In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…

The first word of this item is "imagine". This instruction has the potential to signal a journey through a world of geometry that might leave you spellbound. On the other hand, it could be the start of a roller-coaster ride through three dimensions that will tax both your imagination, and your powers of visualisation. It is likely that you will…

The taxi metric is introduced, compared to the Euclidean metric, and used to define the taxi circle. For all pairs of points "A" and "B" the set of points equally distant under the taxi metric to "A" and to "B" is determined. For any triangle these sets are used to either find the centre of a taxi circle that can circumscribe the triangle or to…

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…

In this article, the author features "Flatland," by Edwin Abbott, a fantastic story about a square who lives in a two-dimensional world and who receives a visitor from the third dimension. Written in 1884 by a teacher-theologian who dabbled in mathematics, the novel is full of rich themes, including social class structure, the treatment of people…

This article discusses two examples of geometric problem solving suitable for middle and high school students. Both problems are related to students' everyday life experience and allow them to discover deep connections between mathematical properties and nature. With the help of dynamic mathematics software, students have the opportunity to…

Reports a proof of a classical geometry problem. The proposition is - In any triangle there are two equal sides, if the angles opposite these sides have angle bisectors with equal lengths. (RP)

Describes some unsolved problems in geometry, as well as some recently solved ones. Indicates that each advance generates more problems than it solves, thus ensuring a constant growth in unsolved problems. (GA)

This article shows how simple instruments may be used to construct angles of certain measures and applies this procedure to more detailed problems. A proof of the Pythagorean Theorem is given using these procedures. (CT)