"Can you guess the rules for generating sequences?... This one was in the New York Times the other day: 2, 3, 3, 5, 10, 13, 39, 43, 172, 177, ... "
Plouffe and Sloane are two researchers who have collaborated on a text about famous and useful sequences of integers. See Brian Hayes' article in American Scientist (Jan.-Feb.1996) about their work together:
Plouffe's website features famous constants such as pi and e, with records of longest computations and a table of many of the best known constants. The Inverse Symbolic Calculator will try to match any number that you enter, or the beginning of one, with constants in its database. A sophisticated version of the lookup can even compare your number to constants transformed by a limited set of simple functions. The site hosts over 400 tables containing over 50 million constants.
Neil Sloane also has a lookup function on his site. Type in a sequence of numbers and it will try to match it to a well-known sequence in its database. Sloane also offers many references to related source materials, and provides number puzzles with solutions.
Fermi questions emphasize estimation, numerical reasoning, communicating in mathematics, and questioning skills. They require estimation of physical quantities to find an answer to an order of magnitude (typically a power of ten) arrived at by making reasonable assumptions.
Students often believe that 'word problems' have one exact answer and that the answer is derived in a unique manner. Fermi questions encourage multiple approaches, emphasize process rather than 'the answer', and promote non-traditional problem-solving strategies.
The Fermi Questions Library on the Web features:
- Classic Fermi questions with annotated solutions - A list of Fermi questions to use with students - Fermi questions with a Louisiana twist - Fermi activities for the K-12 classroom
Prof. Scott W. Williams of the Mathematics Department, SUNY Buffalo, has created a series of Web pages designed "to exhibit the accomplishments of the peoples of Africa and the African Diaspora within the Mathematical Sciences." The contents include:
- The Ancients - Modern Historical Significance - Black Research Mathematicians - Profiles of Black Mathematicians - Special Articles - Related Links - Sources and References