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 geometry of drops hanging on a circular capillary can be determined by numerically solving a dimensionless differential equation that is independent on any material properties, which enables one to follow the change of the height, surface area, and contact angle of drops hanging on a particular capillary. The results show that the application…

This textbook commences with a brief sketch of the history of Elementary Geometry. The definitions throughout have been somewhat amplified, and several notes have been added which it is hoped may be found useful and suggestive. The subject of Ratio has been expanded; a few new propositions have been added; and there is a considerable collection of…

This textbook is designed to be used in a geometry course incorporating the writings of Euclid. The object of this edition now offered to the public, is not so much to give the writings of Euclid the form which they originally had, as that which may at present render them most useful. The author believes that the use of algebraic signs and…

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…