This paper discusses methods of sketching various types of algebraic functions from an analysis of the portions of the plane where the curve will be found and where it will not be found. The discussion is limited to rational functions. Methods and techniques presented are applicable to the secondary mathematics curriculum from algebra through…

The length of the longest ladder which will go round a right-angled bend in a corridor is found by five methods, none of which involves calculus. (MM)

A proof is given of a construction axiom, involving the use of a Mira used to construct a segment of a length cube root of K when segments of lengths 1 and k are given. (MP)

A discussion of the so-called rose curves defined by simple trigonometric functions in polar coordinates. (MM)

The simultaneous solution of equations in polar form does not always yield the points of intersection of their graphs. An explanation is given. (MP)

Given two interesecting lines, the "pencil" of this interesection is the family of all lines passing through the point of intersection. Presented is a characterization of all lines both in the plane and lying in opposite sectors of the plane as determined by one of the original intersecting lines. (JP)

Paper shows that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context. (Author)

A method is developed for finding the equations of two circles that intersect at points with integral coordinates. Such equations are useful for the introducing systems of quadratic equations. (MP)

A method for converting a three-dimensional coordinate system to a two-dimensional coordinate system is explained. (MN)