According to the Merriam-Webster dictionary, a planimeter is "an instrument for measuring the area of a plane figure by tracing its boundary line". Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by "walking" on the boundary. For someone who has…

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

This updated reprint of a classic work presents design analysis of geometric patterns and information helpful to constructing mathematical drawings of industrial and achitectural features. Both simple and complex designs are given. Problems combine both algebra and geometry. The work is divided into six chapters which are further divided into…

This guide is support material for geometry teachers in middle schools or high schools in South Carolina. The guide describes the content of each program in the television series and suggests further learning activities for the students. The geometry that underlies the world around us is presented through applications. Contents of the series…

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in the booklet include points, lines, planes, space, angles, and intersection and union of sets. (MK)

Includes patterns for and a brief discussion of the polyhedra: octahedron, tetrahedron, dodecahedron, cuboid, prism, and star. (PK)

Presents activities which use graphing calculators to explore parametric equations of spirals, circles, and polygons. (MKR)

Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…

We report some findings of the Longitudinal Proof Project, which investigated patterns in high-attaining students' mathematical reasoning in algebra and in geometry and development in their reasoning, by analyses of students' responses to three annual proof tests. The paper focuses on students' responses to one non-standard geometry item. It…

A simple, direct condition is formulated for determining the mode(s) of a probability mass function. This condition is then applied to the Poisson and hypergeometric mass functions.

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…

Geometry, e.g., the shape of the environment, can be used by numerous animal species to orientate, but data concerning the mouse are lacking. We addressed the question of whether mice are capable of using geometry for navigating. To test whether aging could affect searching strategies, we compared adult (3- to 5-mo old) and aged (20- to 21-mo old)…

During the 17th century, Baroque decoration used anamorphism to combine actual architectural elements with illusionistic painting. When viewed from a particular point in space, the architecture blends with painting to form a combined image. In this article, Julian Beever, a leading anamorphic pavement artist, explains to the author the principles…

The author has always been fascinated by the title identity. It's charming and simple, as well as easy to believe after pressing a few calculator keys. Several fine proofs have appeared in the literature, including several proofs without words. His own earlier proof is trigonometric, and he has often been dissatisfied with not being able to…

This article describes two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections.