IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
Non Euclidean Geometry - An Introduction It wouldn't be an exaggeration to describe the development of non-Euclidean geometry in the 19th Century as one of the most profound mathematical achievements of the last 2000 years. Ever since Euclid (c. 330-275BC) included in his geometrical proofs an assumption (postulate) about parallel lines, mathematicians had been trying... Continue Reading →
Non Euclidean Geometry V - Pseudospheres and other amazing shapes Non Euclidean geometry takes place on a number of weird and wonderful shapes. Remember, one of fundamental questions mathematicians investigating the parallel postulate were asking was how many degrees would a triangle have in that geometry- and it turns out that this question can be... Continue Reading →
This post follows on from Non-Euclidean Geometry – An Introduction – read that one first! Non Euclidean Geometry IV - New Universes The 19th century saw mathematicians finally throw off the shackles of Euclid's 5th (parallel) postulate - and go on to discover a bewildering array of geometries which no longer took this assumption about... Continue Reading →
Non Euclidean Geometry - Spherical Geometry This article follow on from Non Euclidean Geometry - An Introduction - read that first!Most geometers up until the 19th century had focused on trying to prove that Euclid's 5th (parallel) postulate was true. The underlying assumption was that Euclidean geometry was true and therefore the 5th postulate must... Continue Reading →
Non-Euclidean Geometry - A New UniverseThis post follows on from Non-Euclidean Geometry - An Introduction - read that one first! The Hungarian army officer and mathematician Johan Bolyai wrote to his father in 1823 in excitement at his mathematical breakthrough with regards to the parallel postulate. "I have created a new universe from nothing." Johan... Continue Reading →
Non Euclidean Geometry - An Introduction It wouldn't be an exaggeration to describe the development of non-Euclidean geometry in the 19th Century as one of the most profound mathematical achievements of the last 2000 years. Ever since Euclid (c. 330-275BC) included in his geometrical proofs an assumption (postulate) about parallel lines, mathematicians had been trying... Continue Reading →