Solution of problems in mathematics, and in particular in the field of Euclidean geometry is in many senses a form of artisanship that can be developed so that in certain cases brief and unexpected solutions may be obtained, which would bring out aesthetically pleasing mathematical traits. We present four geometric tasks for which different proofs…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

This paper tabulates the correlation of Virginia's mathematics performance expectations with Virginia's 2009 mathematics standards of learning.

Today's classrooms pose many challenges for new mathematics teachers joining the teaching force. As they enter the teaching field, they bring a wide range of mathematical experiences that are often focused on calculations and memorization of concepts rather than problem solving and representation of ideas. Such experiences generally minimize what…

In 1999, Richard Lee Colvin published an article in "The School Administrator" titled "Math Wars: Tradition vs. Real-World Applications" that described the pendulum swing of mathematics education reform. On one side are those who advocate for computational fluency, with a step-by-step emphasis on numbers and skills and the…

This paper takes a known point from Brocard geometry, a known result from the geometry of the equilateral triangle, and bring in Euler's [empty set] function. It then demonstrates how to obtain new Brocard Geometric number theory results from them. Furthermore, this paper aims to determine a [triangle]ABC whose Crelle-Brocard Point [omega]…

This textbook covers geometry and trigonometry and presents problems for student consideration. Geometry principles are applied to surface and solid measurement. Tables of logarithms and logarithmic sines are included. [This book was translated from the French of A. M. Legendre. It was revised and abridged by Charles Davies.]

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 book is primarily a scholarly monograph on ancient Chinese theory and application concerning the right triangle, based on evidence contained in classical mathematics texts and scrolls. It is also the first complete English translation of the ninth chapter of the Chiu chang suan chu, the richest source of problems from antiquity dealing with…

This work is chiefly a compilation from other books; and but very little new is added except a more full explanation, than has yet been published, of rectangular surveying, or the method of calculating the area of fields arithmetically, without drawing a plot of them and measuring with a scale and dividers, as has been the common practice; and…

Discussed are implications and derivations from vux" triangles (triangles having one angle the integral multiple of another). (JG)

This article describes how a series of lessons might be used to allow students to discover the size of the Earth, the distance to the Moon, the size of the Moon, and the altitude of Mount Piton on the Moon. Measurement with a sextant, principles of geometry and trigonometry, and historically important scientists and mathematicians are discussed.

The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)

The length of the longest ladder which will go round a right-angled bend in a corridor is found by five methods, none of which involves calculus. (MM)