This textbook covers the first six books of the elements of Euclid, the 11th and 12th books, and the book of Euclid's data. Elements of plane and spherical trigonometry are included.

This textbook is a course in surveying. Geometry, land surveying, chain surveying, plain-table surveying, theodolite surveying, hilly-ground surveying, laying out land, division of land, and levelling are covered.

This textbook covers geometry and trigonometry with addition of a fuller explanation of rectangular surveying, as well as a more particular explanation of the use of natural sines. The book's primary goal is teaching common field surveying. This edition adds practical matter, as well as the only table of natural tangents ever published in this…

The impossibility of a trapezoid having the sum of two adjacent sides equal to the sum of the remaining two sides is proved. (DT)

Develops a model of a non-Euclidean geometry and relates this to the metric approach to Euclidean geometry. (JG)

Describes a field trial of a supplemental geometry unit intended to raise Van Hoele thinking levels in a group of 23 eighth-grade students by having them become more adept at using higher order thinking skills. Sample questions assessing particular Van Hiele thinking levels attitudes toward geometry, as well as field-tests activities yielding the…

This article shows how Pythagorean triples can be generated naturally from a class of infinite series whose sums are zero, making surprising and interesting connections between different areas mathematics. This material can be suitable for use by teachers and students at various levels, but the simplest forms of the ideas may be best understood at…

A right triangle with legs x and y and hypotenuse z in which x, y and z are all positive integers is called a Pythagorean triangle (PT) and the triple denoted by [x,y,z] is a Pythagorean triple. If x, y and z are all relatively prime (gcd is 1), then the triangle is called a primitive Pythagorean triangle (PPT) and the tripe a primitive…

Greek philosopher mathematician, Aristarchus of Samos, in the third century B.C., proposed that the sun held in the central position, casting its light symmetrically outward on the other celestial bodies. He demonstrated the way in which a person could use simple observations and elementary geometry to measure on a cosmic scale.

Reorientation behavior of young children has been described as dependent upon a geometric module that is incapable of interacting with landmark information. Whereas previous studies typically used rectangular spaces that provided geometric information about distance, we used a rhombic space that allowed us to explore the way children use geometric…

Pythagorean triples appear in many areas of mathematics, and they are revealed yet again as one delves into a simple geometric problem.

A hexagon with each pair of opposite sides parallel to a side of a triangle will be called a hexaparagon for that triangle. One way to construct a hexaparagon for a given triangle ABC is to use as vertices the centroids P, Q, R, S, T, and U of the six non-overlapping sub-triangles formed by the three medians of triangle ABC. The perimeter of this…

This article, a play designed around an imaginary conversation between geometric objects, summarizes various approaches to visualizing a tesseract (a.k.a. hypercube--a four-dimensional analog of a cube).

The patterns of handmade quilts made in southern United States are utilized for studying the symmetries of the plane and transformational geometry. Quilts are made without sewing and then from the same block, students can make quilts with different wallpaper patterns by using various combinations of transformations and through this geometrical…