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Eight ninths and the geometry of A4 paper | Universal Hyperbolic Geometry 46 | NJ Wildberger

4,518 views · Published 18 October 2015 · 24:49 · Indexed 27 September 2026

Channel: Insights into Mathematics · 2015 · Education

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The geometry of the regular tetrahedron centres around the spread of 8/9. Here we look at the A series of paper sizes, including the A4 letter paper that is the ISO standard used in almost all of the world outside North America (where 8.5" x 11" is the standard). 

Curiously the shape of the A4 paper has some rather interesting mathematical properties, and the spread of 8/9 plays also a central role. By looking at a cube in the right way, we will explain this seeming coincidence. 

Throughout we adopt the modern powerful point of view of Rational Trigonometry: giving us a lot more control and insight into the geometry of the world around us!

Video Content:
00:00 Introduction
3:23 "The A series" of paper sizes
5:42 The defining property of the A sizes
12:29 Calculations with Rational trig on A4 paper
20:05 An A4 sheet is not realizable  in A²

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