Construction of colorful braided polyhedra can provide upper elementary students with enjoyable geometric experiences. (SD)

A method of bisecting an angle by construction of an isosceles triangle and its axis of symmetry is described. (SD)

The third session of IT@EDU98 consisted of five papers on educational software and was chaired by Tran Van Hao (University of Education, Ho Chi Minh City, Vietnam). "Courseware Engineering" (Nguyen Thanh Son, Ngo Ngoc Bao Tran, Quan Thanh Tho, Nguyen Hong Lam) briefly describes the use of courseware. "Machine Discovery Theorems in Geometry: A…

This column contains brief notes on graphing in three dimensions; patterns in Pascal's triangle; plotting graphs by computer; and an application of the hypocycloid. (MM)

Presents a reexamination of an intuitively geometric view of the nonrelativistic Pauli spinor in a simplified discussion of the connection between the rotation group and special transformations in the plane of projection. This view of the spinor is related to those based on the existence of an istropic or null vector. (SK)

Children's perception and understanding of three-dimensional figures and of operations on them is discussed. Piaget's findings are reviewed and more current research is described. Classroom implications are explored. (SD)

The concept of trigonometric ratios in a right triangle can be clearly presented through the use of interactive-geometry software. Investigation in this manner allows students to see the crucial features of the concepts before they are formalized and to gain ownership of these ideas through discovery. Many examples of the mathematical…

Presents a method for determining the coordinates of the endpoint of a line segment given its slope, point of origin, and length. Applies the notion of similar triangles to quickly solve this type of problem. Includes a calculator program. (KHR)

Examines secondary school students' ability to interpret representations of three-dimensional objects including prototypes of component, perspective drawings, orthogonal views, descriptions by coordinates, verbal descriptions, and verbal quasi-descriptions. Students were given four identical wooden cubes and asked to construct the objects. Reports…

Relationships among the sides are developed for right triangles whose sides are in the ratios 1:3, 1:4, and 1:5. The golden ratio appears in the results which can be used in secondary mathematics. (DC)

Provides a proof that, if two angle bisectors of a triangle are equal in length, the triangle is isosceles (Steiner-Lehmus Theorem) using two corollaries related to a side-side-angle correspondence in a triangle. Introduces historical developments in the discussion of the proof. (MDH)

Presents activities involving multiple embedded figures beginning with the problem of counting the number of squares on a checkerboard. Offers several extensions and assessment suggestions. Includes student worksheets. (MKR)

In California, the typical college-prep course sequence in math includes Algebra I, Geometry, and Algebra II. Students advance through these courses at different rates. A number of students proceed at a quick pace, with some completing Algebra II by the end of 10th grade and a few even earlier. At the other end of the spectrum, some students…

When given opportunities to explore mathematics, make conjectures, and write about what they have discovered, students gain a deeper understanding of this fascinating subject. In this article, the author describes her successful Geometry Portfolio class. In addition to traditional student work, the author frequently added short essay questions or…