English mathematician Arthur Cayley (August 16, 1821 – January 26, 1895), one of the greatest and most prolific mathematicians, helped found the British school of pure mathematics. He was one of the first to realize how many different areas of mathematics could be drawn together by the theory of groups. Together with James Joseph Sylvester, Cayley established the theory of algebraic invariants,...

A distance metric known as non-Euclidean deviates from the laws of Euclidean geometry, which is geometry that governs most physical spaces. It utilized when inappropriate, for dealing with curved surfaces or spaces complex topologies. The ability to apply deep learning techniques domains including graphs, manifolds, and point clouds made possible by learning. use rapidly expanding study real-wo...

We are all familiar with Euclidean geometry and with the fact that it describes our three dimensional world so well In Euclidean geometry the sides of objects have lengths inter secting lines determine angles between them and two lines are said to be parallel if they lie in the same plane and never meet Moreover these properties do not change when the Euclidean transformations translation and r...

This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics. In revealing these issues and challenges, the chapter examines the design of digital technologies and related forms of learning activities fo...

The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially geometry Euclidean spaces. We survey these developments, emphasis on connections computable functions the reals, recent uses proving new theorems classical (non-algorithmic) geometry, and directions for future research.

A historical meditation on non-Euclidean geometry, three Jesuits, a radical egalitarian mathematical philosopher, and the atom bomb, structured by word-count with attention to divisors of 441 Fano plane.