CTK Insights

Archive for May, 2012

26 May

Indivisibles and Infinitesimals

Tweet If you are not a historian of mathematics and do not work in the foundation of calculus, you may easily confuse two concepts - indivisibles and infinitesimals - that are both claimed to underlie modern calculus. For example (see Mikhail Katz and David Sherry) mention a paragraph from C. Boyer (The concepts of the […]

26 May

Optimization by Elementary Means

TweetBelow I list several (quite a few, in fact) optimization problems that admit elementary solutions. By "elementary" I mean solutions that do not invoke the concepts of calculus. Most problems require insight and ingenuity - to a various degree. I am going to enliven the page with a few illustrations, but to avoid making the […]

24 May

Three Checker Game on a One Row Board

TweetThe setup for the 2-players game described below consists of three checkers placed on a K×1 board: A move consists in picking one of the outside checkers and placing it anywhere between the other two. Here's a sequence of two successive moves. As usual, players take turns. The one who can't make a move loses […]

23 May

A Crooked Polygon

TweetHere's a curious problem from a 2008 Moscow Olympiad: Find a polygon and point O on its boundary such that every straight line through O cuts the polygon into two pieces of equal area. The construction starts with placing point O at the origin and forming a polygon for which O lies on the boundary. […]

21 May

Engaging Math Activities for the Summer Break

TweetBelow is a growing collection of resources I designate as "Summer Math Activities". These deal with various (mostly non-computational) aspects of early mathematics and are suitable for young children. There is no good reason not to try these activities at any other time of the year. During summertime, with the kids out of school or […]

21 May

Parity Games

TweetParity is the simplest mathematical concept after counting. 1 is an odd number, 2 is even, and then they come intermittently: 3, 5, 7, ... are odd, 4, 6, 8, ... are even. A pile of an even (but not odd) number of items can be divided into two piles of equal sizes. An odd […]

20 May

X and the City - a Review

TweetIs mathematics all around us? Why, if you want to see it, it is; if you do not, you may also pass by and think of anything else.

19 May

Math Photos

TweetHere's a small collection of my recent photos that seem to have some bearing on questions in mathematics. The first one is the coat of arms atop the Governor's palace, Williamsburg, VA. Perhaps surprisingly, the inscriptions are in French. But in addition, there is a curious combination of symmetry and asymmetry that Here's a perspective […]

18 May

Linear Units of Measurements at the Time of Petrus Ramus

TweetOn the whole, considered in a historic setting, The Way To Geometry by Petrus Ramus (1515 – 26 August 1572) is a geometry text that - like other geometric texts written after Euclid - is more or less modeled after Euclid's Elements. The exception is the first chapter where Ramus states the purpose of geometry: […]

17 May

What They Said of Each Other

TweetI am in line for a review of an uncommonly rich book by Károly Simonyi. The book deserves any praise, such that I am afraid that by focusing in this post on a small trifle I came across in the book I may cause it injustice. I hope that the readers of this blog won't […]

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