# What is the use of quaternion?

## What is the use of quaternion?

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis.

### How did Hamilton discover quaternions?

On October 16, 1843, Hamilton and his wife took a walk along the Royal Canal in Dublin. While they walked across Brougham Bridge (now Broom Bridge), a solution suddenly occurred to him. While he could not “multiply triples”, he saw a way to do so for quadruples.

#### What is quaternion theory?

Quaternions were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors.

**What are four quaternions?**

quaternion. / (kwəˈtɜːnɪən) / noun. maths a generalized complex number consisting of four components, x = x 0 + x 1 i + x 2 j + x 3 k, where x, x 0 … x 3 are real numbers and i² = j² = k² = –1, ij = –ji = k, etc.

**How do you calculate quaternions?**

💡 Quaternions are expressions of the form q = a + b*i + c*j + d*k , where a , b , c , and d are arbitrary real numbers and i , j , and k are base elements sometimes called the basic unity quaternions.

## How do you calculate quaternion?

### What is a quaternion in the Bible?

a group or set of four persons or things. Bookbinding. four gathered sheets folded in two for binding together. Mathematics.

#### What is Hamilton quaternion?

Hamilton defined a quaternion as the quotient of two directed lines in tridimensional space; or, more generally, as the quotient of two vectors. A quaternion can be represented as the sum of a scalar and a vector. It can also be represented as the product of its tensor and its versor.

**Are quaternions 4D?**

The quaternions are a four dimensional vectorspace over the reals. However, being a “4D vector” is more than just having four components. Being part of a vectorspaces says something about how you can interact with other things.

**How many quaternions are there?**

a group or set of four persons or things.

## How to think about quaternions?

Quaternions and 3d rotation. One of the main practical uses of quaternions is in how they describe 3d-rotation.

### Why should quaternions exist?

Avoiding gimbal lock,a problem with systems such as Euler angles.

#### How to combine quaternions?

Constraining any two of b,c and d to zero produces a representation of complex numbers.

**How are quaternions applicable in physics?**

– Introduction. Quaternions have found a permanent place in engineering and computer description of moving objects. – Electromechanics. – Quantum mechanics. – 3D animation. – Topology. – See also.