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 ...

Flat Geometry This is the geometry we learned in school. The angles of a triangle add up to 180 degrees, and the area of a circle is π r2. The simplest example of a flat three-dimensional shape is ...

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in two-dimensional (2D) and three-dimensional (3D) settings. The rules of Euclidean ...

The PSLQ procedure can be regarded as a jazzed-up version of an integer-relation algorithm dating back more than 2,000 years to the Greek geometer Euclid of Alexandria (365–300 B.C.).

Freed from Euclid’s preconditions, Riemann derived an entirely different (non-Euclidean) geometry. It was this geometry that provided the foundation for general relativity — Einstein’s ...

D. N. Sparks, Algorithm AS 58: Euclidean Cluster Analysis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 126-130 ...

THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an ...

Letter Published: 11 August 1910 The Early History of Non-Euclidean Geometry D. M. Y. SOMMERVILLE Nature 84, 172 (1910) Cite this article ...