Discusses a conjecture of a ninth-grade student that extended a geometry theorem about trisecting sides of a triangle. Presents a proof and extensions. (MKR)

Describes how a 3-inch by 5-inch card can be used to develop properties of similar triangles and prove the Pythagorean theorem. (MKR)

Presents interesting investigations and activities for inscribed and escribed circles of right-angled triangles. (ASK)

Around 300 BC, Euclid wrote "The Elements", a major treatise on the geometry of the time, and what would be considered "geometry" for many years after. Arguably "The Elements" is the second most read book of the western world, falling short only to The Bible. In his book, Euclid states five postulates of geometry which he uses as the foundation…

California's education system--the largest in the United States--is an essential resource for ensuring strong economic growth in the state. The Career Technical Education Pathways Initiative (referred to as the Initiative in this report), which became law in 2005, brings together community colleges, K-12 school districts, employers, organized…

While exploring Keith Haring's Web site one day, the author discovered two untitled pieces from 1982 that became inspiration pieces for a lesson on symmetry and complementary colors for her second graders. Haring's simple shapes and colors and playful images are very similar to those found in the margins or on the cover of any typical child's…

The geometric problem of finding the number of normals to the parabola y = x[squared] through a given point is equivalent to the algebraic problem of finding the number of distinct real roots of a cubic equation. Apollonius solved the former problem, and Cardano gave a solution to the latter. The two problems are bridged by Neil's (semi-cubical)…

Due to the popularity of 3D graphics in animation and games, usage of 3D geometry deformable models increases dramatically. Despite their growing importance, these models are difficult and time consuming to build. A distance learning system for the construction of these models could greatly facilitate students to learn and practice at different…

Expanded instructional time has become increasingly popular as a strategy to improve the academic outcomes of low-skilled students, particularly in the 9th grade. We evaluate the efficacy of a double-period algebra policy initiated in the Chicago Public Schools in 2003. This policy required all students with 8th-grade test scores below the…

Most high school mathematics teachers completed a mathematics history course in college, and many of them likely found it intriguing. Unfortunately, very few of them find the time to allow much, if any, mathematics history to trickle into their instruction. However, if mathematics history is taught effectively, students can see the connections…

Geometry certainly is in fashion, at the Henrietta Barnett School for girls in North London. Within the project "Engaging mathematics for all learners", led and funded by the Qualifications and Curriculum Authority (QCA), the Royal Institution of Great Britain (Ri) looked into how mathematical tasks usually reserved for the "gifted…

Justin and Jenny, grade 12 math students, walk with their preschool friends Sean and Meg to the local grocery store. There, two classmates are tending the cash registers. The six of them, along with others, are participating in an in-school "field trip" to Consumer Town, located in the South Windsor High School front lobby. The field…

The prevalence of feature-based 3D modeling in industry has necessitated the accumulation and maintenance of standard feature libraries. Currently, firms who use standard features to design parts are storing and utilizing these libraries through their existing product data management (PDM) systems. Standard features have enabled companies to…

In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D…