discrete variant makes the solution more transparent. For example, think of coffee and cream not as liquids but as collections of molecules. Since the number of molecules in the two glasses remains the same even after repeated iterations, cream molecules in the "water" glass come at the expenses of the water molecules in the "cream" glass and, therefore, the two quantities are equal.

22 Jul

It Fills All Space

Who is it that fills the space? The space itself, of course - whatever that space is. ... Only a 0-dimensional space - "the Abyss of No dimensions," in the words of Abbott - has enough room for a single individual. It's this fellow who fills its space in Flatland and keeps broadcasting the news