What's the difference between vectors and quarternions?
>>7910007
vectors are 3 dimensional, quaternions 3 but with 4 paramaters. Pretty simply actually if we represent a 3d vector as a rotation on x,y,z we get an euler orientation which basically sucks because you can get gimbal lock. Now make a 3d vector to point from a zero point to anywhere to describe an axis and use another variable for the amount to rotate around that axis.
>>7910007
Pretty great video by Numberphile:
https://www.youtube.com/watch?v=3BR8tK-LuB0
>>7910007
Vectors are a tuple of numbers, often used to represent position in an x/y/z kind of way; quaternions are an extension of complex numbers to represent rotations in three dimensions; they have four parameters and map to an axis/angle formulation of rotation. Two quaternion rotations can be combined simply by multiplying them together.
>>7910013
>vectors are 3 dimensional
Since when?
What's the intuition behind quarternio rotations?
Vectors have vector-like properties, e.g. scalability and dimensionality.
Quaternions have number-like properties, e.g. multiplication and inversion.
can we convert one to the other without loss?
>>7911346
Since enginners are being teached math.
>>7910007
It the guy in the pic a retard.... There are 2 pi radians in a circle. Just pi in half a circle.
And how does this blow his mind.... The radian is defined to be precisely that
But to answer your question. A vector is just "an arrow" (can represent a force or whatever); a strait line
A quarternion has an extra parameter (wouldn't call it a dimension) that can describe the rotation of this "arrow"
this fucking thread
to answer your question op, vectors are elements of a vector space (you're probably thinking of R^3 or R^4), and quaternions are elements of the quaternion group, which isn't quite a vector space
the operations defined on those two objects are very different
you could literally just go look at the wikipedia pages for vectors and quaternions why are you making threads
>>7911543
Consider the complex plane. i represents a 90° rotation; -1 represents a 180° rotation, +1 is no rotation. If you multiply these together, it combines those rotations; complex numbers with magnitude 1 represent intermediate rotations, like 1/sqrt(2) + i/sqrt(2) representing 45°. (This close relationship between complex numbers and rotations is where Euler's identity comes from.)
For instance, four multiplications of i bring you all the way around: 1, i, -1, -I, 1, the same way four rotations of 90° would.
Quaternions extend this to four axes of rotation - rotations of an axis about the X, Y, and Z axes, and angle of rotation about that axis. (You need the fourth to keep everything smooth and well-defined)
>>7911826
The picture is a joke.
>>7911798
Then engineers need to learn properly.
>what is a vector space
lol didn't hamilton say that quaternions were devil math or something? who am i thinking of?
>>7912132
When I did that it took me like 2 hours to sort it out and I had a math degree.
The whole set of quaternions is a 4-dimensional vector space over the reals with a noncommutative multiplication. But the quaternions nonmathematicians care about most are the ones with unit length. Those live on a hypersphere that may be parameterized by 3 variables within that 4-d space. Calling those points by their 4-d names is more natural though. Like how you would like to think of a circle as living in a plane even though circles are parameterized by a single dimension. Now this is why plebs care: the unit quaternions correspond to the rotations of 3-d space with multiplication of quaternions corresponding to composition of rotations. However it is not quite a unique correspondence, for every rotation there are two unit quaternion representatives. This doesn't cause problems in the applications though.
Quanternions are a 4 dimensional vector space over the reals.
he is also pleiadian
>>7911570
Many vectors also have those properties. Quaternions are themselves vectors.
>>7915699
The quaternions are very special and worthy of "basically numbers" status. There are exactly three real banach division algebras, the others are R and C.
