CTK Insights

Archive for October, 2011

31 Oct

Magical Mathematics

Tweet Many book authors end their book Introduction expressing the hope that readers will enjoy reading the book as much as the author(s) enjoyed writing it. Persi Diaconis and Ron Graham do not. Nonetheless, their book - Magical Mathematics - oozes their enjoyment at writing it. The authors are master storytellers. Movingly, Martin Gardner wrote […]

25 Oct

Is Parallelism an Equivalence Relation?

TweetThis is a beautiful pieces by Andy Liu, University of Alberta, from the College Mathematics Journal, Volume 42, Number 5, November 2011, p. 372 Parallel lines are usually defined as lines with no points in common. Parallelism is clearly symmetric. If line 1 has no points in common with line 2, then line 2 also […]

24 Oct

Combinatorial Mathematics with Applications: an Example

TweetIn their textbook Discrete Algorithmic Mathematics authors Stephen Maurer and Anthony Ralston offer a light-hearted example [pp. 217-221]: When checking into a hotel nowadays, sometimes a guest receives a four-digit "combination", not a key. On the door of each room is a keypad. Any time those four digits are entered in the proper sequence (regardless […]

23 Oct

Wrapping a Cube

TweetThis puzzle comes from a wonderful Russian site, where its solution is presented as a sequence of animations. (A later remark: through the efforts of Colm Mulcahy who approached David Singmaster an earlier reference has been found: Martin Gardner describes the puzzle at the end of Chapter 5 of his New Mathematical Diversions - a […]

22 Oct

The Parabolic Sieve of Prime Numbers

TweetParabola has an easily verifiable property. The segment joining points and crosses -axis in point . The equation of the segment is , from which . This may be a curious fact in its own right. What does it say? Taken at a face value, it simply shows a way to obtain the product of […]

22 Oct

2x1 rectangle to a square by Socrates

TweetIn a recent post, I have implied that Socrates new how to dissect a 2×1 rectangle into a square. There is actually no evidence that he did. However, he certainly knew how to produce a square half the area of a given one. How would he relate the two problems? A sangaku tablet has preserved […]

18 Oct

Curvy Dissections

TweetNowadays, finding the area of curvilinear shapes falls in the purview of calculus. But the problem of finding areas draw much interest in antiquity and preoccupied mathematicians ever since. One of the acknowledged results by Hippocrates of Chios (470-410 B.C.) is the Squaring of a Lune. The problem of squaring a shape refers to a […]

17 Oct

Education as Service - Educational system as a platform

TweetIf you have not read yet a memo by Steve's Google Platform rant, you should. A first-hand account on management practice and philosophy differences between Amazon and Google. The memo has been intended for internal google distribution but somehow found its way to a wider audience. Besides revealing some truths about the two successful online […]

02 Oct

When Less Is More

TweetYears ago, in a now defunct Borders store I came across two books that partially shared the titles: Christa Brelin (Editor), Strength in Numbers: A Lesbian, Gay and Bisexual Resource, Visible Ink Pr, 1996 Sherman K. Stein, Strength in Numbers: Discovering the Joy and Power of Mathematics in Everyday Life, Wiley, 1996 The incongruous semantics […]

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