Intereting Posts

One of the diagonals in a hexagon cuts of a triangle of area $\leq 1/6^{th}$ of the hexagon
Let the function $f: \to \mathbb R$ be Lipschitz. Show that $f$ maps a set of measure zero onto a set of measure zero
Convergence of a decreasing sequence and its limit.
$\epsilon$-$\delta$ limits of functions question
Notation of the summation of a set of numbers
What is meant by “The Lie derivative commutes with contraction”?
Symmetric Group $S_n$ is complete
4 Element abelian subgroup of S5.
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
Count the number of positive solutions for a linear diophantine equation
A Challenge on linear functional and bounding property
$\sin(x) = \sum{a_n \sin(n \log(x))+b_n \cos(n \log(x))}$
What is a proof?
Learning Homology and Cohomology
Derivative of Determinant Map

In a $1$ dimensional object, the name for the region enclosed by it is the **length** of the object. In a $2$ dimensional object, the name for the region is the **area** of the object. In a $3$ dimensional object, the name is the **volume** of the object. What is the name in a $4$ dimensional object? Hypervolume? In general, what can we call the name of this region in a $n$ dimensional object? (“the region enclosed by this $n$ dimensional object” seems too long and wordy).

- Why is an orthogonal matrix called orthogonal?
- What is linearity?
- Is “converges at” idiomatic English in some regions?
- Which sets are removable for holomorphic functions?
- Is there a term for an “inverse-closed” subring of a ring?
- Etymology of Tor and Ext
- Derive or differentiate?
- Why are even/odd functions called even/odd?
- What is the difference between an indeterminate and variable?
- What is a real number (also rational, decimal, integer, natural, cardinal, ordinal…)?

I would say that just *volume* is actually a fine choice for any dimension $\geq 3$, but if you really want to emphasize the relevant dimension, you could say *$n$-volume* or *$n$-hypervolume*. Take a look at the Wikipedia page on Lebesgue measure.

I think good catch-all terms (i.e., for dimensions $1$ and $2$ as well) would be **measure** or **content**.

How about $n$-volume? Many objects carry the name from 3 dimensions as they are generalized to higher dimensions: $n$-cube, $n$-ball whose boundary is an $(n – 1)$-sphere come to mind.

- A “clean” approach to integrals.
- Describe the topology of Spec$(\mathbb{R})$
- Question about queues
- Proof that $\inf A = -\sup(-A)$
- Are there arbitrarily large gaps between consecutive primes?
- Prove that $e^{-A} = (e^{A})^{-1}$
- Representation of $e$ as a descending series
- Verify if this is correct idea of continuous and homeomorphism
- The index of nilpotency of a nilpotent matrix
- The fractional parts of the powers of the golden ratio are not equidistributed in
- Find $\int_{ – \infty }^{ + \infty } {\frac{1} {1 + {x^4}}} \;{\mathrm{d}}x$
- Four balls with different colors in a box, how many times do I need to pick to see all four colors?
- Required reading on the Collatz Conjecture
- Combination – Infinite Sample Size
- Calculating run times of programs with asymptotic notation