Materials were written for an entire year's course in geometry in which transformations were used to develop the concepts of congruence, similarity, and symmetry, as well as being a vehicle for proof.

The course presents a rigorous treatment of the foundations of Euclidean and non-Euclidean geometries. The discovery of non-Euclidean geometry in the first half of the 19th century shattered the ...

This is a preview. Log in through your library . Publisher Information The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and ...

IN a recent number of NATURE (June 30) there appeared a review of a book by G. Mannoury on the philosophy of mathematics, and the reviewer emphasised a statement of the author to the effect that the ...

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in ...

Virtual reality can take you to some far-out places — mountaintops, distant cities and even fantastical game worlds. A team of artists and mathematicians is now adding to that list: universes where ...

Grid cells, space-mapping neurons of the entorhinal cortex of rodents, could also work for hyperbolic surfaces. A new study tests a model (a computer simulation) based on mathematical principles, that ...