The ancient Greek mathematicians sought to construct, by use of straight edge and compass only, all regular polygons. They had no difficulty with regular polygons having 3, 4, 5 and 6 sides, but the 7-sided heptagon eluded all their attempts. In this article, the authors discuss some cosine relations and the regular heptagon. (Contains 1 figure.)

A table showing the first thirteen rows of Pascal's triangle, where the rows are, as usual numbered from 0 to 12 is presented. The entries in the table are called binomial coefficients. In this note, the authors systematically delete rows from Pascal's triangle and, by trial and error, try to find a formula that allows them to add new rows to the…

The fraction 16 over 64 has a well known, interesting property. If one incorrectly cancels the sixes, a correct answer of 1 over 4 is obtained. This is an example of a lucky fraction. In this article, the author presents several examples of lucky fractions and proves two interesting properties of these fractions. This article provides students the…

In some elementary courses, it is shown that square root of 2 is irrational. It is also shown that the roots like square root of 3, cube root of 2, etc., are irrational. Much less often, it is shown that the number "e," the base of the natural logarithm, is irrational, even though a proof is available that uses only elementary calculus. In this…

In this paper, the authors evaluate the series and integrals presented by P. Glaister. The authors show that this function has the Maclauren series expansion. The authors derive the series from the integral in two ways. The first derivation uses the technique employed by Glaister. The second derivation uses a change in variable in the integral.

Describes how to modify old QBASIC programs to run in visual Basic. (NB)

Describes how the cubic formula can be presented easily at the precalculus level, shows how to verify that the formula is correct, and identifies when it is profitable to use. (KHR)

Because fractal images are by nature very complex, it can be inspiring and instructive to create the code in the classroom and watch the fractal image evolve as the user slowly changes some important parameter or zooms in and out of the image. Uses programming language that permits the user to store and retrieve a graphics image as a disk file.…

The notions of pentagonal numbers and partitions can be understood by students at the precalculus level, and should work well in a first course in programming for high school or college students. Presents opportunities to conjecture properties of partitions from a computer program. (Contains 14 references.) (Author/ASK)

Explains a non-standard definition of an ellipse familiar to astronomers and workers in celestial mechanics but which is not usually given in undergraduate text books on mathematics. (MM)

A right triangle with legs x and y and hypotenuse z in which x, y and z are all positive integers is called a Pythagorean triangle (PT) and the triple denoted by [x,y,z] is a Pythagorean triple. If x, y and z are all relatively prime (gcd is 1), then the triangle is called a primitive Pythagorean triangle (PPT) and the tripe a primitive…