Since its release last December, A Beautiful Mind has been wildly successful with both audiences and film critics. Already this year it has won 4 Golden Globe Awards including Best Pictures, and it is a front-runner for a similar batch of Academy Awards. But the director's premonitions of controversy were correct.
The World's First Mathematics Textbook
Let us look back, as far as we can, on how and why mathematics has been taught. Let us look back at the world's first mathematics textbook that we know about. Since its contents are more than four thousand years old, there can't have been many earlier.
The Instability of Democratic Decisions
If issues are very simple, democratic decisions can be stable. But even a small amount of complexity destroys that stability in the most drastic possible way, and gives ultimate power to anyone who can control the voting agenda.
A Baseball Giant, A Math Giant, and the Epsilon in the Middle
At the actual moment when the 714 record was broken, being more of a mathematician than a baseball fan, I guess, I started looking at interesting properties of the numbers 714 and 715.
Digging for Squares
I had found the only known example by Franklin of a magic square in which both the bent and straight diagonals are magic. Some may call these sorts of novelties math "lite." But I think we should all aspire to see one of our mathematical creations live on, two and a half centuries after we are gone.
Mathematical Femmes Fatales
In the age where literary theorists claim that every story has been told, that all possible characters and situations and combinations thereof are becoming exhausted, mathematicians beg to differ. The last year or two has seen a proliferation of mathematically-inclined characters, most notably in Broadway shows, but in literature and films as well. In short, math is in. Enter a mathematical femmes fatale: blue-jeans, collegiate, hair cute but unkempt, an intense, focused look, pencil behind ear, calculator in back pocket, a twinkle of nervousness, of edgy brilliance.
A Dozen Questions about a Triangle
The remarkable properties of a triangle have not escaped the notice of your dozenal correspondent! Here, for your amusement, are twelve problems about our familiar three-sided friend. Enjoy!
Measuring Diversity in the United States
Diversity is a word we hear frequently these days. But what does it actually mean? Sociologically, the word is used in reference to the number and degree of representation of racial and ethnic groups in a university, a city neighborhood, and so forth. Still, the notion is somewhat vague. What do people really have in mind when they say, for example, that the United States is more diverse than it has been in the past?
Problem Section
S-65.
Proposed by A. Parihar, student, University of Alberta. Let N be a nonnegative integer whose digits are a_0, a_1, ., a_n from left to right. Take a_{-1} = 1 and a_{n+1} = 10. For 0<=i<=n+1, define b_i = 9 - a_i + a_{i-1}.
Let M=10^{n+1} b_{n+1} + 10^n b_n + . + 10 b_1 + b_0.
Determine the minimum and maximum values of M/N.
