CTK Insights

Fermat’s point was the first remarkable point in a triangle discovered after a hiatus of a thousand years. One way to obtain the point in ΔABC is to construct equilateral triangles A’BC, AB’C, ABC’ on the sides of ΔABC and pointing away from it and join the segments AA’, BB’, CC’. The three segments are [...]

Every parent is likely to have had an experience I once read about. A father placed four sweets on a table and asked his 4 year old daughter to count. She did this perfectly: one, two, three, four. On his prompting she also observed that there were 4 sweets. The father suggested she pick one [...]

I always feel apprehension on seeing the number line or x-axis introduced as a horizontal line, with the numbers increasing left to right. When the time comes, the y-axis is commonly introduced as perpendicular to the x-axis and hence vertical. Seldom there is enough time for a trifle observation that the direction of a number line [...]

It’s not simple and sometimes impossible to divide a circle into n equal parts. That is, if the word “circle” signifies the border of a circular region, then, as was shown by the great Gauss, the construction with compass and ruler is only possible when Euler function φ is a power of 2: φ(n) = [...]

I strongly believe that in a few years the thrust of an education reform will converge on the web. The process has begun even if not yet sunctioned by powers that be at the US Congress. The best universities put up their courses online, see, for example, a New York Times article. The general accesibility of [...]

Quiz yourself: how old is that quote: Our standard for high school graduation has slipped badly. Fifty years ago a high-school diploma meant something. We have simply misled our students and misled the nation by handing out high-school diplomas to those who we well know had none of the intellectual qualifications that a high-school diploma [...]

Quiz yourself. Would you know where the quote below comes from? It is to be hoped that the near future will bring reforms in the mathematical teaching in this country. We are in sad need of them. From nearly all of our colleges and universities comes the loud complaint of inefficient preparation on the part [...]