May 14, 2016 05:29 AM
How Euclid once ruled the world
https://plus.maths.org/content/how-eucli...ules-world
EXCERPT: Geometry is obviously a very useful area of maths. We need it to measure things, to understand shapes, and to navigate through the spaces we live in. But I'd like to argue that geometry is much more than that: it interacts with all aspects of human thought and life. To start, let's turn to a person who is universally known as the "father of geometry": the ancient Greek mathematician Euclid. Euclid's work is the earliest example we have of a systematic approach to geometry. When you make a general statement in geometry, such as Pythagoras' theorem, you should prove this statement by deriving it from statements you're convinced are self-evident, using the rules of logic. For 2000 years Euclid's systematic approach seemed to prove truths about geometrical objects, and thereby to achieve certainty....
How new geometries reshaped our world
https://plus.maths.org/content/how-new-g...-our-world
EXCERPT: In the first part of this article we saw how the ancient Greeks' notion of geometry permeated centuries' worth of human thought: from science and philosophy to politics and art. The early 19th century, however, experienced a geometrical revolution. People realised that space didn't have to be exactly like what the ancient Greek Euclid had implied. In this article we'll see how this realisation shaped philosophy, science, culture and art....
https://plus.maths.org/content/how-eucli...ules-world
EXCERPT: Geometry is obviously a very useful area of maths. We need it to measure things, to understand shapes, and to navigate through the spaces we live in. But I'd like to argue that geometry is much more than that: it interacts with all aspects of human thought and life. To start, let's turn to a person who is universally known as the "father of geometry": the ancient Greek mathematician Euclid. Euclid's work is the earliest example we have of a systematic approach to geometry. When you make a general statement in geometry, such as Pythagoras' theorem, you should prove this statement by deriving it from statements you're convinced are self-evident, using the rules of logic. For 2000 years Euclid's systematic approach seemed to prove truths about geometrical objects, and thereby to achieve certainty....
How new geometries reshaped our world
https://plus.maths.org/content/how-new-g...-our-world
EXCERPT: In the first part of this article we saw how the ancient Greeks' notion of geometry permeated centuries' worth of human thought: from science and philosophy to politics and art. The early 19th century, however, experienced a geometrical revolution. People realised that space didn't have to be exactly like what the ancient Greek Euclid had implied. In this article we'll see how this realisation shaped philosophy, science, culture and art....