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Presents theorems about lines and lattice points, and relates these to combinatorial analysis. (RS)

A discussion of intuition, doubt, and surprise in mathematics arising from a problem involving rational points and lines. (RS)

The predicted and actual achievement in college calculus is compared for students who had studied two semesters of calculus in high school. The regression equation used for prediction was calculated from the performance data of similar students who had not had high school calculus. (CT)

For students having had instruction in plane affine geometry and two-dimensional vector spaces. The author describes how the metric concepts of distance and orthogonality can be introduced to secondary school students by the use of conics. (JG)

The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)

Discussed are implications and derivations from vux" triangles (triangles having one angle the integral multiple of another). (JG)

Desargues's theorem proved by vector methods. (MM)

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

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)

All lines which bisect the area of a triangle envelope a three-cusped curve made up of three hyperbolic arcs. (MM)

The third in a series of four articles, this is concerned with establishing the main properties of the general linear transformation of the plane, equations of lines, area, and change of axes. For earlier articles, see MT number 57, Winter 1971, pp. 14-19 and MT number 58, Spring 1972, pp. 49-55. (DT)

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)

Results of a study of the effects of a mathematics laboratory for college freshman mathematics showed that the laboratory produced higher achievement, affected attitude, and reduced the withdrawal-failure rate of students with a deficiency in mathematics. (DT)

An application of the formula for finding the sum of an infinite geometric series is described through the use of Pierre Fermat's method for finding the area under a curve. (JT)

A sequence of ellipses and a sequence of hyperbolas, both graphically approaching some parabola, are expressed algebraically and then shown to approach the parabola. (MN)

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

The authors derive distance formulas in two-and-three-dimensional coordinate geometry utilizing the concept of similar triangles and the Pythagorean theorem. (MN)

Two new types of graph paper are described; focus-focus conic paper and focus-directrix paper. Both types make it easier to draw families of conics. Suggestions for further work are given as is a method for establishing a connection with other ways of looking at the conic sections. (LS)

By translating inequalities into equations (e.g., x greater than 0 can be written x- absolute value of x = 0) and forming equations for unions and intersections of solution sets, students can develop equations for polygons. The method can be generalized to yield equations in three dimensions. (SD)