## Geometry of the Complex Numbers: Rotations

Posted on Fri 23 March 2018 in Thesis • Tagged with thesis, quaternions, complex numbers

In the previous post in this series, we introduced a geometrical interpretation of the complex numbers as vectors in the 2-dimensional plane. That post also explained the geometrical significance of the addition of complex numbers as vector addition. In this post, we'll see how to interpret the multiplication of complex …

## Vectors and the Complex Numbers

Posted on Wed 14 March 2018 in Thesis • Tagged with thesis, quaternions, complex numbers

In the previous post, we first encountered the quaternions, giving an essentially algebraic definition by defining a quaternion as a set of four real numbers and defining operations to add, subtract, multiply, and divide these quadruplets. But my thesis work is in geometry, not algebra, and so it still remains …

## On the Way to the Quaternions: Real and Complex Numbers

Posted on Thu 22 February 2018 in Thesis • Tagged with thesis, quaternions, complex numbers

In the introductory post to this series of posts explaining my thesis, we first heard about "quaternion-Kähler manifolds," a type of geometric object with special curvature properties. These special geometric properties are related to the algebraic properties of the quaternions, a 4-dimensional number system that generalizes the somewhat more familiar …