For example, there is a Geometric Progression but no Exponential Progression article on Wikipedia, so perhaps the term Geometric is a bit more accurate, mathematically speaking? Why are there two terms for this type of growth? Perhaps exponential growth is more popular in common parlance, and geometric in mathematical circles?
21 It might help to think of multiplication of real numbers in a more geometric fashion. $2$ times $3$ is the length of the interval you get starting with an interval of length $3$ and then stretching the line by a factor of $2$. For dot product, in addition to this stretching idea, you need another geometric idea, namely projection.
I need clarified and detailed derivation of mean and variance of a hyper-geometric distribution. If a box contains $N$ balls, $a$ of them are black and $N-a$ are ...
I've included some colorized figures, which might help with the geometric interpretation for some individuals. Perhaps, a good way to think of the equality of mixed partial derivatives is like this: the change in slope (in the y-direction) of the changes in slope (in the x-direction) is the same as the change in slope (in the x-direction) of ...
1 We better interpret the geometric meaning of transpose from the view point of projective geometry. Because only in projective geometry, it is possible to interpret that of all square matrices.
The real eigenvector of a 3d rotation matrix has a natural interpretation as the axis of rotation. Is there a nice geometric interpretation of the eigenvectors of the $2 \times 2$ matrix?
It could be shorter by one: $$2^ {3+1}-1 = 15$$ By the way, similar geometrical explanation can be used for the ever decreasing geometric progression $\sum_ {i=0}^\infty 2^ {-i}$ with the only difference that we do not need to account for the last piece of empty space, because it tends to 0.
