In plane geometry, a lune is the concave-convex area bounded by two circular arcs, while a convex-convex area is termed a lens. The word "lune" derives from luna, the Latin word for Moon.
Formally, a lune is the relative complement of one disk in another (where they intersect but neither is a subset of the other). Alternatively, if A and B are disks, then
L
=
A
−
A
∩
B
{\displaystyle L=A-A\cap B}
is a lune.
== Example ==
In the 5th century BC, Hippocrates of Chios showed that certain lunes could be exactly...
In geometry, a ball is a region in space comprising all points within a fixed distance from a fixed point. An n-ball is a ball in n-dimensional Euclidean space. The volume of an n-ball is an important constant that occurs in formulas throughout mathematics.
== Formulas ==
=== The volume ===
The n-dimensional volume of a Euclidean ball of radius R in n-dimensional Euclidean space is:
V
n
(
R
)
=
π
...
0
good day mathematicians of Math Stack Exchange, I have a bit of curiosity about this exercise that my teacher proposed in class today and says the following:
Determine truth value:
For all $n\in\mathbb{Z}$, if $n^2$ is a multiple of 5, then n is a multiple of 5.
Thanks so much! Please give a proo...
