Posted in Algebra, Algorithms, Combinatorics by: admin

2 Comments

26 Apr

TweetThe other day, while driving my HS senior son to school (he could have taken a bus, but, for one, his time is at a premium; also, the drive gives us an opportunity for a small chat), we talked about how words with different basic meanings may mean the same thing in certain contexts. As […]

Posted in Algebra, Algorithms, Arithmetic by: admin

No Comments

13 Apr

Without ever trying to answer such questions, I was always confident that the poster (if not the author) were smugly awaiting a definite reply, although, even with the most benevolent interpretation, the problem has to be considered ill-posed, like that of asserting the next term in a given sequence

Posted in Algebra, Complex numbers, geometry, Math activities, Problem solving, Weekly report by: admin

No Comments

04 Apr

The present collection supplies a perfect illustration to the fact that even the most simplest of the problems may be looked at from various angles. I wish that the authors of school textbooks that often include only answers or "solutions to the odd-numbered problems" paid more attention to the possibility of alternative view points.

Posted in Algebra, Combinatorics, Problem solving, Trigonometry by: admin

No Comments

01 Apr

TweetI came across the following problem several days ago but hesitated to write about it until April 1st. It is simple, practically trivial, and still, after doodling with it for some time, I was left with an open question. If it appears too trivial, even unworthy of mention, do please make an allowance for the […]

Posted in Algebra, Books to read, geometry, math fun, Puzzles, Uncategorized by: admin

No Comments

01 May

As you may surmise, the path will behave - if I may say so - in a more rational way. Given the incommensurate dimensions of the box it was rational to expect an endless path. This is what you get on the second attempt. But there remains a question to ponder: Why was the first path so short? Jim Henle leaves to his readers to find the answer.

Posted in About math, Algebra, Algorithms, Arithmetic, Homeschooling, Math activities, math fun by: admin

No Comments

17 Oct

TweetIn a well known puzzle, a father willed to his three sons camels, with the proviso that of the inheritance should go to the oldest among them, with being due to the middle one and to the youngest. Shortly after the father's death, a wise man riding on his camel through the village noticed the […]

Posted in Algebra, Curiosity by: admin

No Comments

19 Sep

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)]

Posted in Algebra, Uncategorized by: admin

No Comments

15 Sep

This amounts to a cubic equation for x=a+b: x^3+3x-36=0. The sum of the roots of this equation is -3, their product is 36, and the sum of their squares is 0. The latter implies that two of these are complex conjugates, say, u ± iv and one is a real number w (that is supposed to be 3.)

Posted in Algebra, Combinatorics, geometry, probability by: admin

6 Comments

20 May

Now generalize: cut the cube into nxnxn smaller cubes and ask the same question. The problem is not awfully difficult but needs some figuring out. Following the foregoing pattern, we eventually arrive at 1/n. But here is a delightful shortcut