# dynamic geometry

## A Cyclic Kepler Quadrilateral and the Golden Ratio

A recent paper by Bizony (2017) discussed the interesting golden ratio properties of a Kepler triangle, defined as a right-angled triangle with its sides in geometric progression in the ratio 1 : √φ : φ, where φ =  (1 + √5)/2

## Solution to the ‘Origamics’ Problem

In this note, we offer an explanation to the observations made in the ‘Origamics’ article (November 2013 issue of At Right
Angles).

## Folding and Mapping Turned-Up Folds

Haga’s Origamic activities require students to explore simple, geometric properties found when we fold paper in prescribed ways. The aim of these activities is to give students easy-to-explore paperfolding puzzles so that they can experience a micro-version of the three stages of mathematical research: exploration, conjecture and proof. In this article, we take up another ‘origamics’ exploration by Dr. Kazuo Haga from the chapter 'Intrasquares and Extrasquares' of his book.

## An ‘Origamics’ Activity: X-lines

Haga’s Origamic activities require students to explore simple, geometric properties found when we fold paper in prescribed ways. The aim of these activities is to give students easy-to-explore paperfolding puzzles so that they can experience a micro-version of the three stages of mathematical research: exploration, conjecture and proof.
Here we look at one such activity from the chapter “X-Lines with lots of Surprises”.
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