Hyperbolic Geometry is Projective Relativistic Geometry (Part1)

Part 1 (of 6) of a Pure Mathematics Seminar given at UNSW in the School of Mathematics and Statistics. Assoc Prof N J Wildberger explains a new approach to hyperbolic geometry which links it directly to Einstein and Minkowski's relativistic geometry viewed projectively. The idea is to extend Rational Trigonometry to the hyperbolic setting. The first part of the lecture motivates with a summary of classical hyperbolic geometry, then the purely algebraic set-up is introduced. Quite a few new results are illustrated with diagrams.

This is an advanced lecture, suitable for advanced undergraduates, graduate students and professional mathematicians or physicists. For a more gentle and elementary introduction to Universal Hyperbolic Geometry, see my YouTube series by that name, labelled UnivHypGeom.

Category:

Science & Technology

Tags:

• Mathematics
• seminars
• hyperbolic
• geometry
• Einstein
• relativity
• projective
• quadrance
• spread
• Wildberger

[EclecticSceptic]

I wish I had a clue what is going on.

[njwildberger]

Hi EclecticSceptic,

This is an advanced lecture, not really meant for a general audience: I am talking to graduate students and fellow mathematicians here, who will find it reasonably easy to understand. If you are not in this category, wait for my YouTube series on Hyperbolic Geometry, which hopefully should be starting sometime this year!! In the meantime, study all the WildTrig videos....

[njwildberger]

@EclecticSceptic In fact I can now point you to the series UnivHypGeom which gives a complete and hopefully accessible account of hyperbolic geometry--now done correctly.

[juststuffedsilly]

Agh, this is definitely what I want to do in my life! I'm in 8th grade now, and I just watched a video that mentioned hyperbolic planes a few days ago, and right now I'm crocheting a hyperbolic plane model, a method introduced by Daina Taimina. I don't really understand the vocabulary, but I am addicted to listening to it. Math is a beautiful thing.

[EclecticSceptic]

@njwildberger Yes I've been watching that series, thank you.

[hvutrong]

I had this in my advanced geometry class =)

[EclecticSceptic]

@njwildberger Yeah I appreciate that. I'm only doing 6th year maths (~age 18) at present, so I have limited tools available to me! I'll try to teach myself whatever I am lacking sometime soon. I look forward to your series and, just to let you know, your videos are great! The idea of rational geometry resonates with me very much; when I first listened to you criticise modern geometry I really agreed. I found myself asking 'Yeah! What the hell is an angle?'.

[QuantumMaths]

I retract my last comment, z356 is correct. I simply studied this from the perspective of complex analysis, taking more time. Keep in mind he's talking to graduate students here.

[z356]

No you will not. The mad dash presented in this video, though funny, is pure shit. With a more methodical approach this becomes very reasonable.