This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most ...

Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been ...

LET us suppose Euclidean space to be filled with a medium of variable refractive index. Then to an observer in that medium the curved path of a ray of light will present all the appearances of a ...

In 1847, an eccentric British mathematician named Oliver Byrne released a new edition of Euclid’s famous mathematical treatise, The Elements of Geometry. Byrne added a rather longwinded but ultimately ...

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...

Margaret Wertheim gave a talk for the Australian Mathematical Sciences Institute at their 2016 annual Summer School. We have built a world of largely straight lines – the houses we live in, the ...

Distance geometry is an essential field in computational mathematics and structural biology, providing the theoretical foundation and practical algorithms required to reconstruct the three‐dimensional ...

Reintroduction : View from the twenty-first century -- Augmenting a 1983 history of the fourth dimension in culture and art (1900-1950) : X-rays and ether physics as the context for the "fourth ...

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 ...

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.