# Quaternion theory

1. Jun 12, 2015

### Topolfractal

Quaternions are generalizations of 3- vectors, in the same as complex numbers are generalizations of 2- vectors. Should quaternions be considered an extension of the real numbers as the complex numbers were?

2. Jun 12, 2015

### Staff: Mentor

Wouldn't they be considered generalizations of 4-vectors? A quaternion has four components.

3. Jun 12, 2015

### Topolfractal

Oh I thought quaternions were just adding 1 more part to a complex number. I must be way wrong.

4. Jun 12, 2015

### Staff: Mentor

The "quatern" part comes from Latin, meaning "four times."

A quaternion has the form q = ai + bj + ck + d, where i, j, and k are such that i2 = j2 = k2 = -1.

5. Jun 12, 2015

### DrewD

You are not alone. My recollection is that Hamilton was trying to add one more dimension to complex number to make a three part number. He wasn't able to find a way to make add just one dimension and have it be an extension of the complex numbers. Quaternions, however, are an extension to the complex numbers.

6. Jun 12, 2015

### Topolfractal

Thank you, and ya for the longest time having not researched quaternions in depth, I always thought they were a 3-d version of the real numbers with three components. After reading the Wikipedia article on quaternion I understand Hamilton's motivation behind the four parts now.

7. Nov 10, 2016

### blueberry

Yes, undoubtedly!